The P ang . of  VOLUME THREE OF THE PLANNING OF INVESTMENT PROGRAMS ALEXANDER MEERAUS AND ARDY . STOUTJESDIJK, EDYIORS A World Bank Research Publication The Planning of Investment Programs Alexander Meeraus and Ardy J. Stoutjesdijk, Editors Vol. 1. The Planning of Industrial Investment Prog- rams: A Methodology David A. Kendrick and Ardy J. Stoutjesdijk Vol. 2. The Planning of Investment Programs in the Fertilizer Industry Armeane M. Choksi, Alexander Meeraus, and Ardy J. Stoutjesdijk David A. Kendrick Alexander Meeraus Jaime Alatorre The Planning of Investment Programs in the Steel Industry Published for the World Bank The Johns Hopkins University Press Baltimore and London Copyright @ 1984 by The International Bank for Reconstruction and Development/The World Bank 1818 H Street, N.W., Washington, D.C. 20433, U.S.A. All rights reserved Manufactured in the United States of America First printing March 1984 The Johns Hopkins University Press Baltimore, Maryland 21218, U.S.A. The views and interpretations in this book are the authors' and should not be attributed to the World Bank, to its affiliated organizations, or to any individual acting in their behalf. The maps have been prepared for the convenience of readers of this book; the denominations used and the boundaries shown do not imply, on the part of the World Bank and its affiliates, any judgment on the legal status of any territory or any endorsement or acceptance of such boundaries. Editor: Jane H. Carroll Figures: Pensri Kimpitak Maps: Larry Bowring and Julio Ruiz Library of Congress Cataloging in Publication Data Kendrick, David A. The planning of investment programs in the steel industry. (The Planning of investment programs; v. 3) "A World Bank research publication" Includes bibliographical references and index. 1. Steel industry and trade-Planning-Mathematical models. 2. Steel industry and trade-Mexico-Planning-Mathematical models. I. Meeraus, Alexander, 1943-Il. Alatorre, Jaime. Il1. World Bank. IV. Title. V. Series. HD9510.5.K46 1984 338.4'3669142 83-18722 ISBN 0-8018-3197-0 ISBN 0-8018-3198-9 (pbk.) Contents Editors' Note to the Series xi Preface xiii Part One. General Methodology 1 1. Introduction 3 Previous Work 5 Reader's Guide 5 2. The Production of Steel 7 Mining and Preparation of Raw Material 11 Iron Production 12 Steel Production 13 Rolling of Products 17 3. Model Specification and Investment Programs 20 Set Specification 20 Formulating an Investment Program 28 Part Two. The Mexican Steel Sector: A Case Study 35 4. The Steel Sector in Mexico 37 Demand for Steel Products 37 Domestic Supply of Steel Products 42 Domestic Inputs and Raw Material 49 Imports and Exports of Raw Material and Steel Products 53 5. A Small Static Model Recapitulation of Data on the Mexican Steel Industry 54 The Model 59 Results 71 Appendix A. Notational Equivalence 79 Appendix B. GAMS Statement of the Small Static Model 80 V' vi CONTENTS 6. A Large Static Model 101 Sets 101 Variables 114 Constraints 115 Objective Function 120 Parameters 121 Appendix A. Notational Equivalence 136 Appendix B. GAMS Statement of the Large Static Model 138 7. Results of the Large Static Model 175 Raw Material 176 Steel Mills 180 Markets 193 Experimental Runs 201 8. A Small Dynamic Model 208 Sets 208 Variables 212 Parameters 218 Constraints 230 Objective Function 234 Appendix A. Notational Equivalence 236 Appendix B. GAMS Statement of the Small Dynamic Model 238 Appendix C. Derivation of Part of the Investment Cost 253 9. Results of the Small Dynamic Model 256 Base solution 259 Experiments 267 Conclusions 273 Appendix. Summary Tables of the Results 273 10. Extensions, Summary, and Conclusions 293 Extensions 293 Summary 294 Conclusions 295 11. A Postscript: Observations on Industrial Modeling 297 Multiple Models 298 Modeling Languages 299 Set Specification 299 Model Size Calculations 300 Model Debugging Strategies 301 Industry Experts 302 References 303 Index 305 CONTENTS Vii Tables 2-1 Entities in Steel Production 9 2-2 Alternative Processes for Pig Iron Production 12 2-3 Input-Output Vectors for Steel Production 15 3-1 Productive Units 22 3-2 Production Processes 23 3-3 Commodities 25 3-4 Final Products 32 4-1 Apparent National Consumption, 1970-79 38 4-2 Production of Raw Steel by Plant, 1978-79 43 4-3 AHMSA: Capacity of Some Productive Units, 1979 44 4-4 Fundidora: Capacity of Some Productive Units, 1979 46 4-5 SICARTSA: Capacity of Some Productive Units, 1979 47 4-6 HYLSA and HYLSAP: Capacity of Some Productive Units, 1979 48 4-7 TAMSA: Capacity of Some Productive Units, 1979 49 4-8 Reserves of Iron Ore in Mexico, 1979 50 4-9 Reserves of Coking Coal in Mexico, 1979 51 4-10 Origin and Use of Steel Scrap in Integrated Steel Mills, 1974-75 52 4-11 Imports and Exports of Raw Material and Steel Products, 1974-79 52 5-1 Input and Output Coefficients 58 5-2 Relation between Productive Units and Processes 58 5-3 Capacity of Productive Units, 1979 63 5-4 Prices in the Small Static Model 63 5-5 Rail Distances and Transport Costs between Plants and Markets 64 5-6 Distances and Transport Costs from Plants and from Markets to Nearest Port 65 5-7 Delivered Cost at Market 74 5-8 Shipment Pattern in the First Linear Programming Solution 75 5-9 Slack (Unused) Capacity in the First Linear Programming Solution 76 5-10 Shipment Pattern in the Second Linear Programming Solution, with Higher Natural Gas Price and New BOF Activity 77 5-11 Slack (Unused) Capacity in the Second Linear Programming Solution 78 5-12 Shipment Pattern in the Third Linear Programming Solution, with Export Bound, Higher Natural Gas Price, and New BOF Activity 78 6-1 Subsets of Productive Units in the Large Static Model 107 6-2 Subsets of Production Processes in the Large Static Model 109 6-3 Set of All Commodities (CS) Used at Steel Mills I1 6-4 Subsets of Commodities in the Large Static Model 112 6-5 Parameters in the Large Static Model 122 6-6 Input-Output Matrix for SICARTSA: Pellets to Pig Iron 123 viii CONTENTS 6-7 Input-Output Matrix for SICARTSA: Steel and Billets 123 6-8 Input-Output Matrix for SICARTSA: Shapes 124 6-9 Input-Output Matrix for AHMSA: Some Flat Products 125 6-10 Capacity of Iron Ore Mines and Coal Mines 127 6-11 Capacity of Productive Units in Steel Mills, 1979 128 6-12 Domestic Demand Projections for 1979 129 6-13 Demand for Steel Products from Integrated Steel Mills, 1979 130 6-14 Percentage of Demand for Steel Products in Each Market Area, 1979 131 6-15 Regional Demand for Final Products from the Integrated Steel Industry, 1979 132 6-16 Domestic and International Prices Used in the Large Static Model 134 7-1 Extraction at Mines 179 7-2 Ownership Quota for Pellet Plants 179 7-3 Capacity and Shadow Prices at SICARTSA 182 7-4 Capacity and Shadow Prices at AHMSA 184 7-5 Capacity and Shadow Prices at Fundidora 187 7-6 Steel Production Technologies at AHMSA and Fundidora 188 7-7 Capacity and Shadow Prices at HYLSA 190 7-8 Capacity and Shadow Prices at HYLSAP 192 7-9 Capacity and Shadow Prices at TAMSA 193 7-10 Shipments of Final Products 196 7-11 Imports of Final Products 196 7-12 Shadow Prices on Final Products 200 7-13 Experimental Runs and Cost Differences 201 7-14 Capacity Utilization with and without Interplant Shipments of Ingots and Slabs 203 7-15 Capacity Utilization with and without Interplant Shipment of Ingots, Blooms, and Billets 205 8-1 Variables in the Small Dynamic Model 213 8-2 Parameters in the Small Dynamic Model 218 8-3 Demand Projections for the Small Dynamic Model 220 8-4 Investment Cost Parameters 221 8-5 Site Construction Cost Factors 222 8-6 Prices of Commodities Produced at Mines 224 8-7 Domestic Price of Natural Gas 225 8-8 Location Factor and Price of Natural Gas 226 8-9 Interplant Rail Distances 227 8-10 Rail Distances from Mines to Plants 228 8-11 Coal and Iron Ore Reserves 229 9-1 Summary of Experiments 258 9-2 Base Solution: Expansion of Blast Furnace and Direct Reduction Capacity 260 9-3 Base Solution: Imports of Pellets 261 CONTENTS lx 9-4 Base Solution: Iron Ore Mining 262 9-5 Base Solution: Investment in Blast Furnaces as Percentage of Total Investment in Iron Production Capacity 263 9-6 Base Solution: Steel Production 264 9-7 Summary of Results for Base Case 274 9-8 Summary of Results for Experiment 1: Natural Gas at Domestic Price Level 276 9-9 Summary of Results for Experiment 2: Natural Gas at International Price Level 278 9-10 Summary of Results for Experiment 3: Rising Electricity Price 280 9-11 Summary of Results for Experiment 4: Rising Electricity and Imported Coke Prices 282 9-12 Summary of Results for Experiment 5: Energy Location Factors Equal 284 9-13 Summary of Results for Experiment 6: Double Reserves 286 9-14 Summary of Results for Experiment 7: Upper Bound on Production at Each Site 288 9-15 Comparison of Summary Results 290 9-16 Comparison of Capacity Expansion by Location and Unit 291 9-17 Comparison of Capacity Expansion by Time Period and Technology 292 Figures 2-1 The Making and Shaping of Steel: Conventional Technology 8 2-2 Direct Reduction Technology 10 2-3 Mining and Pellet Production 11 2-4 Steel Production and Ingot and Continuous Casting 14 2-5 Rolling of Flat Products 18 2-6 Rolling of Shapes 19 5-1 Schematic of Technologies 57 7-1 Flows of Coal and Coke 177 7-2 Flows of Ore and Pellets 178 7-3 Commodity Flows at SICARTSA 181 7-4 Commodity Flows at AHMSA 183 7-5 Receipt of Raw Material by Fundidora 185 7-6 Commodity Flows at Fundidora 186 7-7 Commodity Flows at HYLSA 189 7-8 Commodity Flows at HYLSAP 191 7-9 Commodity Flows at TAMSA 192 7-10 Selected Product Flows 194 7-11 Product Flows between Major Mills and Markets 195 7-12 Shipments of Hot Sheet 197 X CONTENTS 7-13 Shipments of Tempered (Cold) Sheet 197 7-14 Shipments of Large-diameter Reinforcing Rods 198 7-15 Shipments of Small-diameter Reinforcing Rods 198 7-16 Shipments of Seamless Pipe 199 7-17 Selected Interplant Shipments of Ingots and Slabs in Run 4 204 7-18 Selected Interplant Shipments of Ingots, Blooms, and Billets in Run 4 206 8-1 Points for the Investment Cost Function Approximation 215 8-2 Three-Segment Investment Cost Approximation 217 8-3 Investment Cost Approximation 253 8-4 Nonlinear Investment Cost Approximation 254 8-5 Linearized Investment Cost Approximation 254 9-1 Base Solution: Steel Shipments in 1981-83 265 9-2 Base Solution: Steel Shipments in 1993-95 266 9-3 Investment in the Base Solution Compared with Seven Experimental Solutions 268 Maps 1 Production Centers and Demand Regions 41 2 Major Steel Mills, Markets, and Sources of Raw Material 55 3 Iron Ore Mines 103 4 Coal Mines and Natural Gas Fields 104 5 Steel Mills and Markets in the Large Static Model 105 Editors' Note to the Series THIS IS THE THIRD VOLUME in a series dealing with the use of mathematical programming methods in investment analysis. The volume focuses on the use of such methods to analyze production and investment problems in the steel industry. The exposition of the methodology follows closely that adopted in the first volume of the series, The Planning ofIndustrial Investment Programs: A Methodology, by David A. Kendrick and Ardy J. Stoutjesdijk. The other applications volumes in the series are The Planning of Investment Programs in the Fertilizer Industry by Armeane M. Choksi, Alexander Meeraus, and Ardy J. Stoutjesdijk; The Planning ofInvestment Programs in the Forest Industry Sector by Hans Bergendorff, Peter Glenshaw, and Alexander Meeraus (forthcoming); and Multi-Country Investment Analysis by Loet B. M. Mennes and Ardy J. Stoutjesdijk (forthcoming). ALEXANDER MEERAUS ARDY J. STOUTJESDIJK  Preface THE STEEL INDUSTRY is one of the cornerstones of the industrial sector of most countries. It has strong linkages to other activities, either as a provider of materials for further processing or as a supplier of capital equipment. Its cost structure therefore has a substantial impact on the cost structure and competitiveness of other activities. At the same time, the cost structure of the steel industry itself depends to a large extent on the efficiency of past investments. These factors suggest that the sector is a fitting subject for a volume in this series. The thesis of this series is that industrial investment projects should be evaluated not individually but rather in groups of interdependent projects. Moreover, it is the investment analyst's responsibility not only to evaluate projects but also to play a significant role in the design of projects. "Design" here means the choice of timing, size, location, technology, and product mix. Consider the problem of the design of projects in the steel industry. As an example, take a country in which existing steel plants are using coal and ore from various mines and supplying products to markets; the demand for steel products is growing and the quality of ores and coal in the mines is declining. What additions to capacity should be made in existing plants and mines and where should new plants and mines be developed? The answer to this question requires the study of a set of interdependent investment projects for different parts of the productive facilities in the existing mines and plants and at the new sites. Xil Xiv PREFACE Furthermore, the size and technology of each project in the system will have substantial effects on the best design of other projects in the system. The analysis of interdependent projects was difficult in the past because of the long and tedious calculations. These difficulties are being removed by steady improvements in computer hardware and software. For example, the research for this volume has benefited greatly from a new economic modeling language called GAMS, which was developed by Alexander Meeraus. This language considerably decreases the time and effort required to construct and use industrial sector models. The book is in two parts. The first part provides an overview of the technology of the steel industry and the problems of doing investment analysis in this industry. The second part contains an application of investment analysis to the Mexican steel industry. We are indebted to Ardy Stoutjesdijk for his support and help from the inception of this project, through the model formulation and the data collection, to the writing and editing of this volume. The officials and executives of the Mexican steel industry have been most cordial in helping us develop the models and obtain the data needed to complete this study. Lic. Jorge Leipen Garay, the director general of SIDERMEX, gave us permission to visit the plants of that government corporation. Alejandro Reyes of SIDERMEX assisted both in the development of the models and the collection of data. Ing. Juan Autrique, the former director of the Coordinating Commission for the Steel Industry, shared with us his understanding of the industry. Aristeo Plehn of that commission worked with us for several weeks on the project in Washington, D.C., and made a Spanish translation of one of the models. Oscar Garaza and David Yanez of Hojalata y Ldmina (HYL) in Monterrey provided particularly helpful comments during a seminar on the models. At the World Bank, we were assisted in the computational work by Albert Cheung, Wilfred Chow, and Sethu Palaniappan. Vivianne Lake provided valuable editorial help. The typing of numerous drafts with many tables and equations was done by In-Ae Lee, Geri Mitchell, and Charlotte Robinson. Also Maurice Meunier and Claus Westmeier provided comments on the steel technology chapter. Finally, J. Scott Rogers of the University of Toronto provided many valuable suggestions for improvement of an earlier draft. At the University of Texas in Austin, David Kendrick's graduate students provided useful comments on various versions of the small models. Particularly helpful were the comments of Ilene Kelfer-Lodde, Mina Mohammadioun, and Jung Sun Suh. PREFACE XV For the help of these individuals and many others we are most grateful. The responsibility for the final product remains our own. DAVID KENDRICK University of Texas ALEXANDER MEERAUS Development Research Department The World Bank JAIME ALATORRE Mexican Ministry of Programming and Budget October 1983  츤， 볍 닉 Z & r珍 & 댜 터 으 ㅇ & H궂 p 승 닐＾ 〔지 올 O 른수 燧‘ ㅇ 口． ㅇ 님＾ ㅇ dq &&  1 Introduction TRADITIONAL INVESTMENT ANALYSIS has employed cost-benefit and rate-of-return calculations to make investment decisions about single projects. In the first volume in this series, Kendrick and Stoutjesdijk (1978) argued that it is more useful to evaluate groups of interdependent projects. Furthermore, they argued that the emphasis should be largely shifted from the evaluation of projects to the design of projects. That is, most of the important economic decisions about projects are made at the design stage and not at the evaluation stage. Consider the following list of decisions: Size of productive units Location of productive units Choice of technology Time phasing of the stages of the project Mix of final products. Most of these design decisions are interdependent. For example, the optimal size of a project may depend on its location, as well as its product mix. The advent of computers has made it possible for the investment analyst to participate in the design of projects by developing models to consider alternatives. The particular kinds of models outlined in Kendrick and Stoutjesdijk (1978) are for an industry or sector. They consider a set of plants and a set of markets. Each plant may contain various productive units. These units transform raw material into final products which are then shipped to markets. The demand for these products is growing, and the investment analyst is faced with the question of which productive units 3 4 GENERAL METHODOLOGY in the existing plants should be expanded and where new plants should be constructed. The model is constructed to find the capacity expansions which will satisfy the growing market requirement at least cost. This is done by developing a linear programming model of the industry. The model is solved to find the set of investment, production, and shipping activities that will minimize cost while satisfying market requirements without violating capacity constraints for the productive units. If there are economies of scale in investment cost-as there usually are in heavy industry-then the linear programming model needs to be converted into a mixed integer programming model. Typically, to make best use of the effort of constructing a sector-wide investment planning model, the model is not solved once to obtain a single optimal set of investment projects, but is solved many times to study the basic economics of the industry. A variety of models with different types of aggregation may be used just as is done in this volume. For example, in the steel industry the following types of questions might be studied: * As the quality of ores in inland mines decreases, should existing plants near mines be expanded or should new plants be constructed at ports to receive imported iron ore? * As natural gas and coal prices change relative to one another, should investments be made in direct-reduction units which use natural gas and pellets to produce sponge iron or in blast furnaces which use coke and iron ore to produce pig iron? * Should large productive units be constructed with plans to export substantial quantities of steel products or should smaller units be built to satisfy only the domestic demand? The models presented in this book do not provide foolproof answers to all these questions, but they do provide a very useful methodology for obtaining quantified insights into these problems. It is important to stress from the outset, however, that the models cannot substitute for sound judgments by sector specialists, whose views should also be sought before decisions are made. That is, the models are used to consider a broad range of issues and so must ignore the details of any given alternative, which only the experts can evaluate. What are the limitations of the models used here? A lengthy discussion is provided in chapter 7 of Kendrick and Stoutjesdijk (1978). Here it suffices to mention a few of these limitations. INTRODUCTION 5 * The methodology assumes fixed demand for final products. * No substitution between final products is permitted, unless explicitly specified in the model. * The prices of many inputs and outputs are treated as fixed. * No uncertainty is considered in the analysis. * The degree of disaggregation is limited by the size of model that computers can solve and humans can understand. Several of these limitations can be mitigated by methods discussed in the chapter cited above. Previous Work Since the previous volumes in this series provide references to the general methodological development in this field, this section will be confined to references to investment analysis work in the steel industry. A mixed integer programming model of the steel industry was constructed and applied to the Brazilian steel industry by Kendrick (1967). A dynamic programming model of the Venezuelan steel industry was developed by Wein and Sreedharan (1968). Westphal (1971) constructed an economy-wide model of the Republic of Korea with special attention to the steel and oil refining industries. Alatorre (1976) built a mixed integer programming model of the Mexican steel industry, which laid the foundations for the present study. A linear programming model of the U.S. steel industry with a focus on pollution control was developed by Russell and Vaughan (1976). Reader's Guide Like the other books in the series this volume is divided into two parts. The first part provides an overview of the technology used in the steel industry and a discussion of the investment problems faced by that industry. The second part provides an application of the methodology to the steel industry in Mexico. Three models are developed: two are static and one is dynamic; two are small and one is large. They are not arranged in a hierarchy, since different models are useful for different kinds of analyses. The two static models are useful for studying operational problems, and the dynamic model is helpful in analyzing 6 GENERAL METHODOLOGY investment decisions. The two small models can be solved repeatedly in doing sensitivity analysis. The large model provides much more useful levels of disaggregation for studying the operation of particular productive units in each plant. We believe that the development of multiple models is an extremely useful way to study an industry. The small models are easier to construct, to solve, and to understand, but they are not disaggregated enough to answer many questions of interest. Separate chapters provide a mathematical description of each of the models and a discussion of the sets, parameters, variables, constraints, and objective function. Appendix A of each model chapter gives a notational equivalence to a bridge between the mathematical de- scription of the model and the computer-readable (GAMs) statement of the model that follows in appendix B. After the models are described, chapter 10 gives extensions of the model, a summary, and conclusions about the application of this kind of model to the steel industry. The book concludes with some observations on industrial modeling. 2 The Production of Steel THIS CHAPTER PROVIDES a brief introduction to the technology of steel production. Those who wish more details about the technology are referred to classic works on the subject, such as United States Steel (1971). The making and shaping of steel can be divided into the following steps: mining and preparation of raw material, iron production, steel production, rolling of products, and coating of products. Figure 2-1 gives an overview of these processes. First, iron ore is mined, concentrated, and turned into pellets or sinter, and coal is mined and converted to coke. Then the iron ore and coke are charged to a blast furnace and heated to remove oxygen from the iron ore and thereby produce molten pig iron (hot metal). The molten pig iron is transported to basic oxygen furnaces where it is oxidized-that is, oxygen is blown into the liquid to remove carbon and thereby make steel. At the same time, other impurities are removed by additives such as lime. The steel is then poured into continuous casting units to make billets or slabs. The billets are rolled into shapes such as reinforcing rods, and the slabs are rolled into flat products such as plate and hot or cold sheet. Cold sheet can be coated with zinc or tin to produce galvanized sheets and tin plate. In the mathematical modeling of the steel industry, it is useful to divide the entities in figure 2-1 into three groups: the commodities which are transformed from inputs to outputs in the system, the productive units which are used to transform these commodities, and the processes by which the commodities are transformed. Table 2-1 lists these three groups. The distinction between productive units and processes may seem subtle, but it is basic to the mathematical modeling of the industry. 7 8 GENERAL METHODOLOGY Figure 2-1. The Making and Shaping of Steel: Conventional Technology Iron ore Coal Limestone Mining and Lump ore preparation of raw material Pellet plant Coking Calcinating or sinter plant plant plant Pellets Coke or sinter Lime Iron production Molten pig iron Oxygen Blast furnace Steel Basic Steel production oxygen furnace Nonflat products Rolling mills Bilt for shapes 0 00O% Continuous Rolling of 000 casting products Flat () Slabs products Rolling mills for flat products Coating of Galvanized sheets products Coating and tin plate PRODUCTION OF STEEL 9 Table 2-1. Entities in Steel Production Commodities Productive units Processes Iron ore Sinter plant Sinter production Coal Pellet plant Pellet production Pellets Coking plant Coke production Coke Blast furnace Molten pig iron production Molten pig iron Basic oxygen furnace Steel production Water Direct reduction unit Continuous casting Oxygen Continuous casting unit Rolling of shapes Electricity Rolling mills for shapes Rolling of flat products Fuel oil Rolling mills for flat Natural gas products Steel Billets Slabs Shapes Flat products A productive unit is a machine or a piece of capital equipment such as a blast furnace. A process is equivalent to a recipe. For example, two different processes for making pig iron might be used in the same blast furnace. One process would use pellets as an input and a second would use lump ore. Figure 2-1 provides an overview of the most widely adopted technology in the steel industry. There are other methods of producing steel, however, one of which is shown in the schematic diagram in figure 2-2. Natural gas is used instead of coke to reduce the ore to iron, and sponge iron (reduced pellets) is produced instead of molten pig iron. The sponge iron is then charged to an electric arc furnace where it is transformed into steel. The steel is passed through continuous casting units and rolling mills in a manner identical to that used in the conventional technology. Direct reduction uses natural gas instead of coal, which is an advantage in some places where natural gas is abundant and cheap. As the price of natural gas rises relative to coal, however, the direct reduction process becomes less attractive. Direct reduction may be done with other gases, which may be substituted if natural gas prices continue to rise. In the remainder of this chapter each step in the production of steel will be discussed in greater detail. 10 GENERAL METHODOLOGY Figure 2-2. Direct Reduction Technology Iron ore Mining and Lump ore preparation of raw material Pellet plant Natural gas Iron Lime production Direct reduction Electricity Sponge iron 1 production Electric Steel are furnace- Nonflat products Rolling mnlls Billets 00 Rolling of for shapes OO 0 OOO Ooln p odut 000 0 products Continuous Flat Scasting products Rolling mills for flat products Coating of Galvanized sheets products C gand tin plate Coating] PRODUCTION OF STEEL II Mining and Preparation of Raw Material Figure 2-3 provides an overview of the mining and preparation of ores. Iron ore is mined from open pit mines which have roughly 45 to 65 percent iron content. The ore is crushed and sized before it is sent to a concentrator. The type of concentrate produced depends on whether the Figure 2-3. Mining and Pellet Production Lurnp ore Crusher Magnetite Hematite ores ores Concentrate Concentrate Sinter plantPellet I plant Sinter Pellets 12 GENERAL METHODOLOGY ore is magnetite or hematite. Magnetite can be concentrated by magnetic means: after it is crushed and ground, it is passed near large magnetic drums so that the iron can be separated from sand and other impurities. If the ore is hematite, magnetic separation cannot be used and a more expensive flotation process is required. With either one, the result of the concentration process is a slurry of rich ores suspended in water. This slurry can be piped to a pellet plant where the water is removed and the ore is agglomerated into small balls a quarter to a half inch in diameter. These balls (pellets) are baked so that they become hard before they are charged to the blast furnace or to the direct reduction units. Coal is mined from either open pit or underground mines. It is then washed and shipped to coking plants, which are usually located at the steel mills. The coal is heated to very high temperatures to drive off volatile matter and thus reduce it to coke (almost pure carbon). The coke is then charged with pellets to the blast furnace. Iron Production Two technologies for iron production are described here: the conventional blast furnace and the direct reduction process. The first uses sinter, pellets, lump ore, and coke to produce pig iron, and the second uses pellets or lump ore, or both, and natural gas to produce sponge iron. In the blast furnace technology sinter, pellets, lump ore, coke, and limestone are charged to the top of a blast furnace. Three alternative processes for running a blast furnace are given in table 2-2. Inputs are shown as negative numbers and outputs as positive numbers. Thus in the pellets-only process, 1.6 tons of pellets are combined with 0.6 ton of coke Table 2-2. Alternative Processes for Pig Iron Production (metric tons) Inputs Pellets-only Pellets and lump Sinter pellets and and outputs process ore process lump ore process Sinter 0 0 -0.6 Pellets -1.6 -1.4 -0.6 Lump ore 0 -0.2 -0.3 Coke -0.6 -0.6 -0.5 Limestone -0.1 -0.1 0 Molten pig iron 1.0 1.0 1.0 PRODUCTION OF STEEL 13 and 0.1 ton of limestone to produce a ton of pig iron (all tons in this book are metric). In the second process some lump ore is substituted for pellets to produce a ton of molten pig iron. In the third process the burden includes 40 percent lime-fluxed pellets, 40 percent sinter, and 20 percent lump ore to yield a ton of molten pig iron. Sinter is a mixture of ore fines and coal which is baked into small lumps about an inch in diameter and then charged to the blast furnace. A typical steel mill will have one to five blast furnaces, each of which produces I million to 3 million tons of pig iron. So each steel mill produces I million to 15 million tons. In contrast to blast furnaces, direct reduction units use natural gas or lower quality coke to reduce the iron ore. Pellets are heated under pressure in the presence of natural gas and are reduced to sponge iron. Sponge iron looks just like pellets-balls roughly a quarter inch in diameter-but it is slightly less dense. The iron content of pellets ranges from 92 to 96 percent. One process for direct reduction of iron ores is the HYL process developed in Mexico. Another, the Midrex process, was developed in Germany. An input-output vector for the HYL process is: Pellets (metric tons) -- 1.38 Natural gas (thousand cubic meters) -- 0.38 Sponge iron (metric tons) 1.00 The natural gas input of 0.38 thousand cubic meters per metric ton of sponge iron is controversial. This is the reported usage at the HYLSA (Hojalata y Lamina S.A.) plant in Puebla, Mexico. The other HYLSA plant, in Monterrey, Mexico, reportedly uses 0.58 thousand cubic meters per metric ton of sponge iron. New processes under development are said to require only 0.28 thousand cubic meters of natural gas but require 77 kilowatt-hours of electricity per metric ton of sponge iron. Although the blast furnace technology is so widespread that it is relatively easy to check input-output coefficients, the relatively new direct reduction processes are not so widely used, and information on technical characteristics is closely held by a few companies. The next section describes the processes by which molten pig iron and sponge iron are transformed into steel. Steel Production Figure 2-4 provides an overview of steel production and ingot and continuous casting. Three productive units for steelmaking are shown: 14 GENERAL METHODOLOGY Figure 2-4. Steel Production and Ingot and Continuous Casting Oxygen Molten pig iron Scrap Steel Basic oxygen furnace A Billets Oxygen Ingot - - casting Molten Primary Slabs pig iron Scrap Natural gas or fuel oil Steel Open hearth furnace Electricity Sponge iron or molten pig iron Scrap 00 Billets 0 0 Continuous Steel Slabs Electric arc furnace the basic oxygen furnace (BOF), open hearth furnace, and electric arc furnace. BOF is also called BOP (basic oxygen process) and LD (Linz- Donawitz). The BOF has replaced the open hearth technology as the most widely adopted of the three. The electric arc furnace can take a 100 percent cold metal charge such as sponge iron and scrap, while the BOF must have at least a 60 percent hot metal (molten pig iron) charge. PRODUCTION OF STEEL 15 Table 2-3. Input-Output Vectors for Steel Production Inputs Electric Electric and Basic Open arc arc outputs oxygena heartha spongeb scrapb Hot metal - 1.02 -0.77 0 0 Sponge iron 0 0 -1.09 0 Scrap -0.11 -0.33 0 -1.06 Electricity 0 0 - 0.68 - 0.50 Oxygen -0.05 -0.05 0 0 Steel 1.00 1.00 1.00 1.00 a. From AHMSA (Altos Hornos de Mexico S.A.). b. From HYLSA (Hojalata y Lamina S.A.). Therefore, the electric arc furnace is frequently used to melt scrap or to reduce sponge iron. Two casting technologies are also shown in figure 2-4; ingot casting is the older and is being replaced by conti- nuous casting. Input-output vectors for the three steelmaking processes are shown in table 2-3. Two processes for the electric arc furnace are displayed, one using a sponge iron charge and one using a scrap charge. Mixtures of these two charges may also be used. The basic oxygen steelmaking process uses a mixture of hot metal (molten pig iron) and steel scrap in a large vessel about 20 feet high. Once the furnace is charged with the metal, an oxygen lance is inserted at the top. The furnace is blown for about 30 minutes and then tilted to pour the liquid steel into a ladle which carries the steel to the ingot casting or continuous casting operations. Two or three Bo1s are usually installed side by side, and one of the furnaces is relined while the others are in operation. The capacity of such a grouping of furnaces is 1 million to 4 million metric tons of steel a year. Thus a large steel mill may have several "steel shops" with two or three BOFS in each shop. Open hearth furnaces are being replaced by BOFs because the energy input and the time required for each heat in the open hearths are much greater, and therefore both the operating cost and cost per unit of capacity are higher. There are comparative advantages, however, which can be exploited in steel mills that have not already retired their open hearth furnaces. The BOFS can take no more than about 40 percent of the metal charge as cold metal such as scrap or sponge iron; in contrast, the open hearths can be operated even with a 60 to 70 percent cold metal 16 GENERAL METHODOLOGY charge, though heat times are much longer. This has advantages as well, since it is possible to do more exact quality control on open hearth steel than on 3OF steel. Open hearth furnaces did not originally have oxygen lances, but most now have them installed, with a commensurate decrease in heat times and an increase in capacity. In both the basic oxygen furnace and the open hearth furnace, the heat in the hot metal charge and the burning of the contained carbon are the principal sources of energy for the processes. In contrast, the electric arc furnace uses electricity which arcs between two electrodes in the furnace and heats the metal. For this reason, the electric arc furnace can take a 100 percent cold metal charge, but heat times are longer and capital costs per ton of capacity are higher. Pollution problems may be severe for all three technologies. Open hearth furnaces were infamous for the clouds of red smoke that emanated from their chimneys before modern pollution control equip- ment was installed. Similarly, a BOF furnace or an electric arc furnace without proper controls would significantly pollute the air. Thus an important part of the capital cost for all three technologies is the pollution control equipment. After production by one of the three technologies, the steel is taken either to an ingot casting or a continuous casting shop. In the ingot casting shop, the liquid steel is poured into ingot molds that are about 6 feet high, 2 feet thick, and 3 feet wide. The ingots are allowed to cool and, when scheduled for use in the rolling mills, they are moved to the soaking pit where they are uniformly heated. In the primary mill, the ingot is passed back and forth as the rollers are moved closer and closer together to form the ingot into a slab about 30 feet long, 8 inches thick, and 4 feet wide or into a bloom about 10 feet long and 10 inches by 10 inches in cross section. The slabs are later rolled into flat products, and the blooms are rolled into shapes. In continuous casting operations, liquid steel is poured into a container with several holes in the bottom. If the continuous caster is a billet casting machine, the liquid steel slides down tubes below these holes as it is cooled, and then it is guided between rollers that gradually reduce its size to form a strand 4 inches by 4 inches in cross section. The strands are then cut into 20 to 50 foot lengths to become billets. A normal billet casting machine will have four strands. In contrast, a slab casting machine emits a single slab that is roughly 8 inches by 48 inches in cross section. The strand is cut into 20 to 30 foot lengths to form slabs. Since the liquid steel is not allowed to cool until the billets or slabs are formed, the continuous casting process is more energy efficient than PRODUCTION OF STEEL 17 ingot casting. Also, the capital cost for a continuous casting machine is much less than for the equivalent capacity in ingot casting, soaking pits, and primary mills. The capacity of a single continuous casting machine can be anywhere from half a million to several million tons per year. The slabs and billets are next rolled into final products, flat or shapes. Rolling of Products Figure 2-5 provides a schematic drawing of rolling operations for flat products. Slabs are sent either to the plate mill or to the hot strip mill. The plate mill rolls the slabs into steel plates an eighth to three-quarters of an inch thick and 10 or 20 feet in length and width. These plates will be used to build storage tanks or ships or other steel vessels. The preponderance of the slabs are sent to the hot strip mill where they are reheated and then rolled through the mill. The mill usually has four or five stands, each of which rolls the product into a thinner form. The entire mill may be a third of a mile long, with slabs entering one end and coils of hot sheet leaving the other end. The coils contain several hundred feet of hot sheet less than an eighth of an inch thick and 3 to 5 feet wide. Some of these coils are sold as hot sheet and some are sent on to the pickling line for further processing. The pickling line is an acid bath that the unrolled coils are passed through to remove rust and scale before they are rolled up again and sent to the cold strip mill. The cold strip mill has three to five stands located within a few feet of one another, where the pickled sheets are further reduced in thickness. Some of the resulting coils of cold sheet are sold to make automobile bodies, appliances, furniture, and other products. Others are passed through the annealing furnace where they are heated, held at an elevated temperature for several hours, and cooled in a neutral atmosphere to give the metal desirable ductile properties. Then the annealed strip is run through a temper mill and recoiled to be sold as tempered sheet. The rest of the coils are delivered to the tinning lines or galvanizing lines where they are coated with tin or zinc and then recoiled and sold as coils of tin sheet or galvanized sheet. This completes the flat product rolling operations. Shapes are rolled from either blooms or billets. Blooms may be either round or square in cross section with a diameter of about I to 2 feet. Billets are square in cross section and about 1 to 5 inches on a side. Blooms are used for the heavy shapes such as beams for bridges and buildings, and billets are used for light shapes, reinforcing bars, and wire rods. Special blooms are used to produce seamless pipe by extrusion. 18 GENERAL METHODOLOGY Figure 2-5. Rolling of Flat Products Slabs Plate Plate mill Hot sheet Slabs 000 0 0=0 0 ) 0Pickling line Hot strip mill Pickled sheet Cold sheet Cold strip Annealing in furnaces Tempered o sheet -"2 0Tin Temper mill Tinning line Galvanized sheet Galvanizing line Mills that roll flat products are fairly standardized, but a profusion of different collections of rolling mills and stands is used to roll light shapes, bars, and wire rods. Furthermore, the same mills may be used to roll several different products. Therefore, figure 2-6 should be viewed as only a rough approximation of the reality of rolling shapes. Basically, billets are reheated and rolled through a collection of different mills to produce PRODUCTION OF STEEL 19 Figure 2-6. Rolling of Shapes Heavy shapes mill Blooms Heavy shapes Blooms Seamless pipe B i l e sm l e s s p i p eL i h Primary mill ReinorcFiniashn mmi light shapes, bars, reinforcing rods, and wire rods. The capacity of such a collection of mills will range from several thousand to half a million tons of shapes and bars per year. This discussion has outlined the technology of steel production in integrated steel mills. In most countries, there is also a collection of nonintegrated steel mills, most of which use electric arc furnaces to melt scrap and cast billets or which buy billets directly. The billets are then reheated and rolled into light shapes, reinforcing rods, and wire. The models in this book do not attempt to include the nonintegrated steel mills. 3 Model Specification and Investment Programs WHEN INVESTMENT ANALYSIS is done by calculating rates of return on individual projects, the specification of the problem is relatively straightforward. All the inputs and outputs of the project are valued, and these values are discounted, summed over time, and set equal to zero to permit calculation of the rate of return. When investment analysis is done by considering interdependent sets of projects, as is advocated in this book, the specification of the problem is considerably more complicated. The reason is that if all inputs, outputs, processes, plant sites, and markets are included, the problem becomes much too large to analyze and to understand. It is therefore useful to formulate a simplified version of reality, a model, in which one must decide which elements to include and which to exclude. Therefore, in the first part of this chapter the specification of the planning problem is discussed in terms of the size and complexity of the model. The second part of the chapter is devoted to the formulation of investment programs: how one uses a model to focus on the crucial investment issues for the industry. Examples are investments to break bottlenecks in capacity, selection of new sites, choice of technology, size of new units to be installed, and the timing of capacity expansion. Set Specification The three principal parts of the process of model specification are set specification, development of the constraints and the objective function, 20 MODEL SPECIFICATION 21 and data input and transformation. This section is devoted primarily to the first of these, set specification. Although the constraints and objective function have a similar structure for models of different industries (see Kendrick and Stoutjesdijk 1978), the set specification differs con- siderably across industries. Therefore, this section provides a discussion of set specification for models of the steel industry. The sets considered are mines, plants, productive units, processes, commodities, markets, time periods, new sites, and expansion units. Following this is a brief discussion of the modeling of transport. Mines Mines may be of crucial importance in determining the overall pattern of investment in the industry, or they may be of little or no importance and therefore omitted from the model specification. If the ores or coking coal for the industry are supplied from domestic mines and if the quality of ores is declining rapidly, the mines should be included in the model. If, however, the ores and coking coals for the industry are mostly imported or if the output of existing domestic mines is unlikely to decline in quality during the planning period, then the mines may be excluded from the set specification, thus simplifying the model. When mines are used, one must decide how many of them to include in the model. In some countries, there are so many small coal mines and ore mines that it is impossible to include all of them. In this case, one may include only the largest mines or collections of smaller mines aggregated into a single mine in the model. Plants Two kinds of steel mills exist in the industry: integrated and nonintegrated. The integrated mills contain the entire set of processes from iron and steel production through rolling of final products. The nonintegrated steel mills do not have the processes for iron production and in many cases do not have the processes for steel production. These plants may have an electric arc furnace in which scrap is melted to make steel or they may simply buy billets from the integrated mills. The billets or slabs are reheated and rolled into light shapes, bars, reinforcing rods, plates, cold rolled products, and coated products. These plants are also called rerolling mills. Since there are usually only a few large integrated steel mills but many small nonintegrated mills, it is common to include only the integrated 22 GENERAL METHODOLOGY mills in models of the steel industry. The part of domestic steel demand that is satisfied by the rerollers is subtracted from the total, and the models are solved without including these small plants. The model may be further reduced in size and complexity by excluding nonflat products. This is a useful abstraction since economies of scale are more pronounced in flat product rolling mills than in those for nonflat products. Thus, the model may be restricted to include only flat products. In most countries, however, a variety of integrated steel mills produces both flat products and shapes so that separation is not useful. Productive Units Table 3-1 provides a list of the major productive units in an integrated steel mill. A small, highly aggregated model would include only a few of these productive units: blast furnaces, basic oxygen furnaces, continuous casting units, and hot and cold strip mills. A large, disaggregated model would include all of them. Obviously, every steel mill does not include all these productive units. But the set of productive units for the model includes all the large productive units used in one or more of the steel mills. Table 3-1. Productive Units Mines Ingot and continuous casting Trucks and crushers Ingot casting units Coal washing units Continuous casting units for billets Magnetic concentrators Continuous casting units for slabs Flotation concentrators Rolling mills Preparation of raw material Flat products Pellet plants Slabbing mills Sinter plants Plate mills Coke ovens Hot strip mills Oxygen plants Pickling lines Iron production Cold strip mills Blast furnaces Annealing furnaces Direct reduction units Temper mills Tinning lines Steel production Nonflats Basic oxygen furnaces Blooming mills Open hearth furnaces Heavy section mills Electric arc furnaces Billet mills Merchant bar mills Wire rod mills Seamless pipe mills MODEL SPECIFICATION 23 The art of model building is to include in the model only the elements that significantly affect the outcome. For example, if two adjacent productive units in a process line are always installed at the same size, it would be necessary to include only the one joint unit in the model. An example is the pickling line and the cold strip mill. If all the materials which pass through the pickling line also pass through the cold strip mill, the two units would have the same capacity and could be treated in the model as a single productive unit. Processes Table 3-2 lists the production processes that might be included in a large model. A smaller model would include only a few of these processes. For the most part, there is one process listed for each Table 3-2. Production Processes Mines Ingot and continuous casting Mining coal Ingot casting Washing coal Continuous casting of billets Mining ore Continuous casting of slabs Crushing ore Magnetic concentration olng Flotation concentration Rolling of slabs Preparation of raw material Rolling of plate Pellet production Rolling of hot strip Sinter production Pickling Coke production Rolling of cold strip Oxygen production Annealing Iron production Tempering Pig iron production with lump ore Production of tin plate Pig iron production with pellets Production of galvanized Sponge iron production N hets Steel production Rolling of blooms Steel production in open hearths Rolling of heavy sections Steel production in basic oxygen Rolling of billets furnaces Bar production Steel production in electric arc Wire rod production furnaces with a high percentage of Seamless pipe production scrap iron in the charge Steel production in electric arc furnaces with a high percentage of sponge iron in the charge 24 GENERAL METHODOLOGY productive unit in table 3-1. In some cases, however, two or more processes can be run in the same productive unit. For example, a blast furnace may be run with either a high percentage of lump ore or a high percentage of pellets in the metal charge. An electric are furnace may be charged with a high percentage of scrap steel or with a high percentage of sponge iron. Thus, as the mix of inputs is changed for a given productive unit a new process is specified. In principle, an infinite number of processes can be used in a given productive unit, and table 3-2 shows only a small number of these. Again, the art of modeling is to include only the processes that are necessary to capture the essential economics of the industry. Some of the inputs and processes for which substitution is important are: * Coke, natural gas, and fuel oil in the blast furnace * Lump ore, sponge iron, pellets, and sinter in the blast furnace burden * Scrap, sponge iron, and molten pig iron in the basic oxygen and open hearth furnaces * Scrap and sponge iron in electric arc furnaces. The simplest way to model these substitution possibilities is to include two processes-one at each extreme of the substitution possibilities- and let the model solution give the best mix of the two activities. For example, one activity for the basic oxygen furnace might include 35 percent scrap and 65 percent pig iron, and another activity would include no scrap and 100 percent pig iron. It is by now apparent that the choice of elements in each set is not independent of other choices. For example, the choice of plants to include in the model necessitates the choice of certain productive units, which in turn require that certain processes be included in the model. Likewise the choice of processes dictates that certain commodities be included in the model. Commodities The model should include in the set of commodities all the major inputs to and outputs from the processes. For example, a process for steel production in a basic oxygen furnace would have inputs of pig iron, scrap, refractories, and oxygen, and the output would be liquid steel. The model may or may not include minor inputs such as ferroalloys and lime. Putting them in the model permits all the significant items of cost to be included but does so at the expense of increasing the size of the model. MODEL SPECIFICATION 25 Table 3-3. Commodities Mines Ingot and continuous casting Iron ore of various types and qualities Ingot steel (magnetite and hematite with Billets different concentrations of iron, Slabs sulfur, and phosphorous) Electricity Coal of various qualities Rolling operations Washed coal Flat products Concentrated ore Electricity Preparation of raw material Plates Pellets Hot sheets Sinter Pickled sheets Coke Cold sheets Coke oven gas Annealed sheets Limestone Tempered sheets Oxygen Tin Iron production Nonflats Pig iron Blooms Sponge iron Heavy shapes Fuel oil Light shapes Blast furnace gas Bars Reinforcing rods Steel production Wire Scrap steel Seamless pipes Ferroalloys Rails Refractories Dolomite All processes Lime Labor Electrodes Liquid steel Electricity BOF gas Table 3-3 provides a list of commodities that might be used in a disaggregated model. A smaller model would include only a fraction of these commodities. One commodity, labor, deserves special attention. Under certain circumstances, it can be argued that labor should be treated in the model not as a commodity but as a productive unit. The argument is that labor inputs cannot change as production fluctuates, but that once people are hired to run the mill at full capacity, they are employed no matter how output levels change. Thus, the cost of labor would not be related to the production of the plant but rather to the capacity of the plant. 26 GENERAL METHODOLOGY Markets Steel products are used at many different locations, but the model would become much too large if all possible locations were included. Thus, representative market centers are used, and it is assumed that all the steel used in the area around the center is consumed at the center. For example, a small model might include three market centers and a large model would have twenty or so. This might seem like a small number of market centers to have in a large model, but the model includes shipment activities from every plant to every market. If it is important to include many more markets, creating subsets of plants that are permitted to ship to each market would keep the model from becoming too large. Time Periods The dynamic models must cover a long enough time horizon to permit an interesting study of the investment possibilities in the industry. Because of distortions caused by the finite horizon of the models, it is common practice to solve them for a number of years past the period of interest. For example, if the gestation time to design and construct projects is five years, the planning period of interest is fifteen years, and the allowance for finite horizon effects is five, then the planning horizon would need to be twenty-five years. If each time period were to cover a single year, then the model would have twenty-five time periods. Since this would make the model too large to solve, it is customary to include two to five years in each time period. Thus a model with a time horizon of twenty-four years might include eight time periods of three years each or six time periods of four years each. New Sites The set of new sites is like the set of plants. A static model would include in the set of plants only those already in existence. A dynamic model would include both the existing plants and potential sites for new plants. For example, a model might include eight existing plants and potential sites for three new plants. The investment problem is then to determine what productive units should be installed at these new sites as well as what increases in capacity should be made at the existing plant. Of course, considerable engineering and design work may go into the MODEL SPECIFICATION 27 selection of the new sites. They may be located at ports, near mines, or near markets. They must already have infrastructure or the potential for it to be constructed at reasonable cost. They may be near pools of relatively low-cost labor. Thus, the original screening of many potential sites may be done outside the model. Then a small group of the choice candidates is included as new sites in the model. Depending on the solutions obtained, it may be desirable to add to the model some of the sites which did not at first look promising. Thus, model building is not done in a single pass but rather by moving backward and forward as one's understanding of the economics of the industry or subsector increases. At both the existing and new sites, one must consider which productive units might be increased in capacity. These units are called the expansion units for the industry. Expansion Units Expansion units are the productive units that are considered in expansion plans. Thus, the set of expansion units may exclude some of the types of productive units in existing plants and some productive units not yet installed in any of the existing plants. Some of the productive units in the existing plants may embody technologies that have become outmoded. These units will be excluded from the set of expansion units. For example, open hearth furnaces, ingot casting facilities, and primary mills would be included in the set of productive units but excluded from the set of expansion units. The set of expansion units may also include some types of capital equipment not yet installed in the existing plants. For example, direct reduction units may not exist in some countries, but new discoveries of natural gas may make them a viable alternative for capacity expansion. They would not be included in the set of productive units in a static model but would be included in both the set of expansion units and the set of productive units in a dynamic model. Transport Although transport is not included as a set in the model, it is useful to discuss it here. Most of the major inputs to and outputs from the steel industry are moved by rail. However, there are important exceptions. Trucks often carry a significant share of the final products. Ships may also be used both to move ore and coal and to ship final products out of-and sometimes even within-a country. 28 GENERAL METHODOLOGY It would be possible to introduce alternative modes of transport into the model and let the solution indicate the most efficient mode for each commodity in each shipment link. This is usually a needless com- plication, however, because the most efficient mode of transport for each commodity in each link in the transport system is well known, and that mode and the associated cost should be built directly into the model. Within-plant transport may be a major item of cost. It has not been modeled in this book but is large enough in some cases to merit special attention. Formulating an Investment Program Once the planning model is fully specified, it can be used to formulate an investment program for the industry. Such a program would consider: Additions to capacity in existing plants Construction of plants at new sites Choice of technology Size of capacity expansions Timing of additions to capacity Product mix Transport Foreign trade policy Budget constraints In the following subsections, these aspects of the program are considered in turn. Additions to Capacity in Existing Plants In the steel industry, a substantial part of the total additions to capacity come from investments in existing plants. In part, this is because the infrastructure and skilled labor are already available at those plants, and it is therefore less expensive to expand existing facilities than to build entirely new ones. In addition, certain aspects of steel technology often make this attractive. For example, in a steel shop with two basic oxygen furnaces, one of the furnaces operates while the other is being relined. Much less than half the operating time is required to reline the furnace, but a steady throughput of steel can be maintained by operating one furnace at a time. If a third basic oxygen furnace is installed to add to the MODEL SPECIFICATION 29 capacity of the plant, then two furnaces will be operated at a time while the third is being relined. Thus, a 50 percent increase in the capital cost of the original facility results in a doubling of output. In anticipation of this situation, the blast furnace of the original facility may have been designed with a capacity to produce enough pig iron for twice the original steel production. For a time, the steel shop would therefore have half the capacity of the blast furnace and would be a bottleneck on the production capacity of the plant. The investment in the third basic oxygen furnace would remove the bottleneck. Since this kind of addition to capacity within existing plants is important in the steel industry, the model includes a constraint for the capacity of each productive unit rather than for each plant. Furthermore, the investment alternatives considered in the model include both additions to capacity within existing plants and expansion at new sites. Construction of Plants at New Sites When plans are made to expand steel production, a variety of new sites is usually considered. The sites may be at ports with good access to imported pellets and coal. Alternatively, they may be near demand centers or at points near iron ore and coal deposits where the raw materials can be brought together at low cost. New sites may be chosen for their potential for market incursion on a rival steel company or as a result of direct or indirect government intervention to achieve political balance or to decentralize the industry. Defense and security con- siderations may also be important in selecting sites. No matter what the reasons were for choosing the alternative sites, the model offers a means of calculating the implications of the choice to build steel mills at any combination of the potential sites. For example, the model may be used to study how the construction of a new plant near existing facilities will cause the existing plants to lose parts of their established markets and be forced to serve more distant and less lucrative markets. Or the model may be used to cost-out quickly the implication of building a new plant at a port, near a mine, or near a market. Moreover, the calculations do not assume that the existing plants continue to operate in the same way but rather that they adapt to the presence of the new plant. Finally, the model may be used to study which technology to use-for example, direct reduction units or blast furnaces-at the new site or sites. 30 GENERAL METHODOLOGY Choice of Technology One of the most difficult problems in the development of expansion programs in the steel industry is the choice of technology. At times, this problem is caused by the development of new technologies, such as the basic oxygen furnace or continuous casting methods. At other times, it is due to a shift in the relative prices of inputs, such as a change in the cost of natural gas, so that the choice between direct reduction units and blast furnaces becomes a difficult one. In such cases, it is not sufficient to calculate the total cost of inputs for each of the competing technologies and to choose the technology with the lowest cost of inputs. One productive unit may have a much higher cost of inputs but a lower capital cost than the other. Moreover, one unit may have strong economies of scale and the other little or no economies of scale in investment cost. Thus, a small unit would favor one technology and a large unit the other technology. Moreover, the choice of technology may be influenced by the location of plants. As is the case for energy inputs in many countries, government policies may strongly affect the relative prices of inputs. It may be desirable to use the models to ask "what if" questions about government policy, such as: What will be the best technology to use for capacity expansion if the government should suddenly decontrol natural gas prices, or slowly but surely let natural gas prices rise over a ten-year period, or offer lower natural gas prices and electricity prices in some locations than in others. The models are designed to address these questions by including production activities for alternative technologies and the associated capacity expansion options in alternative types of productive units. Size of Capacity Expansion One of the most important aspects of investment decisions is what size of unit to install. Should one large plant be built at a central location or a number of small plants at decentralized locations? Should a large plant be built now even though there is not yet enough demand or should a number of small plants be built, spread out over time? These two questions give examples of the tradeoff between economies of scale on the one hand and transport cost and time discounting on the other. If transport costs are low and economies of scale are pronounced, one large central plant should be constructed. But if transport costs are high and economies of scale small, a number of small plants at decentralized MODEL SPECIFICATION 31 locations will be more economical (see Vietorisz and Manne 1963 or Kendrick 1967). If economies of scale are small and discount rates high, small plants should be constructed every few years. But if economies of scale are pronounced and discount rates are low, large plants should be constructed only infrequently (see Manne 1967). The timing may also be affected by the price of imports and exports. If exports are priced relatively high, it may be advantageous to build capacity ahead of domestic demand and export the surplus. If import prices are relatively low, it may be useful to let domestic capacity fall below domestic demand and provide the needed materials with imports for a time (see Chenery 1952). Economies of scale also have a tradeoff with reliability which may be important. If the probability of breakdown is independent across plants, a system of many small plants will be more reliable but also more expensive than a system with a few large plants. These four tradeoffs with economies of scale-space, time, in- ternational trade, and certainty-make the problem of the size of additions to capacity an interesting one. (In this book, however, only the first three tradeoffs are included in the models.) Furthermore, when additions to capacity are considered in the context of existing plants, the best size may be determined by the presence of complementary slack capacity in existing units. Timing of Additions to Capacity The best timing for the construction of new units was discussed above as it is affected by economies of scale and discount rates. Timing may also be affected by the cost of imports and the value of exports. For example, it might be economical in some cases to build a fairly large blast furnace and steel shop together with a smaller facility for rolling shapes. The excess steel might then be sold as billets to rerollers or exported in the form of billets or slabs for a time until demand had grown enough to justify the installation of rolling facilities for flat products. The timing decision in this example is whether or not to delay the construction of the flat product rolling facility while exporting billets and slabs and importing flat products. Usually, new steel mills are constructed and existing steel mills are expanded in stages. For example, the plan for stage one might include two basic oxygen furnaces and the plan for stage two would include a third. The timing of these stages depends on the growth of demand and even on capacity expansions that may be occurring at other steel mills in 32 GENERAL METHODOLOGY the area. The model allows the careful study of the costs associated with changes in timing of all the interdependent projects in a system of plants. The plants may belong to different corporations or some may be owned by the government and others by private companies. Nonetheless, the investment decisions in them are interdependent and the model provides a means of analyzing these interdependencies. Product Mix If there are substantial economies of scale in the investment cost of productive units, one would expect different plants to specialize in different products. For example, one would not expect every plant to have a rolling mill for large shapes since there are substantial economies of scale in the investment cost for such a mill. Nor would one expect that every integrated steel mill would have flat product rolling mills. Instead, some mills would be expected to specialize in flat products and others in shapes. Thus, the problem of product mix is an important one in the design of investment projects. Table 3-4 lists the final products that might be included in a disaggregated model. It is unlikely that any steel mill would produce all these products. Thus, the problem is to find a niche for the new productive units. The new units may be installed in the existing plants to permit more efficient use of the existing capacity or they may be installed at new plants. For example, a new cold strip mill might be added to take advantage of excess capacity in the hot strip mill. The possibility of interplant shipments further compounds the choice of product mix. For example, a company may want to install a plate mill in order to produce welded pipe but may lack the steelmaking capacity to service this unit. If another plant should have some excess steel capacity, a shipment of slabs might be arranged. This would allow the Table 3-4. Final Products Non flat products Flat products Billets Plates Heavy shapes Hot sheets Light shapes Cold sheets Bars Tin plates Reinforcing bars Galvanized sheets Wire rods Seamless pipes Rails MODEL SPECIFICATION 33 one plant to enter the welded pipe market and permit the other to make more efficient use of its steelmaking facilities. Once the products are fabricated, the question is how they will be transported to market. Transport The shipment not only of products to markets but also of rawmaterial to plants makes transport problems important in the design of investment projects. There are occasional bottlenecks in the transport structure of any country, and the steel industry's demand for transport services is substantial. For example, a country may experience shortages of railroad cars or bottlenecks on certain links in the rail system. Anticipation of these kinds of difficulties may substantially affect the choice of where to construct new facilities. This can be studied in the models by adding constraints to certain shipments or by increasing the cost of transport in parts of the system. One can then study the implications for investment in the steel industry of bottlenecks in the transport system. Foreign Trade Policy If there are large economies of scale in investment cost, one would expect plants to expand beyond the level of the domestic market and to export the excess output for a time. As demand grows, a new plant will not be built as soon as domestic supply equals domestic demand; instead, imports will be used until there is sufficient demand to justify the installation of another large facility. Thus, international trade policy may play a key role in the design of investment projects in the steel industry. The economics of the steel industry at some locations may look favorable enough to support a facility that is largely or entirely devoted to the export market. A study of this possibility can be carried out by including export possibilities in the model. If the facility is thought to be large enough to have some impact on prices within a certain part of the world, declining export prices can be built into the model. The model may also be used to study the question of whether to use domestic or imported raw material. If the domestic raw material is declining in quality, then the new facilities should probably be built at ports, and the remaining ores or coal should be used by the plants already located nearby. 34 GENERAL METHODOLOGY Finally, trade in intermediate products may play a role in the design of steel investment projects. A small country might find it advantageous to invest first in rolling mills for nonflat products and to import the billets. At a later stage, it might install electric arc furnaces and import sponge iron or scrap. Later still it might invest in the facilities to produce sponge iron and import pellets. Thus, trade policy may affect the design of investment projects with respect to raw material, intermediate products, and final products. This chapter has provided a discussion of the specification of the planning problem and of the formulation and design of investment projects in the steel industry. The application chapters of this volume will translate this first into mathematical statements and then into a language that can be read by computers. PART TWO The Mexican Steel Sector: A Case Study THE CASE STUDY INCLUDES a chapter describing the situation in the Mexican steel industry in 1979 when this study was begun, a chapter on a small static model, two chapters on a large static model, and two chapters on a small dynamic model of the industry. These models provide a slow increase in complexity from small to large and from static to dynamic; each has its own comparative advantage in analyzing the industry. The static models can be used for studies of operational efficiency, and the dynamic model is useful for analyzing investment possibilities. The small models are easier than the large to explain and less expensive to solve when sensitivity tests are performed. The two small models are calculated in dollars and in millions of metric tons of inputs and outputs. The large model is calculated in pesos and in thousands of metric tons of inputs and outputs. 35  4 The Steel Sector in Mexico THE MEXICAN STEEL SECTOR provides a useful example for this volume on investment analysis in the steel industry. It is large enough to include a diversity of production technologies and products. Yet it is small enough that a relatively small model can capture the essential economics of the industry. Furthermore, a variety of interesting economic issues con- fronted the industry at the time of this study. First, natural gas prices in Mexico were lower than international prices by roughly a factor of ten. This fact influenced the choice of technology for the future: direct reduction with natural gas or blast furnace reduction with coke. Second, the domestic iron ores in Mexico were severely limited, and it appeared likely that the industry would have to rely on imported iron ore in future years. This had important implications for where new capacity should be built. Third, the government of Mexico was attempting to encourage the decentralization of industry by offering lower natural gas prices in uncongested areas. These differences in price were great enough to affect decisions about where to add to capacity. Finally, the oil boom in Mexico was causing demand for steel products to grow ra]pidly so that the industry was likely to expand markedly in the coming decades. Against this background, this chapter provides a brief overview of the steel sector in Mexico. It begins with overall demand for and supply of steel products and then discusses in turn raw material, transport, and imports and exports. Demand for Steel Products Since the mid-1940s, Mexico has been engaged in an industrialization process that has produced a steady growth in the demand for steel 37 Table 4-1. Apparent National Consumption, 1970-79 (thousand metric tons) Increment Flat Increment Nonflat Increment Seamless Increment Year Steel (percent) products (percent) products (percent) pipe (percent) 1970 3,965 9.3 1,367 11.3 1,367 5.5 174 9.4 1971 3,735 -5.8 1,361 -0.4 1,268 -7.2 160 -8.0 1972 4,276 14.5 1,585 16.5 1,410 11.2 183 14.4 1973 5,351 25.1 2,062 30.1 1,670 18.4 207 13.1 1974 6,205 16.0 2,420 17.4 1,954 17.0 203 - 1.9 1975 6,444 2.6 2,365 -2.3 2,127 8.9 238 17.2 1976 5,951 -7.7 2,100 -11.2 2,036 -4.3 241 1.3 1977 7,018 17.9 2,322 10.6 1,919 -5.9 246 2.1 1978 8,056 14.8 3,049 31.3 2,203 14.8 286 16.2 1979 9,096 12.9 3,278 7.5 2,694 22.3 392 47.0 Source: Department of Economic Studies, CANACERO. Note: Doubt can be raised about the validity of a few numbers in the table(in thousands of metric tons). The total consumption of steel in 1977 should be 6,098 instead of 7,018 if it is to be consistent with the projected growth from 1976. The growth from 1976 to 1977 is given as Flats 222 Nonflats -119 Seamless 5 108 Then using a ratio of 1.359 tons of steel per ton of products one obtains a growth of (108) (1.359) = 147 thousand tons of steel. This added to the apparent consumption in 1976 of 5,951 yields an apparent consumption in 1977 of 5,951 + 147 = 6,098 in contrast to the figure in the table of 7,018. Our manpower resources have not been sufficient to enable us to track down the source of the inconsistency. THE STEEL SECTOR 39 products. In the mid-1940s, there was only one major steel plant, and it had an installed capacity of 120,000 tons. Because the demand for iron and steel products was estimated to be over 350,000 tons, imports played an important role in satisfying internal demand. Traditionally, demand for finished steel products has always exceeded supply, and increments to capacity have been a result of large excess demand. It is only in recent years that Mexico has had installed capacity that exceeded current demand. Since the 1970s, the steel industry's main concern has been to maintain an adequate exploration rate for iron ore reserves and to improve productivity in some of the older steel mills. Aggregate demand for steel from 1970 to 1979 is given in table 4-1. The figures correspond to "apparent national consumption," a term frequently used as an estimate for demand and obtained by the relation: production + imports - exports. The fluctuations in demand for steel shown in table 4-1 follow the world pattern. The leading steel-producing countries, such as the United States, Japan, and the European Economic Community, had a record steel consumption in 1974 followed by a decrease in 1976 as a result of the world economic recession and a reduction of international steel trade because of the protectionist actions of some major countries. The fluctuations in the Mexican steel industry also present a cyclical pattern that reflects the economic slowdown following a change of adminis- tration every six years-in this case, 1970-76. Classification of Steel Products Traditionally, Mexican steel products have always been classified under the categories of flat, nonflat, and seamless pipe products. The relative share of the market that each of these holds has been: flat products, 51 percent; nonflat products, 44 percent; and seamless pipes, 5 percent. In view of the future expansion of the Mexican petroleum industry and the requirement it will have for seamless pipe and flat products, however, their relative share of demand is expected to increase in the near future. As shown in table 4-1, from 1972 to 1974, when the Mexican economy was expanding, the relative shares and the percentage increments of seamless pipe and flat products increased considerably. This result would be expected in a country trying to establish capital goods industries, and with an oil industry becoming increasingly important. 40 MEXICAN CASE STUDY Regional Distribution of Demand Even though Mexico has a surface of 2 million square kilometers, industrial activity is heavily concentrated within three relatively small areas surrounding Mexico City, Monterrey, and Guadalajara. Approximately 85 percent of total demand for steel products takes place within these cities, but it is expected that a decentralization program of the government, along with the natural development that the oil- producing areas will generate, will more evenly spread the demand for steel. If the regional distribution of demand were to continue its historical pattern, 60 percent would be in Mexico City, 25 percent in Monterrey, and 15 percent in Guadalajara. As shown in map 1, these three locations form a triangle that leaves out the northwestern and southeastern regions of the country. In the next few years, the oil-associated activity offshore in the Gulf of Mexico will do little to change the isolated situation of Campeche, but inshore activity in Chiapas will improve conditions there. For the near future, it is expected that four major demand regions- Mexico City, Monterrey, Guadalajara, and Coatzacoalcos-will have about 75 percent of total demand. The regions are identified by the major city in each, which can be considered a center of distribution for steel products. Depending on the success of the decentralization program, the northwestern region could be included as an important potential consumer, having its distribution center in Culiacan. Projections of Future Demand Recent dramatic increases in Mexico's oil reserves have prompted a large expansion plan in the petrochemical industry and corresponding expectations of a boom in Mexican industrial development. Steel plays a vital role in such development, mainly because steel pipe and steel sheet are essential inputs for the petrochemical sector. In addition, the growing capital goods sector will continue to demand steel ingots and various special steel products. To obtain a more disaggregated demand for steel products, it is necessary to determine the relative shares of demand for each type of flat and nonflat product. In the near future, the structure of demand is expected to be: 32' 329- UNITED STATESOF AMERICA 32° 32 UNITED STATES OF AMERICA \i \I. Gulf 0f 24° \11-1 -LI ..-1 1 I 1 J . \Jt \| -| Kl kP. - ML \It 0 Production Centers and Demand Regions - * Stecl plant, * Nlarkeiirg i:·n rs 1Dem.nd regicn,i o P,ienial nte li fOlln Inernajtnl boundarnes 41 42 MEXICAN CASE STUDY Percent Flat products Steel plates 14 Hot strip sheets 11 Cold strip sheets 20 Tin mill products 6 Subtotal 51 Nonflat products Heavy shapes 4 Light shapes 5 Bars 5 Reinforcing rods 19 Wire 9 Rails 2 Subtotal 44 Seamless pipes 5 Nine demand regions have been identified (see map 1) and are expected to have the following shares of total demand: Percent Percent Mexico City 40 Puebla 4 Monterrey 26 Quer6taro 3 Guadalajara 8 Toluca 14 Coatzacoalcos 2 San Luis Potosi 2 Lizaro Cdrdenas 1 Domestic Supply of Steel Products In Mexico there are three types of steel producers: integrated, semi- integrated, and nonintegrated plants. As discussed earlier, integrated steel plants include all processes in steelmaking. Their operation begins with the preparation of basic raw material such as iron ore and coal and ends with the rolling process of finished products. Integrated plants usually achieve large economies of scale above a certain plant size, are complex to operate, require highly skilled labor, and produce both flat and nonflat products. Semi-integrated steel plants do not reduce iron ore to produce steel. Their main input is steel in the form of scrap, and their first operation consists of melting the scrap in electric furnaces to obtain intermediate products such as blooms or billets. This type of plant usually specializes in the production of nonflat light products, such as bars and wire rods, which do not require large rolling mills. Flat products are not produced THE STEEL SECTOR 43 Table 4-2. Production of Raw Steel by Plant, 1978-79 (thousand metric tons) Plant 1978 1979 Altos Hornos de Mxico S.A. (AHMSA)a 2,447 2,541 Fundidora de Monterrey S.A. (FMSA)a 949 888 Siderurgia Ldzaro Cdrdenas-Las Truchas S.A. (SICARTSA)a 586 646 Hojalata y Lamina S.A. Monterrey (HYLSA)i 1,431 1,548 Hojalata y Ldmina S.A. Puebla (HYLSAP) Tubos de Acero de M6xico S.A. (TAMSA) 420 420 Total integrated plants 5,833 6,043 Semi-integrated plants 942 1,051 Total 6,775 7,094 a. Publicly owned companies. by semi-integrated plants, since they require larger-scale iron and steel production and rolling units. Nonintegrated steel plants also reroll steel products. They do not have to be large to be efficient, and their main input is scrap. There were six integrated steel plants in Mexico in 1978-79, which accounted for 85 percent of total production. Three of these plants were controlled by the government. Table 4-2 shows the production of raw steel in 1978 and 1979. Altos Hornos de Mixico S.A. (AHMSA) AHMSA was established in 1941 with the Mexican government as majority shareholder and private investors as minor participants. The steel mill was built in Monclova, Coahuila, a city in a desert region in the north of Mexico, which had no previous industrial infrastructure. The plant was originally projected to produce 100,000 tons a year of finished flat products, and it was built with second-hand equipment and a small initial investment. In recent years, the company's expansion policy has been to preserve about 40 percent of the market share. As a result, AHMSA is the largest steel producer in Mexico, supplying almost every type of finished product. AHMSA has the concession for exploiting several iron ore mines in the northern states of Mexico. The largest mine, La Perla in the state of Chihuahua, has 49 million tons of positive reserves with 58 percent iron content. AHMSA also controls more than 530 million tons of medium quality coal in Coahuila, near the city of Monclova. 44 MEXICAN CASE STUDY A successful operation of the mines and intensive exploration for new reserves are essential conditions for an efficient development of the company. Since it is not located near port facilities, it depends mainly on the extraction of its own coal and iron ore. The plant itself is a combination of old and new equipment. It reflects the pattern of additions to capacity that old plants usually follow, trying to keep pace with technological improvements. The older part of the steel complex, known as Steel Mill No. 1, is a mixture of steel technologies; as proficiency was being achieved in some of the traditional processes (such as open hearth furnaces), improvements were being made in the use of modern equipment (such as basic oxygen furnaces). Steel Mill No. 2 has been constructed recently. AHMSA, as its name indicates (altos hornos in Spanish translates as "blast furnaces"), uses blast furnace technology for the reduction of iron ore. The metallic charge was traditionally a blend of sinter and iron ore chunks. The company has the only sintering plant in Mexico and a pelletizing plant at the iron ore mine of La Perla in Chihuahua. The installed capacity for each productive unit is given in table 4-3. Steel Mill No. I has four blast furnaces of different capacities, ranging from 250,000 to 550,000 tons a year. In steelmaking, the plant has eight open hearth furnaces and two basic oxygen furnaces for a total steelmaking capacity of 2.75 million tons a year. Casting is done by pouring molten steel into ingots. The first rolling operation consists of passing the steel ingots through a primary roughing mill to obtain slabs Table 4-3. AHMSA: Capacity of Some Productive Units, 1979 (thousand metric tons) Productive unit Steel Mill No. 1 Steel Mill No. 2 Sinter plant 1,500 0 Pellet planta 600 0 Coke ovens 1,000 1,100 Blast furnace 1,800 1,500 Open hearth furnace 1,500 0 Basic oxygen furnace 1,250 820 Continuous casting unit 0 710 Roughing mill 1,850 0 Hot rolling mill 1,600 0 Cold rolling mill 700 800 Shapes rolling mill 200 0 Wire rolling mill 270 0 a. In the iron ore mine at La Perla, Chihuahua. THE STEEL SECTOR 45 and blooms. The finishing section consists of hot and cold rolling mills with a total capacity of 1.6 million tons a year of flat products. The production of nonflat products plays a lesser role in the company output since the rolling capacity for nonflat is only 0.65 million tons a year. Steel Mill No. 2 began operation in 1976. It is a fully integrated plant that operates independently of Mill No. 1, even though shipments of some intermediate products between the two mills occur. The main productive units in the plant are a set of coking batteries, a large blast furnace, a basic oxygen furnace, a continuous casting unit, a pickling line, and a cold rolling mill. AHMSA also has a small steelmaking plant in the border town of Piedras Negras, Coahuila, north of Monclova. This plant includes a blast furnace and three open hearth furnaces that account for a small installed capacity of 0.15 million tons of steel ingots a year. The production of this plant is sent to the rolling facilities in Monclova to be processed into finished products. Fundidora de Monterrey S.A. Fundidora, as it is commonly known, is located in the city of Monterrey and was founded in 1900. It was the first integrated steel mill in Latin America, originally designed to produce rails for the railroad companies and shapes for the construction industry. For halfa century it was the leading steel plant in Latin America, but in recent years decreases in productivity because of aging equipment have reduced its relative importance. For years, some of the best iron ore mines in Mexico were under the control of Fundidora. Cerro del Mercado in the state of Durango and Hercules in Coahuila provided the company with high-grade ore, and, even though these mines are becoming exhausted, the relative position of Fundidora with respect to reserves is fairly good. The same cannot be asserted for coal, since total reserves are close to 100 million tons, about a fifth as much as the coal reserves of AHMSA. The main iron-bearing material used by Fundidora in the past to feed its blast furnaces was lump ore. This was possible owing to the high quality of the ore. The declining grade of the remaining mineral in the mines, however, and the accumulation of ore fines (residue too fine to be charged directly) have generated the need for a pelletizing plant. The two blast furnaces and eight open hearth furnaces that Fundidora has in operation are fairly old. In an effort to maintain efficiency, the blast furnaces have been modified and a BOF shop with two furnaces has 46 MEXICAN CASE STUDY Table 4-4. Fundidora: Capacity of Some Productive Units, 1979 (thousand metric tons) Productive Unit Capacity Pellet plant 750 Blast furnace 1,400 Open hearth furnace 850 Basic oxygen furnace 1,500 Roughing mill 1,450 Hot rolling mill 870 Cold rolling mill 500 been installed. Forming of semifinished products is done by ingot casting and roughing mills. A variety of hot and cold rolled sheet and commercial shapes is produced by the rolling mills. Table 4-4 gives the capacity of the main productive units of Fundidora in 1979. The main problems the company has faced in the past decade have been labor strikes and decreasing productivity that developed into a crisis in 1976. Until that year, Fundidora had been under the control of private investors, but its mounting problems made it necessary for NAFINSA, a government credit institution, to intervene and Fundidora became a government-controlled steel mill. Siderurgia Lazaro Cirdenas-Las Truchas S.A. (SICARTSA) SICARTSA is the newest steel mill in Mexico. The decision to construct the new plant on the coast of Guerrero was made by the government in 1971. It was originally designed to be constructed in four stages, the first to be completed in 1976. SICARTSA was to have been operating at full capacity by 1980 and producing I million tons a year of nonflat products. The plant was located in accordance with the iron ore reserves assigned to SICARTSA for its exploitation. More than 100 million tons of iron ore reserves of medium grade are located near the plant, and the mineral is transported from the mine to the pelletizing unit in a slurry pipe. Another important determinant of the seashore location of the plant is the need to import coal (mainly from Australia), since domestic reserves are located in the north of Mexico and have a high level of volatile material. (The high volatility of Mexican coal means that input- output coefficients are very high-2.2 tons of coal are required to obtain a ton of coke-and it is therefore inefficient to transport.) Reduction and THE STEEL SECTOR 47 Table 4-5. SICARTSA: Capacity of Some Productive Units, 1979 (thousand metric tons) Productive unit Capacity Pellet plant 1,850 Coke ovens 660 Blast furnace 1,100 Basic oxygen furnace 1,300 Continuous casting unit 1,300 Light section mill 600 Rod and bar mill 600 refining of steel is done by blast furnace and BOF units, and a continuous casting unit that is designed to produce over a million tons a year provides billets to be used in the merchant bar and wire rod mills. The first stage of SICARTSA was designed to produce 0.5 million tons of commercial shapes and 0.5 million tons of wire and wire rod. The capacity of the key productive units is given in table 4-5. Hojalata y Lamina S.A. (HYLSA and HYLSAP) Hojalata y Lamina was the only private integrated steel company competing with government-owned companies in Mexico in 1979. It was created in 1942 in the city of Monterrey as a subsidiary of a large brewery to provide the tin plate for beer cans. By 1957, the company had developed the HYL process to reduce pellets to sponge iron by direct reduction with natural gas. This technological development supported the growth of the company, and by the mid- 1960s the plant had become an important producer of flat products. In recent years, the HYL process has gained international recognition, and the company has increased considerably the export of its technology to countries such as Venezuela and Iran that produce natural gas. In addition to the plant in Monterrey, which will be identified as HYLSA, the company established in the 1960s a new plant near the city of Puebla to produce nonflat steel products. This plant, known as HYLSAMEX and identified in this study as HYLSAP, is not near the iron ore mines, but rather near the most important market for its final products: the metropolitan area of Mexico City. The company has control over iron ore reserves in the states of Jalisco, Michoacdn, and Colima for a total of 70 million and 210 million tons of positive and possible reserves, respectively. The pellets required by both 48 MEXICAN CASE STUDY Table 4-6. HYLSA and HYLSAP: Capacity of Some Productive Units, 1979 (thousand metric tons) Productive unit HYLSA HYLSAP Direct reduction unit 660 1,000 Electric furnace 1,000 560 Continuous casting unit 0 560 Roughing mill 1,000 0 Hot strip mill 900 0 Cold strip mill 600 0 Bar mill 0 430 Wire rolling mill 0 200 HYLSA and HYLSAP are concentrated in a pelletizing plant in the state of Colima, with an annual production of 1.5 million tons of pellets. HYLSA (MONTERREY). The HYLSA plant had three direct reduction units, independent from one another, and a steel shop of seven electric furnaces that gave it a total capacity of 0.77 million tons of raw steel in 1979. The rolling processes include a primary and a secondary roughing mill, a pickle line, a cold rolling mill, and a tinning line. Recent modifications in the hot rolling mill, together with the addition of another electric furnace in the steel shop, have increased total capacity to 1.2 million tons of raw steel. The location of the plant within the city of Monterrey limits considerably its expansion possibilities. Future expansion seems likely to take place either in HYLSAP near Puebla or in some other new location. HYLSAP (PUEBLA). The HYLSAP plant in Xoxtla, very close to the city of Puebla, was designed to produce nonflat products, and it has been doing so since 1969. It consists of a direct reduction unit with four reactors, a steel shop with three electric furnaces, a continuous casting unit, and the finishing mills for reinforced bars and wire rod. Total installed capacity for the production of nonflat products added up to 0.45 million tons in 1979. The breakdown for both plants is given in table 4-6. Tubos de Acero de Mexico S.A. (TAMSA) Tubos de Acero de M&xico, commonly known as TAMSA, is near the city of Veracruz on the Gulf of Mexico. It was founded in 19:52 as a nonintegrated steel plant, where imported steel ingots were to be THE STEEL SECTOR 49 Table 4-7. TAMSA: Capacity of Some Productive Units, 1979 (thousand metric tons) Productive unit Capacity Direct reduction unit 270 Electric furnace 450 Extrusion mill 280 Seamless pipe mill 280 Bar mill 80 transformed into seamless steel pipe. With the addition of a steel shop, TAMSA became a semi-integrated plant. Nevertheless, difficulties in the supply of steel scrap and substantial instability in the price of this input encouraged the firm to become the fourth integrated steel plant in Mexico in the mid-1960s. The plant was installed near its principal market, the oil fields of Poza Rica, Veracruz, and it was conceived as a supplier of seamless pipe for the oil industry. TAMSA has control over a small deposit of iron ore but has not, in the past, engaged in mining activities. Most of its pellets have been purchased directly from HYLSA and other sources. It also maintains a close relation with HYLSA with respect to steelmaking technology, since it uses the HYL process for direct reduction of the pellets. The steel shop consists of four electric furnaces with a total capacity of 0.58 million tons of raw steel, In the finishing section, besides a hot extrusion mill with a capacity of 0.28 million tons of seamless pipe, TAMSA has a bar mill with a capacity of 0.25 million tons of steel bars. Table 4-7 gives a capacity breakdown. Domestic Inputs and Raw Material The main inputs in steelmaking are iron ore, coal, scrap, natural gas, and electricity. Of these, only iron ore and coal are mined independently by the steel companies. Scrap is either purchased in local and foreign markets or obtained by recycling processes in the rolling mills of each plant. Natural gas and electricity are provided by government monop- olies in oil and gas (PEMEX) and electricity production (CFE). Mining of Raw Material As indicated above, mining of raw material is done individually by each company, and the permits to exploit each resource are granted by 50 MEXICAN CASE STUDY the Mexican government. By law, the mineral resources are part of the national reserve and are considered national property. Nevertheless, when considered applicable, the government gives concessions for the exploitation of some of the reserves to private companies. A common classification of mineral reserves is that of positive, probable, and possible. Measured reserves are those that have been surveyed in detail to determine the shape and mineral content of the deposit; estimated and actual values of the reserves could differ by more than 20 percent. Indicated reserves are those that have been partially specified by sampling methods. Inferred reserves are those that have been estimated by using geological studies of the field. Surveys and measurements are rarely made of inferred reserves. Iron Ore Mining Table 4-8 shows the amount of iron ore reserves under the control of each company. The figures include the participation of each firm in a mining consortium created in 1974 with the participation of all steel companies except SICARTSA. The iron ore mining consortium called Consorcio Minero Benito Juarez-Pefia Colorado, commonly known as Pefia Colorado, is in the state of Colima. It has a low-grade ore with 45 to 48 percent iron content that requires beneficiation methods to be of any use for the steel mills. Not far away from the mining site there is a pelletizing plant with an annual capacity of 3 million tons. The production is distributed between the steel companies. Total positive and probable reserves of the field are 104 million and 6 million tons respectively. The ownership of the reserves and the production of the pelletizing plant are distributed Table 4-8. Reserves of Iron Ore in Mexico, 1979 (thousand metric tons) Company Measured Indicated Inferred AHMSA 113,450 17f600 23,000 Fundidora 77,820 46,460 60,820 HYLSA 71,310 22,570 210,600 SICARTSA 105,600 11,600 0 TAMSA 17,140 1,020 0 Other reserves 41,172 37,024 26,148 Total reserves 426,492 136,274 320,668 Source: La Industria Siderurgia, vol. i, p. 45. THE STEEL SECTOR 51 among the participating companies as follows: AHMSA, 50 percent; FUNDIDORA, 5 percent; HYLSA, 28.5 percent; and TAMSA, 16.5 percent. This type of organization has achieved great efficiency in distribution and operations, and because of the economies of scale in large pelletizing units, it could be the organizational mode for future mining expansions. Coal Mining Coal fields are concentrated in the northern part of the state of Coahuila, not far from AHMSA. Because Mexican coal has high volatility, transportation of coal would be much more inefficient than that of iron ore. This is probably the main reason that the first steel mills established in Mexico were closer to the coal mines than to the iron ore mines. Mining of coking coal has traditionally been done by AHMSA and Fundidora. The only other steel company that consumes coal as a primary input is SICARTSA, but most of its coal is imported. The concessions to develop coal mines are obtained by private companies in the same way as those for iron ore. The government grants permits to exploit a certain coal field, but only to Mexican companies. Table 4-9 shows total positive, probable, and possible reserves, and the concession under which such reserves are being exploited. Most of Mexico's coal is mined underground. Because of the thinness of the seams (a maximum of 1.5 meters), the extraction of coal is limited to a maximum of 300 meters in depth. This is severe constraint on the availability of new coal reserves and on the technology to exploit them. Steel Scrap Steel scrap is an important input to the steel industry, regardless of the technology used in the reduction process-BOF, open hearth, or electric Table 4-9. Reserves of Coking Coal in Mexico, 1979 (thousand metric tons) Company Measured Indicated Inferred AHMSA 532,400 20,800 5,000 Fundidora 66,290 21,660 8,820 Carbonifera de San Patricio S.A. 15,000 0 0 Industrial Minera Mxico S.A. 32,400 0 0 Other reserves 0 60,358 1,431,000 Total reserves 646,090 102,818 1,444,820 52 MEXICAN CASE STUDY Table 4-10. Origin and Use of Steel Scrap in Integrated Steel Mills, 1974-75 (thousand metric tons) Plant and origin of scrap 1974 1975 AHMSA Recycled 653 590 Domestic purchase 64 75 Imported purchase 96 222 Total 813 887 Fundidora Recycled 238 315 Domestic purchase 0 8 Imported purchase 40 1 Total 278 324 HYLSA Recycled 147 167 Domestic purchase 244 183 Imported purchase 203 337 Total 594 687 TAMSA Recycled 91 106 Domestic purchase 44 57 Imported purchase 0 24 Total 135 187 Table 4-11. Imports and Exports of Raw Material and Steel Products, 1974-79 (thousand metric tons) Raw material and steel products 1974 1975 1976 1977 1978 1979 Imports Coal 369 461 94 631 391 582 Scrap 796 1,192 524 351 318 491 Steel slabs and billets 130 154 50 27 39 87 Flat products 305 294 202 309 459 476 Nonflat products 138 179 141 76 128 251 Pipes 54 48 61 825 568 601 Exports Flat products 8 2 15 32 14 13 Nonflat products 38 5 23 82 250 156 Pipes 71 60 96 104 84 73 THE STEEL SECTOR 53 furnace. Although used intensively in the integrated steel mills, scrap is even more important for the semi-integrated and nonintegrated steel plants. They depend solely on purchases of steel scrap, and since the local market experiences shortages in supply, imported steel scrap plays a major role. Integrated steel plants satisfy their need for steel scrap either by domestic or imported purchases or by their own production. The latter is obtained with the cutting and finishing operations in the rolling mill section. This kind of first-grade scrap is called "recycled." Table 4-10 shows the use of different types of scrap by plant between 1974 and 1975. Imports and Exports of Raw Material and Steel Products In the early 1970s Mexico was self-sufficient in basic steel products. Most of its imports were special steel products, for which demand was not large enough to encourage domestic production. After 1974, however, excess demand for both flat and nonflat products considerably increased the need to import basic steel. In 1979 the excess demand for steel products was due not only to the increase in consumption, but also to a decline in the production of flat products by Fundidora. In spite of the increase in the price of imported steel because of a major devaluation of the Mexican currency in 1976, there was an increase in imports of nonflat products and pipe in 1977. Imports and exports by product types are given in table 4-11. 5 A Small Static Model THIS CHAPTER, WHICH DRAWS in part on the study of Alatorre (1976), presents a primer on the planning of industrial programs in the steel industry, through the development of a small static model of the Mexican steel industry. First, the sets of steel mills and markets for steel products in Mexico are defined. This section overlaps slightly with the previous chapter but contains only the information required for the model. This is followed by the presentation of the small model of the industry, a listing of the data used in the model, and a discussion of the solution to the model. Later chapters in this book will use considerably more complicated models. Recapitulation of Data on the Mexican Steel Industry Map 2 presents an overview of the integrated steel industry in Mexico. Five of the six major steel mills in the country are included in the model; TAMSA is excluded because most of its production is for a single final product, seamless pipe. The ingot steel production capacity (in millions of metric tons) of the five plants in 1979 was: Altos Hornos (AHMSA), Monclova, Coahuila 3.57 Fundidora, Monterrey, Nuevo Le6n 2.35 SICARTSA, Ldzaro Cardenas, Michoacin 1.30 HYLSA, Monterrey, Nuevo Le6n 1.13 HYLSAP, Puebla, Puebla 0.56 Total 8.91 54 32. L-2i[ IJ 'l S i_~~~~ i. t- Ll 5 Ni \ n u~ Kl iL l f 28° - \ mme, -24°- ininei . Nmr1Pýfci Inera,,na.l hoI,' e MAP - MIE \lI ¯ C Major Steel Milils, Markets - and Sources of Ran Material * L.arge sieel mil% * Large market. N< Ircn øre nrne, ? Coal nne- £ lNarurul IJs tielJdP licO ai --inrernanonalaIboundanes 55- 56 MEXICAN CASE STUDY Briefly, the Altos Hornos plant is near coal and iron ore deposits, the Fundidora and HYLSA plants in Monterrey are in an important market area and not far from coal and iron ore deposits, the HYLSAP plant in Puebla is near the large Mexico City market area, and the SICARTSA plant is at a good port near iron ore deposits and not too far from the major market in Mexico City and a lesser market in Guadalajara. A rough estimate of the size of the market for steel products was obtained by using the demand projections of the Coordinating Commission for the Steel Industry for final products of 5.209 million tons and multiplying this figure by 1.4 to convert it to ingot tons: (5.209) (1.4) = 7.296. It was assumed that 55 percent of the total market requirement was in Mexico City, 30 percent in Monterrey, and 15 percent in Guadalajara. The estimated requirement (in millions of metric tons of ingot steel) in 1979 was: Mexico City 4.01 Monterrey 2.19 Guadalajara 1.09 Total 7.29 The capacity shown above of about 9 million tons and a market requirement of roughly 7 million tons overstate the excess capacity in 1979. The new plant at SICARTSA was not operating at full capacity at the beginning of that year, and 1.5 million tons of ingot steel capacity at Altos Hornos and 0.85 million tons of capacity at Fundidora were in the older and less efficient open hearth furnaces rather than in the newer and more efficient basic oxygen furnaces (BoF). For the purposes of this demonstration, however, we will not adjust the capacity figures down- ward but will leave them as they are. This will cause the model solution to show somewhat larger exports than was actually the case. The technology employed differs from plant to plant Altos Hornos, Fundidora, and SICARTSA have blast furnaces that use coke and iron ore pellets to produce pig iron, which is subsequently refined to steel by reduction in either open hearth furnaces or basic oxygen furnaces. HYLSA and HYLSAP employ a direct reduction technique in which iron ore pellets are first reduced by natural gas to sponge iron pellets, which are then further reduced in electric arc furnaces. Figure 5-1 provides a schematic of these processes in the simplified manner in which they are used in this small static model. For a more detailed description of the technology, see chapter 2. Table 5-1 provides the input-output coefficients for the technologies used by the plants. The rows show the commodities used in the model. A SMALL STATIC MODEL 57 Figure 5-1. Schematic of Technologies Coke Coke Iron ore pellets Scrap Open Steel hearth --b Scrap Basic oxygen furnace AHMSA, Fundidora, and SICARTSA Natural gas J-Iron ore pellets Electricity Sponge ironSte Direct reduction Electric are unit furnace HYLSA and HYL SAP For convenience, these commodities are divided into three groups. The first group is raw material that enters the tables only with negative coefficients; that is, the commodities are used only as inputs: iron ore pellets, coke, natural gas, electricity, and scrap. The second group enters some columns of the table with positive coefficients and others with negative coefficients; that is, the commodities are produced by some processes and consumed by others. They are called intermediate products and include pig iron and sponge iron. The third group enters 58 MEXICAN CASE STUDY Table 5-1. Input and Output Coefficients AHMSA, Fundidora, and SICARTSA HYLSA and HYLSAP Steel Sponge Steel production Steel iron production Pig iron in open production pro- in electric Commodity production hearths in BOF duction arc furnaces Iron ore pellets (tons) - 1.58 - - - 1.38 - Coke (tons) -0.63 - - Scrap (tons) - -0.33 -0.12 - - Pig iron (tons) 1.00 -0.77 -0.95 - Natural gas (1,000 cubic meters) - - - -0.57 - Sponge iron (tons) - - - 1.00 - 1.09 Electricity (megawatt-hours) - - - - 0.58 Steel (tons) - 1.00 1.00 - 1.00 -Not applicable. the tables with only positive coefficients. These commodities are called final products. In this model, there is only one final product, steel. The columns in table 5-1 represent the processes used in the industry. Thus, three processes are used in the first group of plants and two processes are used in the second. Closely related to processes are productive units. In fact, in this model there is a one-to-one relationship between processes and productive units, shown in table 5-2. A "l" in the table indicates that the process in the column uses the productive unit in Table 5-2. Relation between Productive Units and Processes Process Steel Steel Sponge Steel Pig production produc- iron produc- Productive iron pro- in open tion in produc- tion in unit duction hearth 3OF tion electric arc Blast furnace 1 - - - Open hearth - 1 - - BOF - - I - - Direct reduction - - - 1 - Electric arc - - - - -Not applicable. A SMALL STATIC MODEL 59 the corresponding row. The models discussed later in this book will have alternative processes that use the same productive unit. For example, the electric arc furnaces can be charged either with relatively high amounts of sponge iron and small amounts of scrap or with the reverse of these proportions. From the information given above one can begin to construct a small model of the industry to analyze the relative efficiency of the five different plants in meeting the product requirements for ingot steel in the three market areas. The model can also be used to identify the major bottlenecks that constrain production in the system of plants. The model will be structured to find the pattern ofproduction levels in the steel mills and shipments from the mills to the markets that will meet the market requirements at the least cost. The purpose of this model is not to show which steel producer in Mexico is the most efficient, but rather to illustrate how a linear programming model can be used to study the steel industry. The Model Sets As discussed in chapter 3, it is convenient in modeling an industry to think in terms of sets of plants, markets, productive units, processes, and commodities. One can describe these sets in a formal manner, which will later aid in the construction of a computer model. For example, let the index i be an element of the set I of steel plants or, more formally, ici = {Altos Hornos, Fundidora, SICARTSA, HYLSA, HYLSAP). This reads "i belongs to the set I of steel mills which includes Altos Hornos, Fundidora, etc." Thus, all the sets used in the model are defined as follows: iel = plants jeJ = markets me M = productive units peP = processes ceC = commodities where I = {Altos Hornos, Fundidora, SICARTSA, HYLSA, HYLSAPJ J = {Mexico City, Monterrey, Guadalajara} 60 MEXICAN CASE STUDY M = {blast furnaces, open hearth furnaces, basic oxygen furnaces, direct reduction units, and electric arc furnaces} P = {pig iron production, steel production in open hearths, steel production in BOF, sponge iron production, and steel production in electric arc furnaces} C = {iron ore pellets, coke, natural gas, electricity, scrap, pig iron, sponge iron, and steel} The last set, C, can be further divided into three groups in order to simplify the specification of the mathematical model. This separation may be written verbally as C consists of the three subsets CF (final products), CI (intermediate products), and CR (raw material), and mathematically as C =CFuCIuCR where u = indicates the union of sets CF =final products CI = intermediate products CR = raw material with CF = {steel} CI = {pig iron, sponge iron} CR = {iron ore pellets, coke, natural gas, electricity, and scrap} Variables The variables which relate all these sets to one another represent production, shipments, exports, imports, and domestic purchases of raw material. Consider first the production (or process-level) variables: z = process level for process p in plant i. For example, if pig iron production at Altos Hornos were 3 million tons a year, one could write Zpig iron production, Altos Hornos = 3. Since it is clumsy to write out these long subscripts, the production levels will usually be described mathematically as z, for pePi,icl; that is, as the process levels for all the processes p belonging to the set Pi A SMALL STATIC MODEL 61 which are available at plant i, and this for all the plants i in the set I. For example, the set P for Altos Hornos can be written (see table 5-1): PAItos Hornos = {pig iron production, steel production in open hearths, and steel production in BOFi. The variables for shipment levels represent the shipment of final products from plants to markets for each of the final commodities and are written as xeij = shipment of commodity c from plant i to market j. These variables are defined for all plants and markets but are not for all commodities-only for final products. Therefore, they may be written as xCif for cECF, iel,jeJ. For example, the shipment of 800 thousand tons of steel from SICARTSA to Mexico City would be written as XSteeL, SICARTSA, Mexico City = 0.8 since the units used in the model are millions of metric tons. Briefly, the other variables used in the model are eci = exports of commodity c from plant i vC = imports of final product c to market j u,= purchases of domestic raw material c by plant i. The model also includes variables for total cost and for certain subcategories of cost: = total production and shipment cost = raw material cost = transport cost = import cost = export revenues In summary, the variables of the model are z = process levels (production) x = shipments of products to markets e = exports of final products v = imports of final products u = domestic purchases of raw materials = total cost = cost groups 62 MEXICAN CASE STUDY = raw material cost = transport cost = import cost = export revenues Parameters Only one more set of definitions-those of the parameters of the model-is required before the mathematical model can be stated. Parameters are required for input-output coefficients, capacity uti- lization, market requirements, prices, and transport cost. The input-output coefficients given in table 5-1 relate commodities to processes. They are defined mathematically as a,= input (-) or output (+) of commodity c by process p when it is operated at the unit level. For example, from table 5-1 airon ore pellets, pig iron production = - 1.58 acoke, pig iron production = - 0.63 apig iron, pig iron production = 1.00. That is, 1.58 tons of pig iron pellets and 0.63 ton of coke are needed as inputs to the blast furnace to produce 1.00 ton of pig iron. Second, the capacity utilization coefficients given in table 5-2 are represented mathematically as b m I if productive unit m is used by process p "mp0 if productive unit m is not used by process p. For example, bopen hearth furnace, steel production in open hearths and bopen hearth furnace, steel production in BOF = 0. Capacity parameters must be defined for each productive unit in each plant: kmi = capacity of productive unit m in plant i in metric tons per year. These parameters values are given in table 5-3 where the rows represent productive units and the columns represent plants. A SMALL STATIC MODEL 63 Table 5-3. Capacity of Productive Units, 1979 (million metric tons) Productive unit AHMSA Fundidora SICARTSA HYLSA HYLSAP Blast furnace 3.25 1.40 1.10 - Open hearth 1.50 0.85 - BOF 2.07 1.50 1.30 - Direct reduction - - - 0.98 1.00 Electric arc - - 1.13 0.56 -Not applicable. The notation for market requirements is de = market requirement for final product c at market j in million tons per year. For example, dsteeL Mexico City = 4.01 million tons. Prices require a somewhat more disaggregated treatment. A distinc- tion will be made between the prices paid by the steel mills for domestic raw materials, the prices paid by the market areas for imported final products, and the prices received by steel companies for final products which they export. The notation for these parameters is p, = price paid for domestic purchases p" = price paid in market areas for imported final products pe= price received by steel mills for exported final products. Table 5-4. Prices in the Small Static Model (dollars per unit) Domestic Import Export Commodity price price price Iron ore pellets (metric tons) 18.70 - - Coke (metric tons) 52.17 - - Natural gas (1,000 cubic meters)a 14.00 - Electricity (megawatt-hours) 24.00 - - Scrap (metric tons) 105.00 - - Steel (metric tons) - 150.00 140.00 -Not applicable. a. There are 0.0283 cubic meters per cubic foot. So ($14 per thousand cubic meters) (0.0283 cubic meters per cubic foot) = $0.396 or 39.6 cents per thousand cubic feet. The 1979 world price of S3.60 per thousand cubic feet was therefore equal to S127 per thousand cubic meters. 64 MEXICAN CASE STUDY The prices used in the model are given in table 5-4. It has been assumed that the import price of the final product steel is higher than the export price. This is ordinarily the case since freight, insurance, and other costs separate the two prices. If export prices are greater than import prices the model might have an unbounded solution since money can be made by importing and immediately reexporting. The last set of parameters is the unit transport cost for shipping final products from plants to markets. These parameters are represented by the notation f{ = unit transport cost for shipping final products from plant i to market j. These parameters are computed from a table of distances (table 5-5) and from a cost per ton mile with the expression where 6{ = distance between plant i and market j in kilometers a= constant term # = proportional term. For the model at hand, a = $2.48 per ton and 0 = 0.0084 per ton kilometer. The resulting transport costs are given in table 5-5. In a similar manner, the unit transport cost for shipping exports from steel mills to the nearest port is If = unit transport cost for shipping final products from steel mill i to the nearest port. with = + pab Table 5-5. Rail Distances and Transport Costs between Plants and Markets Mexico City Monterrey Guadalajara Plant Kilometers Cost Kilometers Cost Kilometers Costa AHMSA 1,204 12.59 218 4.31 1,125 11.93 Fundidora 1,017 11.02 0 2.48 1,030 11.13 SICARTSA 819 9.36 1,305 13.44 704 8.39 HYLSA 1,017 11.02 0 2.48 1,030 11.13 HYLSAP 185 4.03 1,085 11.59 760 9.50 a. Dollars per metric ton. A SMALL STATIC MODEL 65 Table 5-6. Distances and Transport Costs from Plants and from Markets to Nearest Port Distance Transport cost Plant and market (kilometers) (dollars per metric ton) Plant AHMSA 739 8.69 Fundidora 521 6.86 SICARTSA 0 2.48 HYLSA 521 6.86 HYLSAP 315 5.13 Market Mexico City 428 6.08 Monterrey 521 6.86 Guadalajara 300 5.00 where the parameter b7 and the transport cost y are given in table 5-6, and the parameters a and # are 2.48 and 0.0084 respectively. Also, the import transport cost are gi = unit transport cost for shipping final products from the nearest port to market j with / = a + fb6 and the 6' and transport cost y are given in table 5-6. In summary, then, the parameters of the model are a = process inputs ( -) or outputs (+) b = capacity utilization k = initial capacity d = market requirements p = prices of domestic raw materials pv = prices of imports of final products pe= prices of exports of final products Pf= transport cost of final products fe= transport cost of exports yv= transport cost of imports The mathematical model can now be stated using the notation and data discussed above. 66 MEXICAN CASE STUDY Constraints The constraints of the model require that (1) no more final products be shipped to domestic markets and to other countries than are produced, (2) no more intermediate products be used than are produced, (3) no more raw material be used than is purchased, (4) no more capacity be used than is available, (5) the demand requirements of each market be satisfied, and (6) exports be less than a reasonable upper bound. Each constraint is discussed in turn. MATERIAL BALANCE CONSTRAINTS ON FINAL PRODUCTS (5.1) Yacpzpi c!Yxij + ci ceCf pePi jej iel Production of Shipment offinal] Exports o final products > products to domestic final iL,l markets products The symbols on the right margin of this inequality, ceEf and iel, indicate that there will be an inequality like this in the model for each combination of final products in the set CF and plants in the set I. Since there is only one final product, steel (ST), and there are five plants, there will be five such inequalities in the model. The symbols on the left-hand side of inequality (5.1), that is, (5.1a) Z acpz ceCF PEPj iEI then reads: "the summation over all the processes p in plant i of the coefficient a times the process level z." Consider, for example, the inequality for the plant Altos Hornos (AH). Since there are three production processes at this plant (table 5-1), PAH = (pig iron production (PIP), steel production in open hearths (SOH), and steel production in BOF (SBF)}. So the coefficients ap of interest for Altos Hornos are those in table 5-1 for the row "steel" and the columns in the set PAH above. Thus the terms in equation (5.1a) may be written as (5.1b) aST,PIPZPIP,AH + ST,SOH ZSOH,AH + aST,SBFZSBF,AH. A SMALL STATIC MODEL 67 However, from table 5-1 these coefficients are aST,PIP = 0 aST,SOn = 1 aST,SBF. -1I that is, no steel is either used by or produced by the pig iron production process. One unit of steel is produced by both the steel-open hearth and the steel-BOF processes. So the entire expression (5.1) for c = steel and i= Altos Hornos can be written (5.1c) ZSoH,AH + ZSBF,AH Y, XST,AH,j + eST,AH' jeJ Production of steel in Shipments of steel Exports of open hearths and Bo to all markets j s+ steel from s at Altos Hornos rom Altos Hornos Altos Hornos Thus inequality (5.1) requires that the total production of each final product in each plant must exceed the shipments to domestic markets and the exports. MATERIAL BALANCE CONSTRAINTS ON INTERMEDIATE PRODUCTS (5.2) Y acpzpi 0 ce CI iel L Net production of intermediate prod- > 0 ucts Some processes will produce intermediate products-that is, have positive elements acP-and other processes will use those intermediate products-that is, have negative elements acp (recall table 5-1). This constraint then requires that at least as much of the intermediate product must be produced as is used. For example, consider the Altos Hornos plant and the intermediate product pig iron, PI. Since the summation in equation (5.2) runs across the elements of the set of processes at Altos Hornos (PAH), this inequality may be written as (5.2a) aPI,PIPZPIP,AH + ap,soHZSOH ,AH + ap,,SBFZSBF,AH 20, and from table 5-1 ap,pIp = 1.00 aPI,SOH = - 0.77 aPI,SBF = - 0.95; 68 MEXICAN CASE STUDY that is, pig iron is produced by the pig iron production process and used by the steel-open hearth and the steel-BoF processes. Thus, equation (5.2a) can be written as (5.2b) 1.00zPIP,AH + ( - 0.77zsOH,AH) + (- 0.95zSBF,AH) 0. That is, pig iron production in the blast furnace at Altos Hornos must exceed the pig iron used in the open hearth and BOF steelmaking processes at that plant. MATERIAL BALANCE CONSTRAINTS ON RAW MATERIAL (5.3) acpzpi +uci 0 ceCRi Perj iel Raw material used + [Raw material] >0 1 purchased - At least as much raw material must be purchased as is used. Note that the coefficients acp for raw material will be negative. CAPACITY CONSTRAINTS (5.4) Y b.pzp,< km meM PEP, iElI [ Capacity Capacity required i available] No more capacity can be used than is available in each productive unit m in each plant i. MARKET REQUIREMENTS (5.5) X'xc +c j dj ceCf je J S ]+Imports offinal] Requirementfor hip ents romrket product c to final product c market j at market j Sufficient final products must be either produced or imported to meet market requirements. MAXIMUM EXPORT (5.5a) eci,< cECF iel A SMALL STATIC MODEL 69 [ Total exports of Bound on exports commodity c I of commodity c I An upper bound is placed on the total exports of each commodity c. This bound is the same for each of the commodities. The bound could be different for each commodity if in (5.5a) were replaced with e, NONNEGATIVITY CONSTRAINTS zPi >0 pePi, icl xe; > 0 ceCF,icl,jE e, >0 ceCF,iel Vej 0 cc-CF,jeJ uc_ >0 cECR,iEl Objective Function The above constraints must be satisfied while the analyst seeks to minimize the cost of production, transport, and imports less export revenues. (Note that both capital and labor costs are ignored in this model because they are considered to be fixed.) (5.6) 0=4 + O; + . - 0 Total Raw Transport Import Export F material i cost i cost + cost revenues I I cost where (5.7) #= p,uci cCR iE Ra m Domestic price times] comte quantity purchased cos of raw material (5.8) 1 Z y4 lxa ceCF iel jeJ [ Transport Cost of shipping final products cost from steel mills to markets cecp ie ceCF jeJ [ Cost of shipping final products + Cost of shipping imported final om steel mills to nearest ports products from ports to marketsj 70 MEXICAN CASE STUDY (5.9) y= E >PeVv' ceCF jeJ [ Import] _ Cost offinal products cost] L imported to markets (5.10) = pee, ceCF iel [ Export Price times quantity revenuesj of exports Size of the Model Computing the size of the model provides two kinds of information. First, it allows the analyst to estimate the computing time required to solve the problem and thus to decide on a set specification which is disaggregated enough to capture the essential elements of the problem and aggregated enough to be readily solved. Second, the computations help the analyst to check that the model specified in the equations or in the input to the matrix generator is actually the model being solved by the linear programming code. The size of the small model is determined by the number of constraints and variables. For this section only, the notational convention is adopted that the symbols for sets represent not the set but rather the number of elements in the set. For example, CF is used to represent the number of final products rather than the set of final products in the model. With this convention the number of elements in the model can be written as: CONSTRAINTS Equation Number (5.1) CF-I (5.2) CiI (5.3) CR-I (5.4) M-I (5.5) CF-J (5.5a) CF (5.6) (5.7) (5.8) (5.9) (5.10) Total (CF + CI + CR + M)-I + CF-(1 +J) +5 A SMALL STATIC MODEL 71 VARIABLES Variable Number zpi P-1 xcij CF-I-J e, CF-I ve; CF-J uci CR-I ' 00, 0,~ 0. 0. 5 Total = (P + CF-J + CF + CR). I + CF-J + 5 For the problem at hand, P= 5 1= 5 M=5 J= 3 C= 8 CF = 1 CI= 2 CR =5 Therefore the number of constraints is: Constraints = (CF + CI + CR + M)-I + CF-(1 + J) + 5 =(1 +2+5+5)(5)+(1)(4)+5 = (13)5 + 9 = 74 and the number of variables is: Variables = (P + CFJ -+ CF + CR)-I + CF-J+ 5 = (5 + (1)(3) + I + 5)(5) + (1)(3) + 5 = (14)(5) + 3 + 5 = 70 + 8 = 78. In summary, the small model has 74 constraints and 78 variables. Many of these constraints and variables are not necessary, but the model has not been reduced to eliminate activities that cannot occur because plants lack the necessary productive units. Results Two different categories of results are presented here. First are the preliminary results achieved by using the data to do some simple comparative cost calculations. These results can be obtained quickly and easily and provide insight into the results in the second category- namely, the solutions to the linear programming model. 72 MEXICAN CASE STUDY Preliminary Results The small model discussed in this chapter has a structure that simplifies the calculation of comparative cost. This structure lies in the fact that (1) the sets CR, CI, and CF partition the entire set of commodities C into three sets with null intersections (that is, the subsets are nonoverlapping and cover the entire set); (2) the production technology does not include alternative processes for producing the same commodity (with one exception-the production of the final commodity steel by three alternative processes); and (3) there are no alternative processes in the model for using domestic or imported raw material and intermediate commodities. First, it is useful to divide the set of processes into those that produce intermediate products (PI) and those that produce final products (PF). For the model at hand. PI = {pig iron production, sponge iron production} PF = {steel production in open hearths, steel production in BOF, and steel production in electric arc furnaces. Then let Qn= cost of production for intermediate commodities ceCI by processes pePI, so that (5.11) C= acop. ceCI ceCR CP ca p ePI Unit input of raw material ceCR per unit of output of intermediate product ccCl times the domestic prices of raw LP material ceCR Also let Cf = cost of production for final product ceCF by process pePF so that (5.12) Cac = I a' ± p n ce c'ECR, c'eCI, pePF where CRc = set of raw materials used in producing commodity c A SMALL STATIC MODEL 73 CI, = set of intermediate commodities used in producing commodity c. For example, consider the cost of production for the intermediate product pig iron. Then using the input-output data from table 5-1 and the price data from table 5-4 one can calculate intermediate cost: Cpig iron, pig iron production = (1.58 tons of pellets per ton of pig iron) ($18.70 per ton of pellets) + (0.63 ton of coke per ton of pig iron) ($52.17 per ton of coke). = $29.54 + $32.87 = $62.41 per ton of pig iron. Then the final cost of steel produced in the open hearths can be calculated as steel, steel production in open hearths = (0.33 ton of scrap per ton of steel) ($105 per ton of scrap) + (0.77 ton of pig iron per ton of steel) ($62.41 per ton of pig iron) = $34.65 + $48.05 = $82.70 per ton of steel produced in open hearths. Steel can also be produced in BOFS, so seel, steel production in BOFS = (0.12 ton of scrap per ton of steel) ($105 per ton of scrap) + (0.95 ton of pig iron per ton of steel) ($62.41 per ton of pig iron) $12.60 + $59.28 $71.88 per ton of steel produced in BOFS. Similar calculations can be made for sponge iron, sponge iron production = (1.38)(518.70) + (0.57)(514) = $33.79 and Isteel, steel production in electric arc furnaces = (0.58)($24) + (1.09)(833.79) = $50.75. A summary of these production costs (in dollars per metric ton) shows that steel produced by the sponge iron-electric are furnace method is less expensive than BOF steel, which in turn is less expensive than open hearth steel for the particular input prices used here: 74 MEXICAN CASE STUDY Steel production Pig Sponge iron pro- iron pro- Open Electric duction duction hearth BOF arc Pig iron 62.41 - - Sponge iron - 33.79 - - - Steel - 82.70 71.88 50.75 The sensitivity of these results to energy cost are shown by repeating the calculations with a natural gas price of $70 per thousand cubic meters, equivalent to roughly $2 per thousand cubic feet [($70 per thousand cubic meters) (0.0283 cubic meters per cubic foot) = $1.98 per thousand cubic feet] and with an electricity price of $50 per megawatt- hour ($.05 per kilowatt-hour). The cost of steel produced by the sponge iron-electric arc furnace method then goes from $50.75 per metric ton to $100.62 per metric ton. This is greater than the cost of steel produced by the open hearth or the BOF. In problems of industrial location one is interested not only in the cost of producing goods but also in the cost of delivering them to the markets. To set up these calculations, let C .= cost of making final product c by process p at plant i and delivering it to market j =f +c [Production cost ] Transport cost at plant i + from plant i to Lat plnt J L market j i Table 5-7. Delivered Cost at Market (dollars per metric ton) Plant Mexico City Monterrey Guadalajara AHMSA 84.47 76.19 83.81 Fundidora 82.90 74.36 83.01 SICARTSA 81.24 85.32 80.27 HYLSA 61.77 53.23 61.88 HYLSAP 54.78 62.78 60.25 Note: Table 5-7 shows the delivered price of steel produced in the aOF process rather than the open hearth process for Altos Hornos and Fundidora since this is the least expensive of the two processes. These delivered costs reflect only the cost of raw material and not the costs of capital, labor, administration, and marketing. A SMALL STATIC MODEL 75 The production costs are given above and the transport costs in table 5-5. The resulting production plus transport cost is given in table 5-7. The most striking result of table 5-7 is the low delivered cost of steel from the sponge iron-electric arc furnace process at HYLSA and HYLSAP. With prices of natural gas and electricity nearer current world market levels this advantage changes to the blast furnace-BOF process. Second, the table shows that SICARTsA has a transport cost advantage over both Altos Hornos and Fundidora in serving the Mexico City and Guadalajara markets. Fundidora has a transport cost advantage over Altos Hornos in all three markets. Since it is not absolute but rather comparative cost advantage that counts in determining which plants will serve which markets, it seems likely that the Monterrey market will receive steel from Fundidora and HYLSA, the Mexico City market will be served by some combination of HYLSAP, Altos Hornos, and SICARTSA, and the Guadalajara market will be served by Altos Hornos or SICARTSA. Linear Programming Results The shipment pattern results from the linear programming are shown in table 5-8. (Several solutions to this problem have the same cost because the shipment costs from Fundidora and HYLSA to the markets are identical.) Fundidora and HYLSA serve the Monterrey market and Altos Hornos and HYLSAP serve the Mexico City market. SICARTSA sends steel not to Mexico City, but rather to Guadalajara and then exports the rest of its product. SICARTSA has a relative advantage as an exporter because it is located at a port, while the other plants are some Table 5-8. Shipment Pattern in the First Linear Programming Solution (million metric tons) Mexico Mon- Guadala- Plant City terrey jara Exports Total AHMSA 3.105 0 0.465 0 3.570 Fundidora 0 1.634 0 0 1.634 SICARTSA 0 0 0.629 0.529 1.158 HYLSA 0.346 0.553 0 0 0.899 HYLSAP 0.560 0 0 0 0.560 Total 4.011 2.187 1.094 0.529 7.821 76 MEXICAN CASE STUDY Table 5-9. Slack (Unused) Capacity in the First Linear Programming Solution (million metric tons) Productive unit AHMSA Fundidora SICARTSA HYLSA HYLSAP Blast Furnace 0.129 0 0 0 0 Open Hearth 0 0 0 0 0 BOF 0 0.715 0.142 0 0 Direct reduction 0 0 0 0 0.390 Electric arc 0 0 0 0.231 0 distance from ports and thus incur higher transport charges if they are to export. There are no imports in the solution. One curious aspect of the solution was confusing at first and resulted in the conclusion that there was an error in the input data. This is shown in table 5-9 which displays the slack or unused capacity in the solution for each plant. Fundidora has both open hearth furnaces and BOFS. Since the BOFs are newer and more efficient one would expect them to be used fully and the slack capacity to appear in the open hearths. As shown in table 5-9, however, the solution gives the reverse answer. This kind of check against intuition is one of the best ways to debug a linear program. A search was therefore made for an error in the inputs or in the specification of the model which would produce this strange result. A close check of the data revealed no errors, but, the problem was discovered while checking the specification of the model. Table 5-1 provides the following input-output coefficients for the open hearth and BOF processes. Open Hearth BOF Scrap -0.33 -0.12 Pig iron -0.77 -0.95 Steel 1.00 1.00 This shows that the BOF process is the more pig iron intensive of the two processes. Furthermore, table 5-9 reveals that the blast furnaces at Fundidora are fully utilized, and thus they act as a bottleneck on production. For this reason the total cost of production and shipping in the country is minimized by using the relatively less efficient open hearth process to produce a larger amount of steel at Fundidora than would be possible with the use of the BOFs. In fact, BOFS can be charged with a higher percentage of scrap than is used in this particular production activity. HOES can utilize an upper limit A SMALL STATIC MODEL 77 of 30 to 40 percent of the charge as cold metal (scrap) while open hearths can utilize much higher percentages of cold metal charges-even up to 100 percent scrap. This kind of result could thus occur in reality in a steel plant. Two possibilities offered themselves as ways of modifying the small model in the face of this problem. A new BOF activity was introduced with the following input-output coefficients: Old BOF New BOF activity activity Scrap -0.12 -0.25 Pig iron -0.95 - 0.82 Steel 1.00 1.00 One possibility was to add the new activity to the model and the other was to use it to replace the old activity. It was decided to replace the old activity to keep the model as simple as possible. One other change was also made before the model was run again. The natural gas price was increased from $14 per thousand cubic meters (equivalent to 50.40 per thousand cubic feet) to $70 per thousand cubic meters (equivalent to approximately $2 per thousand cubic feet) to make this price closer to the 1979 world market price. The model was then solved again, and the resulting pattern of shipments is shown in table 5-10. A comparison of this solution with the first solution in table 5-8 shows that exactly the same set of shipping activities is employed. Minor changes in magnitude, however, reflect, in part, the fact that more steel can be produced in the system with the new activity since blast furnace capacity at Fundidora is no longer a bottleneck. In addition, the BOFs are now fully utilized at Fundidora, and there is excess capacity in the open hearths. This result is shown in table 5-11. Table 5-10. Shipment Pattern in the Second Linear Programming Solution, with Higher Natural Gas Price and New BOF Activity (million metric tons) Mexico Monter- Guadala- Plant City rey jara Exports Total AHMSA 3.020 0 0.550 0 3.570 Fundidora 0 1.721 0 0 1.721 SICARTSA 0 0 0.540 0.760 1.300 HYLSA 0.430 0.469 0 0 0.899 HYLSAP 0.560 0 0 0 0.560 Total 4.010 2.190 1.090 0.760 8.050 78 MEXICAN CASE STUDY Table 5-11. Slack (Unused) Capacity in the Second Linear Programming Solution (million metric tons) Productive unit AHMSA Fundidora SICARTSA HYLSA HYLSAP Blast furnace 0.398 0 0.034 0 0 Open hearth 0 0.629 0 0 0 BOF 0 0 0 0 0 Direct reduction 0 0 0 0 0.390 Electric arc 0 0 0 0.231 0 Total 0.398 0.629 0.034 0.231 0.390 A third solution to the linear programming was obtained by limiting total exports from the country to be less than 0.2 million metric tons per year. The resulting shipment pattern is shown in table 5-12. A com- parison of total output in tables 5-10 and 5-12 (second and third solutions) shows that all plants except HYLSA produce at the same level as before. With the higher natural gas prices, HYLSA and HYLSAP are more expensive producers than the other three plants. (Of course, this balance might be changed again if higher coke prices were used.) The result is that when SICARTSA cuts back its exports from 0.76 million metric tons in the second solution to 0.20 million tons in the third solution, it uses the remaining 0.56 million tons to drive Altos Hornos out of the Guadalajara market completely. Altos Hornos in turn drives HYLSA out of the Mexico City market and HYLSA suffers a loss in production. As mentioned above, the purpose of this discussion is not to determine the most efficient producer of steel in Mexico but rather to illustrate how a linear programming model is set up, debugged, and used to study the steel industry. In fact, when building large models of an industry that Table 5-12. Shipment Pattern in the Third Linear Programming Solution, with Export Bound, Higher Natural Gas Price, and New BOF Activity (million metric tons) Mexico Monter- Guadala- Plants City rey jara Exports Total AHMSA 3.440 0 0 0 3.440 Fundidora 0 1.721 0 0 1.721 SICARTSA 0.010 0 1.090 0.200 1.300 HYLSA 0 0.469 0 0 0.469 HYLSAP 0.560 0 0 0 0.560 Total 4.010 2.190 1.090 0.200 7.490 A SMALL STATIC MODEL 79 include thousands of constraints and variables, it is useful to begin the study with a small model of this sort. Appendix A contains a table of equivalencies between the mathemati- cal notation and the GAMS notation, and appendix B provides a listing of the GAMS input. Appendix A. Notational Equivalence Inequalities Mathematical GAMS Material balance constraints on final products (5.1) MBF Material balance constraints on intermediate products (5.2) MBI Material balance constraints on raw material (5.3) MBR Capacity constraints (5.4) CC Market requirements (5.5) MR Maximum export (5.5a) ME Variables Mathematical GAMS z Z x X e E V V u U Parameters Mathematical GAMS a A b B k K d D p' PD p" PV pe PE itf MUF 1Ae MUE A MUV 80 MEXICAN CASE STUDY Constraints: Some Examples Math: (5.1) acppi c ij e ceCF PEP jEJ e~ GAMS': MBF(CF, 1).. SUM(P, A(CF, P)*Z(P, I) = G = SUM(J, X(CF, 1, J)) +E(CF, I) Math: (5.2) Y acz > 0 ce CI Pil GAMS: MBI(CI, I).. SUM(P, A(CI, P)*Z(P, 1)) = G = 0 Appendix B. GAMS Statement of the Small Static Model The GAMS statement is divided into nine sections as follows: 1. Sets 2. Parameters 3. Variables 4. Equations 5. Reference map 6. Equation listing (only the first three equations of each type) 7. Column listing (only the first three columns of each type) 8. Matrix generation summary 9. Solution report a. Objective function b. Dual solution c. Primal solution In the primal section of the solution report one can observe that there are constraint rows for capacity units which do not exist, such as direction reduction units at AHMSA (see page 16 of the following GAMS listing). There are also activities for processes that do not exist, such as sponge iron production at SICARTSA (GAMS listing, page 18). These activities cause no harm, but they could be eliminated by model reduction of the kind discussed in Kendrick and Meeraus (1981). In large models it is important to employ model reduction procedures. DAMS 1.0 M E X I C 0 - MINI STEEL MODEL 01/13/83 13.33.48. PADE SET DEFINITIONS 4 SET I STEEL PLANTS / AHMSA ALTOS HORNOS - MONCLOVA NEW MARGIN 002-120 5 FUNDIDORA MONTERREY 6 SICARTSA LAZARO CARDENAS 7 HYLSA MONTERREY 8 HYLSAP PUEBLA 1 0 11 12 J MARKETS / MEXICO-DF, MONTERREY, GUADALAJA / 13 14 C COMMODITIES / PELLETS IRON ORE PELLETS - TONS 15 COKE TONS 16 NAT-GAS NATURAL DAM - 1000 N CUBIC METERS 17 ELECTRIC ELECTRICITY - MWH 18 SCRAP TONS 00 19 PIG-IRON MOLTEN PIG IRON - TONS 20 SPONGE SPONGE IRON - TONS 21 STEEL TONS 22 23 CF(C) FINAL PRODUCTS / STEEL / 24 25 26 CI(C) INTERMEDIATE PRODUCTS / SPONGE, PIG-IRON / 27 28 CR(C) RAM MATERIALS / PELLETS, COKE, NAT-GAS, ELECTRIC, SCRAP / 29 30 P PROCESSES / PIG-IRON PIG IRON PRODUCTION FROM PELLETS 31 SPONGE SPONGE IRON PRODUCTION 32 STEEL-O STEEL PRODUCTION: OPEN HEARTH 33 STEEL-EL STEEL PRODUCTION: ELECTRIC FURNACE 34 STEEL-BOF STEEL PRODUCTION: MOF 35 36 M PRODUCTIVE UNITS / BLAST-FURN BLAST FURNACES 37 OPENEARTH OPEN HEARTH FURNACES 38 BOF BASIC OXYGEN CONVERTERS 39 DIRECT-RED DIRECT REDUCTION UNITS 40 ELEC-ARC ELECTRIC ARC FURNACES 41 GAMS 1.0 M E X I C 0 - MINI STEEL MODEL 01/13/83 13.33.48. PAGE 2 MODEL PARAMETERS 43 TABLE A(C,P) INPUT-OUTPUT COEFFICIENTS 44 45 PIG-IRON SPONGE STEEL-OH STEEL-EL STEEL-BOF 46 47 PELLETS -1.58 -1.38 48 COKE -.63 49 NAT-GAS -.57 50 ELECTRIC -.58 51 SCRAP -.33 -.12 52 PIG-IRON 1.0 -.77 -.95 53 SPONGE 1.0 -1.09 54 STEEL 1.0 1.0 1.0 55 56 57 TABLE B(M,P) CAPACITY UTILIZATION 58 59 PIG-IRON SPONGE STEEL-OS STEEL-EL STEEL-BO 60 61 BLAST-FURN 1.0 62 OPENHEARTH 1.0 63 BOF 1.0 64 DIRECT-RED 1.0 65 ELEC-ARC 1.0 66 67 68 TABLE E(M,I) CAPACITIES OF PRODUCTIVE UNITS (BILL TPY) 69 70 ARMSA FUNDIDORA SICARTSA HYLSA HYLSAP 71 72 BLAST-FURN 3.25 1.40 1.10 73 OPENHEARTH 1.50 .85 74 BOF 2.07 1.50 1.30 75 DIRECT-RED .98 1.00 76 ELEC-ARC 1.13 .56 79 SCALARS DT TOTAL DEMAND FOR FINAL GOODS IN 1979 (MILLION TONS) / 5.209 / 80 RSE RAW STEEL EQUIVALENCE (PERCENT) / 40 81 PARAMETERS D(C,J) DEMAND FOR STEEL IN 1979 (MILL TPY) 82 DD(J) DISTRIBUTION OF DEMAND / MEXTCO-DF 55, MONTERREY 30, GUADALAJA 15 /; 83 84 D("STEEL",J) = ST * (1 + RSE/100) * DD(J)/100; 85 GAMS 1.0 M EX I C I - MINI STEEL MODEL 01/13/83 13.33.48. PAGE 3 MODEL PARAMETERS 87 TADLE RD('.-) RAIL DSTANCEE FROM PLANTS TO MARKETE (EM) 87 89 MEXICO-IF MONTEEREY GUADALAJA EXPORT ?? ANMSA 1204 218 1125 739 92 FUNDIDORA 1017 1030 521 93 ICARTSA 819 1305 704 94 MYLSA 1017 1030 521 95 HYLSAP 183 1085 760 313 96 IMPORT 428 521 200 97 98 99 PARAMETER MP(E,J) TRANSPORT RATE: PENAL PRODUCTS(US$ PER TON) 100 MEN(J) TRANSPORT RATE: IMPORTS (01$ FEE TON) 101 MIE(S) TRANSPORT RATE: EPORTS (US$ PER TON) 102 103 104 MUF(S,J) 2.48 + .0084*RD(I,J)) $RD(1,J); 105 MUV(J) -(2.48 + .0084*RD("IMPORT.,J))$RD("IMPORT",J); 106 MUE(I) C2.48 + .0084*RD(l,EXPORT*))$RDI(I,"EXPORT"); 107 106 109 110 TABLE PRICES(C,*) PRODECT PICES (00$ PEE ENIT) 111 112 DOMESTIC IMPORT EXPORT 113 114 PELLETS 18.7 115 COKE 52.17 116 NAT-GAS 14.0 117 ELECTRIC 24.0 118 SCRAP 105.0 119 STEEL 150. 140. 120 121 122 123 PARAMETERS PD(C) DOMESTIC PRTCES(US$ PER UNIT) 124 PV(C) IMPORT PRICES (UD$ PER ONIT) 125 PE(C) EXPORT PRICES (05$ PER UNIT) 126 E EXPORT NOUNS (MILL TPY) 127 128 PD(C) -RICES(C,"OMEIC); 129 PV(C) - PRICES(C,"IMPORT); 130 PE(C) - PRICES(C,*EXPORT"); 131 ER - 1.0; 132 GAMS 1.0 M E XI C 0 - MINI STEEL MODEL 01/13/83 13.33.48. PAGE 4 MODEL DEFINITION 134 VAREABLES Z(P,I) PROCESS LEVEL (MILL TPY) 135 X(C,I,J) SPMENT OP PENAL PEGDUCTS (NELL T8Y) 1 36 U(C,1) PUECEASE GF DOMEETIC MATERIALS (NELL SMITE PEE TEAR) 137 0(1,J) IOS (NILL TPY) 138 E(C,I) EXPORTS (MILL TPT) 139 PHI TOTAL COST (MILL 88$) 140 PSIPSI SAW MATERIAL COST (NELL US$5 141 PHILAM TEANSPORT COOT (NELL US$) 142 PEEPS EMPOET COST (MILL 00$) 143 PHIEPS EXPORT REVENEE (MILL US$) 144 145 POSITIVE VARIABLES C, X, U, V, E 146 147 EQUATIONS MBF(C,I) MATERIAL BALANCES: PIMAL PRODUCTS (MILL TPY) 148 MB81(C,I) MATERIAL BALANCES: INTERMEIATES (MILL TPT) 109 MBR(C,0) MATERIAL BALANCES; RAWl MATERIALS (MILL T81) 158 CC(M,I) CAPACITY COMSTRAINT (MILL TPY) 1 51 01R(C,J) MAREIET REQIEMENTS (MILL TPT) 152 M0(1) MAIMEN EXPORT (MILL T8Y) 153 0BJ ACCO1INTING: TOTAL COST (MILL US$) 154 API ACCOUNTING: RAW MATEEIAL COST (MELL 88$) 155 ALAM ACCOENTING: TRASPOET COST (NELL US$) 156 APE ACCOENTIEG: IMPOST COST (MILL 81$) 00157 AEPS ACCOENTING: EXPORT CGST (NELL 55$); 158 159 MBF(CF,O). . SUM(P, A(CF,P)*Z(P,I)) =G= SUM(J, XI(CF,E.J)) + E(CF,1); 160 161 MB11(C1,l).. SUM(P, A(CI,P)*l(P,I)) -G- 10 152 153 103 MBR(CSR,E).. SUM1(P, A(CR,P)*Z(P,I)) + U(CR,0) -G= 0 154 TO1 11(M1,).. SUM(P, B(M,P)*C(F,E)) -L- K(M,I); 166 i67 MR(CF,J). . SUM(I, X(18,0,J)) + V(CP,J) =0= D(CP,J); 168 160 NE(CF).. S0UM(1, 0(81) L- EB 170 1ll OBJ.. PHI -E= PHIPSI + PHILAM + PHIPI - PHIPPS 172 1 73 APSI. . PHEPSE =E- EUM((CR,E), PD(CR)*O(CR,I))1 174 175 ALAM.. PHILAM =E= SUM((CF,E,.J), NUF(I,J)*X(CF,I,J)) 17 6 + SUIM((CF,J), MUV(J)*V(C,JE)) 177 + SOM((CF,I) , KUVE(IE 1P,)) 178 170 API.. PI8I -E= SUM((CF,J), PV(CF)*V(1F,J)) 180 1 81 AEPS.. PHIEPS =E SUM((CP,I), PE(CF)*E(CF,I)) 182 183 MODEL MEXSS SMALL STATIC PROBLEM / ALL/ 184 jol SOLVS MCXSS USING LP MINIMIZING PHI CAMS 1.0 M E X I C 0 - MINI STEEL MODEL 01/13/83 13.33.48. PAGE 5 REFERENCE MAP OF VARIABLES VARIABLES TYPE REFERENCES A PARAM REP 159 161 163 DEFINED 43 DCL 43 AEPS EQU DEFINED 181 DCL 157 ALAN EQU DEFINED 175 DCL 155 API EQU DEFINED 179 DCL 156 APSI EQU DEFINED 173 DCL 154 B PARAM REF 165 DEFINED 57 DCL 57 C SET REP 23 26 28 43 81 110 123 124 125 128 129 130 135 136 137 138 147 148 149 151 152 DEFINED 14 CONTROL 128 129 130 DCL 14 CC EQU DEFINED 165 DCL 150 CF SET REP 3*159 3*167 169 175 176 177 2*179 2*181 DEFINED 23 CONTROL 159 167 169 175 176 177 179 181 DCL 23 CI SET RES 161 DEFINED 26 CONTROL 161 DCL 26 CR SET REP 2*163 2*173 DEFINED 28 CONTROL 163 173 DCL 28 D PARAM REF 167 DEFINED 84 DCL 81 DD PARAM REF 84 DEFINED 82 DCL 82 IT PARAM REF 84 DEFINED 79 DCL 79 E VAR REF 145 159 169 177 181 DCL 138 EB PARAM RES 169 DEFINED 131 DCL 126 I SET REF 68 99 101 2*104 2*106 134 135 136 138 147 148 149 150 3*159 161 2*163 2*165 167 169 173 2*175 2*177 181 DEFINED 4 CONTROL 104 106 159 161 163 165 167 169 173 175 177 181 DCL J SET REP 81 82 84 99 100 2*104 2*105 135 137 151 159 3*167 2*175 2*176 179 DEFINED 12 CONTROL 84 104 105 159 167 175 176 179 DCL 12 K PARAM REF 165 DEFINED 68 DCL 68 M SET REF 57 68 150 2*165 DEFINED 36 CONTROL 165 DCL 36 MBF EQU DEFINED 159 DCL 147 MBI EQU DEFINED 161 DCL 148 MBR EQU DEFINED 163 DCL 149 ME EQU DEFINED 169 DCL 152 MEXSS MODEL RES 185 DEFINED 183 DCL 183 MR EQU DEFINED 167 DCL 151 MUE PARAM REP 177 DEFINED 106 DCL 101 MUF PARAM RES 175 DEFINED 104 DCL 99 MUV PARAM RES 176 DEFINED 105 DCL 100 OBJ EQU DEFINED 171 DCL 153 P SET REF 43 57 134 2*159 2*161 2*163 2*165 DEFINED 30 CONTROL 159 161 163 165 DCL 30 PD PARAM REF 173 DEFINED 128 DCL 123 PE PARAM REF 181 DEFINED 130 DCL 125 PHI VAR RES 171 185 DCL 139 PHIPS VAR RES 171 181 DCL 143 PHILAM VAR RES 171 175 DCL 141 PHIPI VAR REP 171 179 DCL 142 PHIPSI VAR RES 171 173 DCL 140 GARS 1.0 M E X I C O - MINI STEEL MODEL 01/13/83 13.33.48. PAGE 6 REFERENCE MAP OF VARIABLES VARIABLES TYPE REFERENCES PRICES PARAM REF 128 129 130 DEFINED 110 DCL 110 PF PARAM REF 179 DEFINED 129 DCL 124 RD PARAM REF 2*104 2*105 2*106 DEFINED 87 DCL 87 RSE PARMS REF 84 DEFINED 80 DCL 80 U VAR REF 145 163 173 DCL 136 VAR REP 145 167 176 179 DCL 137 O VAR REF 145 159 167 175 DCL 135 O VAR REF 145 159 161 163 165 DCL 134 SETS C COMMIIES CF FINAL FRODUCTS CI INTERPLANT CR RAW/MATERIALS I STEEL FLARTS iMARKETS M PRODUCTIVE ENIS F FROCESSES PARAMETERS Go 01A INPUT-OTPT COEFFECIENT B CAPAEITT ETILIZATION D DEMAND FOR STEEL IN 1979 (HELL TPY) DD ISTRIBUTION OF DEMAND DT TOTAL DEMAND FOR FINAL GOODS SN 1979 (MILLION TONS) BE EXPORT BODED (MILL TFY) K CAPACITIRS OFPFRODUCTIVE URITS (MILL TPY) ERR TRANSPORT RATE: EXPORTS (08$ PER TON) MEF TRANSPORT NATE: PENAL FRODUCTS(US$ PER TON) flEE TRANSPORT RATE: IMPORTS (118$ PER TON) pp DOMESTIC PRIES(US$ PER NST) PR EXPORT PRICES (08$ PER UNIT) FRIEES PRODUCT FRICES (118$ PER UNIT) PV IMPORT PRICES (111$ FEE UNIT) RD RAIL DISTANCES PROM PLANTS TO MARKETS (KME) RSE RAW STEEL EQUIVALENCE (FERCENT) VARIABLES E EXPORTS (MILL TPT) FEEl TOTAL COST (MILL 115$) FHIEFS EXPORT REVENUE (MILL 118$) FHILAM TRANSFORT COST (MILL 118$) FHEPI IMPORT COST (MILL 110$) FHIPSI RAW MATERIAL COST (MILL 118$) FEPRCHASE OF DOMESTIC MATERIALS (MELL EXITS FEE TEAR) VIMPORTS (MILL TPY) I HIPMENT OP FINAL FROUCTS (MILL TPY) CAMS 1.0 M E X I C 0 - MINI STEEL MODEL 01/13/83 13.33.48, PAGE 7 REFERENCE MAP OF VARIABLES VARIABLES Z PROCESS LEVEL (MILL TPY) EQUATIONS AEPS ACCOUNTING: EXPORT COST (MILL US$) ALAM ACCOUNTING: TRANSPORT COST (MILL US$) API ACCOUNTING: IMPORT COST (MILL US$) APSI ACCOUNTING: RAW MATERIAL COST (MILL US$) CC CAPACITY CONSTRAINT (MILL TPY) MBF MATERIAL BALANCES: FINAL PRODUCTS (MILL TPY) MBI MATERIAL BALANCES: INTERMEDIATES (MILL TPY) MBR MATERIAL BALANCES: RAW MATERIALS (MILL TPY) ME MAXIMUM EXPORT (MILL TPY) MR MARKET REQUIREMENTS (MILL TPY) OBJ ACCOUNTING: TOTAL COST (MILL US$) MODELS MEXSS SMALL STATIC PROBLEM RSi ni ni n i ni if n i 1i n i i 0 i n i ni ni i H H H tni ti ni n ni i t ni ni i ni t 8 8 W W |¤ - ni nie e ni ni n . ti ni ni ni ni . . r/ niw ni ni -n t o •i ni niv ni ni - - i i ni n -> ni ni • ni niHni ni ni n niNni i ti n N N n ti ni + I ni i t n ni ni i N H t* O H |Ø t ni ni - ni - a N O |o i O O > i ni n i | | M A i 2 I |2; ni ni ni ni O H i i. $ Hn-i ni - n i + t O H N t O pa | th ni i- ni H t | O O M 52 O M m ni ni n t | H i i | M • ni '- ni ci H0 ni nin ni i ni t O !© Þ ;Ø H M | H ni ni ni = + M O 2 j> O C v ni + -' H i - 2 % >ni 2 i i- nI N n o - o io 0 l t ni i- ni + | ni ni ni niS ni ni n t O C v > t/a O •i ni |i |i V SG W t* • i tt > ni n is GAMS 1.0 M E X I CO - MINI STEEL MODEL 01/13/83 13.34.08. PAUE 9 EQUATION LISTING ---- CC =L= CAPACITY CONSTRAINT (MILL TPY) CC(BLAST-FURN,AHMSA).. Z(PIG-IRON,AHMSA) =L= 3.25 ; CC(BLAST-FURN,FUNDIDORA).. Z(PIG-IRON,FUNDIDORA) =L= 1.4 CC(BLAST-FURN,SICARTSA).. ZIPIG-IRON,SICARTSA) =L= 1.1 ; ---- MR -G= MARKET REQUIREMENTS (MILL TPY) MR(STEEL,MEXICO-DF).. X(STEEL,AHMSA,MEXICO-DF) + X(STEEL,FUNDIDORA,MEXICO-DF) + X(STEEL,SICARTSA,MEXICO-DF) + X(STEEL,HYLSA,MEXICO-DF) + X(STEEL,HYLSAP,MEXICO-DF) + V(STEEL,MEXICO-DF) =G= 4.01093 ; MR(STEEL,MONTERREY).. X(STEEL,AHMSA,MONTERREY) + X(STEEL,FUNDIDORA,MONTERREY) + X(STEEL,SICARTSA,MONTERREY) + X(STEEL,HYLSA,MONTERREY) + X(STEEL,HYLSAP,MONTERREY) + V(STEEL,MONTERREY) -G- 2.18778 ; 0o MR(STEEL,GUADALAJA).. X(STEEL,AHMSA,GUADALAJA) + X(STEEL,FUNDIDORA,GUADALAJA) + X(STEEL,SICARTSA,GUADALAJA) + X(STEEL,HYLSA,GUADALAJA) + X(STEEL,HYLSAP,GUADALAJA) + V(STEEL,GUADALAJA) =G= 1.09389 ---- ME -L- MAXIMUM EXPORT (MILL TPY) ME(STEEL).. E(STEEL,AHMSA) + E(STEEL,FUNDIDORA) + E(STEEL,SICARTSA) + E(STEEL,HYLSA) + E(STEEL,HYLSAP) -L= 1 ---- OBJ -E- ACCOUNTING: TOTAL COST (MILL US$) OBJ.. PHI - PHIPSI - PHILAM - PHIPI + PHIEPS -E- 0 ; ---- APSI -E* ACCOUNTING: RAW MATERIAL COST (MILL US$) APSI.. PHIPSI - 18.7*U(PELLETS,AHMSA) - 18.7*u(PELLETS,FUNDIDORA) - 18.7*U(PELLETS,SICARTSA) - 18.7*U(PELLETS,HYLSA) - 18.7*u(PELLETS,HYLSAP) - 52.17*U(COKE,AHMSA) - 52.17*U(COKE,FINDIDORA) - 52.17*U(CORE,SICARTSA) - 52.17*U(COKE,HYLSA) GAMS 1.0 M E X I C 0 - MINI STEEL MODEL 01/13/83 13.34.08. PAGE 10 EQUATION LISTING APSI =E= ACCOUNTING: RAW MATERIAL COST (MILL US$) - 52.17T)(COKE,HYLSAP) - 14*U(NAT-GAS,AHMSA) - 14*U(NAT-GAS,FUNDIDORA) - 14*U(NAT-GAS,SICARTSA) - 14*U(NAT-GAS,HYLSA) - 14*U(NAT-GAS,HYLSAP) - 24*U(ELECTRIC,AHMSA) - 24*U(ELECTRIC,FUNDIDORA) - 24*U(ELECTRIC.SICARTSA) - 24*U(ELECTRIC,HYLSA) - 24*U(ELECTRIC,HYLSAP) - 105*U(SCRAP,AHMSA) - 105*U(SCRAP,FUNDIDORA) - 105*U(SCRAP,SICARTSA) - 105*U(SCRAP,HYLSA) - 105*U(SCRAP,HYLSAP) =E= 0 ; ---- ALAM -E= ACCOUNTING: TRANSPORT COST (MILL US$) ALAM.. PHILAM - 12.5936*X(STEEL,AIMSA,MEXICO-DF) - 4.3112*X(STEEL.AHMSA,MONTERREY) - 11.93*X(STEEL,AHMSA,GUADA-LAJA) - 11.0228*X(STEEL,FUNDIDORA,MEXICO-DF) - 11.132*X(STEEL,FUNDIDORA,GUADALAJA) - 9.3596*X(STEEL,SICARTSA,MEXICO-DF) - 13.442*X(STEEL,SICARTSA,MONTERREY) - 8.3936*X{STEEL,SICARTSA,GUADALAJA) - 11.0228*X(STEEL,HYLSA,MEXICO-DF) 10 - 11.132*X(STEEL,HYLSA,GUADALAJA) - 4.034*X(STEEL,HYLSAP,MEXICO-DF) - 11.594*X(STEEL,HYLSAP,MONTERREY) - 8.864*X(STEEL,HYLSAP,GUADALAJA) - 6.0752*V(STEEL,MEKICO-DF) - 6.8564*V(STEEL,MONTERREY) - 5*V(STEEL,GUADALAJA) - 8.6876*E(STEEL,AIMSA) - 6.8564*E(STEEL,FUNDIDORA) - 6.8564*E(STEEL,HYLSA) - 5.126*E(STEEL,HYLSAP) =E= 0 ---- API =E= ACCOUNTING: IMPORT COST (MILL US$) API.. PHIPI - 150*V(STEEL,MEXICO-DF) - 150*V(STEEL,MONTERREY) - 150*V(STEEL,GUADALAJA) =E= 0 ---- AEPS =E= ACCOUNTING: EXPORT COST (MILL US$) AEPS., PHIEPS - 140*E(STEEL,AHMSA) - 140*E(STEEL,FUNDIDORA) - 140*E(STEEL,SICARTSA) - 140*E(STEEL,HYLSA) - 140*E(STEEL,HYLSAP) -E 0 ; 75 ROWS AND 231 ENTRIES PROCESSED. 22 ROWS AND 128 ENTRIES PRINTED. 《 〉卜卜 魚計魚 Jg嗣 j』悶 芝方蠶 久＇~& 口贓 切口悶 卜→01 0么必O →＇、＇■｀中QH&＇、p ～司《→《口■→X《→H馬→ d裊霄細，霄霄饗蕊望寫8呂焜忠台話認他 Q肥功亡〈的的靨→望→禺么H→I魚Q■禺卜啊→ 雯霄乏荔霄吃望圭至然霄誘乏誘吃悶話翁8認日8必雜8講 開〝《閏之h工《《0。上〝叩悶《蠶〔H OZH閑VH蠶 悶馴Z｀蠶闔《〈〝｀田叩口之口HZ｀罟網自p×卜Hk→口 話二乏呂糁乏配委f卹嬰甲乏吃呈吃乏屆語吃豐日k跑芝他望誘吃 馴丰g江主f自甩華邑莖蠱g丰邑丰豐皂遲丰f話豳C號萬d羹必言 州j闔闕闖O《闐‘叫《唱I曰H。凶〝細闐魚曰闕〝細闐｀卜闐 之H么么。州O。‘之州閑的A的‘卜p曉曰闖的卜j驕臼J的曰 姿法由面日奮甚憂奮萬日居舅蓄奮萬居華羹諾歪邑群歪罷諾丰三鬱蓄去至日 。‘訌尼叩。的t劉叩。中蠶名萬。么的名〔《們叢寫《的萬瀾《O曉蠶叩《《 ，鑒旦可萬可邑齋齋齋奐薔 H么的闖 開個嗡啊 UH悶悶』 閑山斗魚 H偶嘔必闐必視必 k叩叩n怕卜卜鬥訪N叭0 中j Qn『｀鬥頃O州必 二SH了‘HH中’一州”“中H公7一丰丫州伶丫一叩寫 『實，叫 I HN贓闐 豐1 11 O■．1 91 GhH5 1-0 M , X I C 0 - MINI SIEZI, gOnEL 01113183 13.34.08. PAGE 12 COLUMN LISTING E -PL* EXPORTS (MILL TPY) E(STEEL FUNDIDORA) -1. MBF(SýEEL,FUNDIDORA) 1. ME(STEEL) - 6.8564 ALkm -140. AEPS E(STEEL,SICARTSA) -1. MBF(STEEL,SICARTSA) 1. ME(STEEL) -14o. AEPS u *PL- PURCHASE OF DOKESTIC MATERULS (MILL UNITS PFR YEAR) U(PELLETS,AllMSA) 1. MBR(PELLETS,AIIMSA) -18.7 APS T U(COKE,AHMSA) 1. MBR(CDKE,AIIMSA) -52.17 APSI U(NAT-GAS,AHMSA) 1. MBR(NAT-GAS,AFIMSA) -14. APSI v *PL- IMPOKTS (MILL TPY) V(STEEL,MEXICO-DF) 1. MR(STEEL,MEXICO-DF) -6.0752 ALAM ~150. API V(STEEL,MONTF.RREY) 1. MR(STEEL,MONTERREY) -6,8564 ALAR -150. API V(STLLL GUADALAJA) 1. MR(STýFL,GUADALAJA) -5. ALAM -150. API GAMS 1.0 M X I C 0 - MINI STEEL MODEL 01/13/83 13.34.08. PAGE 13 COLUMN LISTING - PHI *FR* TOTAL COST (MILL US$) PHI 1. OBJ 1, OBJ - PHIPSI *FR* RAW MATERIAL COST (MILL US$) PHIPSI -1. OBJ 1. APSI ---- PHILAM *FR* TRANSPORT COST (MILL US$) PHILAM -1. OBJ 1. ALAN ---- PMIPI *FR* IMPORT COST (MILL US$) PHIPI -1. OBJ 1. API --PIlIlEPS *FR* EXPORT REVENUE (MILL USS) PHIESP 1. OBJ 1. AEPS 78 COLS AND 231 ENTRIES PROCESSED. 20 COLS AND 57 ENTRIES PRINTED. GAMS 1.0 M E X I C 0 - MINI STEEL MODEL 01/13/83 13.34.08. PAGE 14 MPS GENERATION MATRIX GENERATION SUMMARY EQUATIONS VARIABLES MPS MATRIX MPS BASIS TYPE NUMBER TYPE NUMBER SECTION NUMBER STATUS ROWS COLUMNS FREE 1 FREE 5 ROWS 75 LOWER 0 78 EQUAL 5 POSITIVE 73 COLUMNS 231 UPPER 0 0 GREATER 43 NEGATIVE 0 RHS 16 BASIC 75 0 LESS 26 FIXED 0 BOUNDS 5 USED 0 0 RANGED 0 BINARY 0 RANGES 0 TOTAL 75 INTEGER 0 TOTAL 327 TOTAL 78 FIELD LENGTH OR WORKSPACE REQUESTED 16758 0405668 MAXIMUM FIELDLENGTH - 130560 377000B WORK OPTION REQUESTED 0 00000 SAMS 1.0 ME X I C O - MINI STEEL MODEL 01/13/83 13.34.21. PAGE 15 SOLUTION REPORT A P EX - I C 0 N T R 0 L P R 0 R A M APEX-I 1.014 FIELD LENGTH 040600 OCTAL EQUATIONS VARIABLES NON-ZEROS MISC.TOTALS TYPE NUMBER NAME NUMBER NAME NUMBER EQ (E) 5 COLUMNS 78 AIJS (COL) 231 MINOR ERRORS 0 LI (L) 26 RHS I AIJS (RHS) 16 DENSITY 0/0 3.949 GE (G) 43 TOTAL 79 TOTAL 247 UNIQUE VALUES 51 FR (N) 1 MIN FL(8) 035000 AVER NZ/CO 2.96 INDIRECT NAMES B TOTAL 75 REC FL(8) 035000 AVER NZ/RO 3.08 TOTAL VALUES 51 * COUNT OF PRIMAL INFEASIBILITY 0 * COUNT OF MAJOR ITERATIONS 48 * COUNT OF MINOR ITERATIONS : 100 .**** TERMINATION STATUS I OPTIMAL SOLUTION TOTAL UTILIZATION .590 * VALUE OF OBJECTIVE FUNCTION = 538.81 ---- MBF MATERIAL BALANCES: FINAL PRODUCTS (MILL TPY) RHS LOWER ROW ACTIVITY RHS UPPER MARGINAL STEEL .AHMSA . . +INF -136.46360 GE STEEL .FUNDIDORA . . +INF -138.03440 GE STEEL .SICARTSA . . +INF -140.00000 GE STEEL .HYLSA . . +INF -138.03440 GE STEEL .HYLSAP , . +INF -145.02320 GE ---- MBI MATERIAL BALANCES: INTERMEDIATES (MILL TPY) RHS LOWER ROW ACTIVITY RHS UPPER MARGINAL PIG-IRON .AHMSA . . +INF -62.41310 GE SPONGE .AHMSA . . +INF -33.78600 GE PIG-IRON .FUNDIDORA . . +INF -132.03621 GE SPONGE .FUNDIDORA . . +INF -33.78600 GE PIG-IRON .SICARTSA , . +INF -134.10526 GE SPONGE .5ICARTSA . . +INF -33.78600 GE PIG-IRON .HYLSA . . +INF -62.41310 GE SPONGE .HYLSA . . +INF -113.86642 GE PIG-IRON .HYLSAP , . +INF -62.41310 GE SPONGE .HYLSAP . . +INF -33.78600 GE CAMS 1.0 M E X I C 0 - MINI STEEL MODEL 01/13/83 13.34.21. PAGE 16 SOLUTION REPORT ---- MBR MATERIAL BALANCES: RAW MATERIALS (MILL TPY) RHS LOWER ROW ACTIVITY RHS UPPER MARGINAL PELLETS .AHMSA . . +INF -18.70000 GE COKE .AHMSA . . +INF -52.17000 GE NAT-GAS .AHMSA . . +INF -14.00000 GE ELECTRIC .AHMSA . . +INF -24.00000 GE SCRAP .AHMSA . . +INF -105.00000 GE PELLETS .FUNDIDORA . . +INF -18.70000 GE COKE .FUNDIDORA . . +INF -52.17000 GE NAT-GAS .FUNDIDORA . . +INF -14.00000 GE ELECTRIC .FUNDIDORA . . +INF -24.00000 CE SCRAP .FUNDIDORA . . +INF -105.00000 GE PELLETS SICARTSA * . +1MF -I.70000 GE COKE .SICARTSA . . +INF -52.17000 GE NAT-GAS .SICARTSA . . +INF -14.00000 GE ELECTRIC .SICARTSA * * +INF -24.00000 GE SCRAP .SICARTSA . . +INF -105.00000 GE PELLETS .IYLSA . . +INF -18.70000 GE COKE .HYLSA . . +INF -52.17000 GE NAT-GAS .HYLSA * . +INF -14.00000 GE ELECTRIC HYLSA . . +INF -24.00000 GE SCRAP HYLSA . . +INF -105.00000 GE 01 PELLETS .HYLSAP . . +INF -18.70000 GE COKE .HYLSAP * * +INF -52.17000 GE NAT-GAS .HYLSAP . . +INF -14.00000 GE ELECTRIC .HYLSAP . . +INF -24.00000 GE SCRAP .HYLSAP . . +INF -105.00000 GE ---- CC CAPACITY CONSTRAINT (MILL TPY) RHS LOWER ROW ACTIVITY RHS UPPER MARGINAL BLAST-FURN.AHMSA -INF 3.12150 3.25000 . BLE OPENHEARTH.AHMSA -INF 1.50000 1.50000 53.75551 LE BOP ARMSA -INF 2.07000 2.07000 64.57116 LI DIRECT-RED.AHMSA -INF . . . BLE ELEC-ARC .AHMSA -INF . . 85.71686 LE BLAST-FURN.FUNDIDORA -INF 1.40000 1.40000 69.62311 LE OPENHEARTH.FUNDIDORA -INF .85000 .85000 1.71652 LE BOF .FUNDIOORA -INF .76474 1.50000 . BLE DIRECT-RED.FUNDIDORA -INF . . . BLE ELEC-ARC .FUNDIDORA -INF . 87.28766 LE BLAST-FURN.SICARTSA -INF 1.10000 1.10000 71.69216 LE OPENHEARTH.SICARTSA -INF . . 2.08895 LE BOF .SICARTSA -INP 1.15789 1.30000 . BLE DIRECT-RED.SICARTSA -INF . . . BLE ELEC-ARC .SICARTSA -INF . . 89.25326 LE BLAST-FURN.HYLSA -INF . . . BLE CAMS 1.0 M E XI C S - MINI STEEL MODEL 01/13/83 13.34.21. PAGE 17 SOLUTION REPORT CC CAPACITY CONSTRAINT (MILL TPY) RHS LOWER ROW ACTIVITY RHS UPPER MARGINAL OPENHEARTH.HYLSA -INF . . 55.32631 LE BOF .HYLSA -INF . . 66.14196 LE DIRECT-RED.HYLSA -INF .98000 .98000 80.08042 LE ELEC-ARC .HYLSA -INF .89908 1.13000 . BLE BLAST-FURN.HYLSAP -INF * . L OPENHEARTH.HYLSAP -INF . . 62.31511 LE BOF .HYLSAP -INF . . 73.13076 LE DIRECT-RED.HYLSAP -INF .61040 1.00000 . BLE ELEC-ARC .HYLSAP -IMF .56000 .56000 94.27646 LE ---- MR MARKET REQUIREMENTS (MILL TPY) RHS LOWER ROW ACTIVITY RKS UPPER MARGINAL STEEL MEXICO-DF 4.01093 4.01093 +INF -149.05720 GE STEEL .MONTERREY 2.18778 2.18778 +INF -138.03440 GE STEEL .GUADALAJA 1.09389 1.09389 +INF -148.39360 GE ---- ME MAXIMUM EXPORT (MILL TPY) RHS LOWER ROW ACTIVITY RHS UPPER MARGINAL STEEL -INF .52911 1.00000 . BLE RHS LOWER ROW ACTIVITY RHS UPPER MARGINAL 0N B . -1.00000 EQ ACCOUNTING: TOTAL COOT --- APSI . * . -1.00000 EQ ACCOUNTING: RAW MATERIAL COST ---- ALAM . -1.00000 EQ ACCOUNTING: TRANSPORT COST ---- API * . . -.95596 EQ ACCOUNTING: IMPORT COST ---- AEPS . . 1.00000 EQ ACCOUNTING: EXPORT COST z PROCESS LEVEL (MILL TPY) COL LOWER COL ACTIVITY COL UPPER MARGINAL PIG-IRON .AHMSA . 3.12150 +1NF . BPL SPONGE .AHMSA * . +INF . BPL STEEL-ON .AMSA * 1.50000 +INF . BPL STEEL-EL .AMSA . . +EMPBPL STEEL-BOF .AHMSA . 2.07000 +INF . BPL PIG-IRON .FUNDIDORA . 1.40000 +INF . BPL SPONGE FUNDIDORA . +INF B OPL 0S 0i >-0 O00000000000O0O H O ±+-O-++++++++-+O - 2.0 tri Ou O in .0 oo . Ou. . 0 .4 - 00 00 00 00 00 0 . o 0 .0 o t 0 -~++++ ++++ ++++ +++ 00 oA -A 0 3 00 0'O 0 0A 1 . - - 0. o ' .4 - 00000 A A0r , - .4 I 0 0000 0.98 GAMSE 1.0 M X I C 0 - MINI STEEL MODEL 01/13/83 13.34.21. PAGE 19 SOLUTION REPORT E EXPORTS (MILL TPY) COL LOWER COL ACTIVITY COL UPPER MARGINAL STEEL .AHMSA . . +INF 5.15120 PL STEEL .FUNDIDORA . . +INF 4.89080 PL STEEL SICARTSA . .52911 +INF . BPL STEEL .HYLSA . . +INF 4.89080 PL STEEL .HYLSAP . , +INF 10.14920 PL U PURCHASE OF DOMESTIC MATERIALS (MILL UNITS PER YEAR) COL LOWER COL ACTIVITY COL UPPER MARGINAL PELLETS .AHMSA . 4.93197 +INF . BPL COKE .AHMSA . 1.96655 +INF . SPL NAT-GAS .AHMSA , . +INF . BPL ELECTRIC .AHMSA . . PI . BFL SCRAP .AHMSA . .74340 +INF . BPL PELLETS .FUNDIDORA . 2.21200 +INF . BPL COKE .FUNDIDORA . .88200 +INF . BPL NAT-GAS .FUNDIDORA . . PI . BPL ELECTRIC .FUNDIDORA . . +INF . BPL SCRAP .FUNDIDORA . .37467 +INF . BPL PELLETS .SICARTSA . 1.73800 +INF . BPL COKE .SICARTSA , .69300 +INF . BPL NAT-GAS .SICARTSA . . +INF . BPL ELECTRIC SICARTSA . . PI . EEL SCRAP SICARTSA . .13895 +INF . EEL PELLETS .HYLSA . 1.35240 +INF . BPI COKE .HYLSA . . PI . BPL NAT-GAS .HYLSA .55860 +INF . BPL ELECTRIC .HYLSA . .52147 +INF . BPL SCRAP .HYLSA . . +INF . BPL PELLETS .HYLSAP . .84235 +INF . BPL COKE .HYLSAP . . LN . BPL NAT-GAS .HYLSAP . .34793 +INF . BPL ELECTRIC .HYLSAP . .32480 +INF . BPL SCRAP .HYLSAP . . +1NF . BPL GAS 1.0 M E X I C 0 - MINI STEEL MODEL 01/13/83 13.34.21. PAGE 20 SOLUTION REPORT V IMPORTS (MILL TPY) COL LOWER COL ACTIVITY COL UPPER MARGINAL STEEL .MEXICO-DF . . +INF .41160 PL STEEL MONTERE . lINP 12.21560 PL STEEL .GUADALAJA . ISP . BPL COL LOWER COL ACTIVITY COL UPPER MARGINAL --- PHIE -INF 53.0752 +9F . SFR TOTAL TOOT ---PHISU -INF 556.88558 +SNPF BFR RAN MAERIAL GOST ---PHILAM -IEP 56.00160 +INF BFEP TRANSPORT GOU T ---PRII -INF +IEP BF SUMSPORT GOAT ---PHIEPS -USE 74 .058 +INF BF SUXRPORT REVENUE 6 A Large Static Model ALTHOUGH A SMALL MODEL like the one described in the previous chapter may provide many insights, it may be asked whether those insights are robust to increases in the detail of the model. One way to check this is to construct a larger, more disaggregated model and use the results of the small model to guide the disaggregation into more plant sites, markets, productive units, productive processes, and commodities. More com- plete disaggregation is done in areas of interest indicated by the economics of the small model. Of course, it is not always true that more disaggregated models provide better solutions. In particular, if the disaggregated model has lower-quality data, it may produce inferior results. For the case at hand, however, the disaggregated data is of high quality. The description of the model in this chapter is divided into sections on sets, variables, constraints, the objective function, and parameters. This is followed by a section on the size of the model. The results are presented in chapter 7. Sets The sets considered here are basically the same as for the small model, except that more subsets are used. Of the five primary sets used in the small model-plants, markets, productive units, processes, and com- modities-only the markets are not separated into several subsets. 101 102 MEXICAN CASE STUDY Plants In the small model (also called the minimodel), the only plants were steel mills. That model is expanded here to include iron ore and coal mines. Furthermore, a separate set is added for the pelletizing plants near three of the iron ore mines and a coking plant near some of the coal mines. Thus, the set of plants is now organized into three subsets as follows: (6.1) I = IM u IR u IS where I all plants and mines IM = iron ore mines and coal mines IR = raw material processing plants IS = steel mills. The first subset of plants is the iron ore mines and coal mines, IM. The principal iron ore mines are shown on map 3. The older mines are in the north: La Perla near Camargo in Chihuahua, Hercules near Sierra Jojada in Coahuila, and Cerro de Mercado in Durango. The newer mines are on the Pacific coast west and south of Mexico City. The largest group, near Colima on the border of the states of Colima and Jalisco, includes two pelletizing plants at Alzada and at Pefia Colorado. The mine at Las Truchas is only a few kilometers from SICARTSA, the new steel mill at Lazaro Cardenas. As map 4 shows, the major mines that provide coking coals are in a small area northwest of Monterrey, where there are a number of mines and a coking plant near the town of Sabinas in Coahuila. The map also shows the large natural gas fields near Reynosa in the north and near Coatzacoalcos in the south. Though the location of these gas fields is not explicitly used in this model, it is used implicitly in the small dynamic version of the model. In summary, then, the set of iron ore and coal mines used in this version of the model is IM = iron ore and coal mines = {Peila Colorado, Las Truchas, La Perla, Cerro de Mercado, Hercules, La Chula, El Violin, El Encino, Coahuila coal mines}. The next subset of plants is the pelletizing plants and coking furnaces located at mines rather than at steel mills. These are called raw material processing plants. The pelletizing plants are at Pefia Colorado and I NITID rTiI F \\1 ER k G u 1.1 Gulf - i] 4ex ico SE iTN MI\P3 - Iron re Mines - 53 ron ire miueý f Pelletizimg Ldri, n,ut al steel mil Pac ifc Ocean Internatinal b,undaries 103 u - 1 t N E 1 IT ED STATES --- .- AF AME IR C YiJI IurrKN~ -28'- Ii 1-i - 0 xHUIL x k.n.r,GuI of 24° 24- Mext co X3 M\ \ft- (¯1 TN MAP 4 MEXICO Coal Mines and Natural Gas Fields "3 Coa mines £ Nauural gas fietds Coahuila cal region Paeific Ocean - -- nternational boundane < .)u su UL 8' KaMryler. 1< tA10 2(x9 35- Måe. 104 i E' - I rn -R -28° Gul NN -2-I MAPf E4 \I I C yrr Al-\,,' .I Sicel .ij an Naret strcýý mill -I--\ie MI.\ P Steel Milils and Miarkets !~in the Lar2e Static Model--- * Steel m,IL * Stel markeis - - JIeJriaJl NhcunJjnc% Pacific Ocean -1-li:. ' M 105 106 MEXICAN CASE STUDY Alzada west of Mexico City and at La Perla in the north near Camargo, Chihuahua; the coking furnaces are near the coal mines in the north at Las Esperanzas (see map 4). The set is IR = raw material plants = {Pefia Colorado, La Perla, Alzada, Las Esperanzasl. Next is the set IS of steel mills. In the minimodel this set had five of the six existing integrated plants. Here we add the sixth integrated plant, TAMSA, the seamless pipe mill at Veracruz (see map 5). The set of steel mills shown in that figure is IS = steel mills = {SICARTSA, AHMSA, Fundidora, HYLSA, HYLSAP, TAMSAJ. As indicated in the discussion of the minimodel, in 1979 three of the existing plants were owned by the government (SICARTSA, AHMSA, and Fundidora) and three were privately owned (HYLSA, HYLSAP, and TAMSA). The new SICARTSA plant at Lazaro Cardenas is near iron ore deposits and at a good port. The AHMSA and Fundidora plants are at Monclova and Monterrey, respectively, near the iron ore and coal deposits in the north of Mexico. All three of the government-owned plants use blast furnaces and basic oxygen furnaces to produce steel. In contrast, the privately owned companies use direct reduction of ores with natural gas to produce sponge iron and then produce steel from the sponge iron in electric arc furnaces. Domestic Markets The next set to be considered is the set J of domestic market areas. In the minimodel this set included the three largest cities in Mexico (Mexico City, Guadalajara, and Monterrey); now it is expanded to include five additional cities: Quer6taro and Puebla near Mexico City; San Luis Potosi near Guadalajara; Uzaro Cdrdenas near the SICARTSA steel mill, to include the possibility of a substantial market at this port; and Coatzacoalcos, to pick up the regional demand for pipe and other steel products which the oil and gas boom is causing (see map 5). In summary, the set is J = domestic market areas = (Mexico City, Puebla, Queretaro, San Luis Potosi, Monterrey, Guadalajara, Lhzaro Chrdenas, Coatza- coalcos}. A LARGE STATIC MODEL 107 Export Markets In addition to domestic market areas, it is useful to represent export markets in the model. Because of transport costs, two separate export directions are considered, one via the Gulf coast and the other via the Pacific coast. Thus a new major set L is created: L= export markets = (Gulf, Pacific}. The set is not directly used in the algebraic statement of the model, but the distance from each plant to a port is given as the shorter of the distances to export points for these two markets. Productive Units The set of productive units M is disaggregated in this model into three subsets: productive units at the mines (MM), at the raw material plants (MR), and at the steel mills (MS). Relative to the minimodel a substantial disaggregation is made. The minimodel included five productive units Table 6-1. Subsets of Productive Units in the Large Static Model Productive units in mines (MM) Productive units in steel mills (contd) Mining equipment for coal mines Continuous casting unit tot billets Mining equipment for iron ore mines: Ingot casting trucks and crushers Primary mill and soaking pits: flat Magnetic concentrator products Flotation concentrator Primary mill and soaking pits: nonflat Productive units in raw material products processing plants (MR) Plate mills Pellet plants Hot strip mills Coke oven and by-product units Pickling lines Productive units in steel mills (MS) Cold strip mills Pellet plants Annealing units Sinter plants Temper mills Coke ovens and by-product units Tinning lines Blast furnaces Billet mills Direct reduction units Heavy shapes mills Open hearth furnaces integrated bar mills Basic oxygen converters Integrated wire mills Electric arc furnaces Seamless pipe mills Continuous casting unit for slabs 108 MEXICAN CASE STUDY that cover the range of processes from pig iron production to liquid steel production. The present model does not add productive units within this range of processes but rather extends the range from iron ore and coal mining to the production of final products such as hot and cold sheet, bar, and wire. The result is a model with four productive units in the mines, two in the raw material plants, and twenty-six in the steel mills (see table 6-1). Processes The next group of sets is of production processes. Since alternative processes for producing commodities are frequently used in a given productive unit, models of this type usually have more processes than productive units. The present model is no exception to this rule. There are thirty productive units and fifty processes. Most of the alternative processes are in the mining and concentration of different kinds of ore and in the production of pig iron and steel with different mixes of inputs. The complete set of processes is listed in table 6-2. They may be divided into three groups: processes at mines, raw material processing plants, and steel mills. Two characteristics of the iron ores in Mexico are captured in the manner in which the mining and concentration processes are con- structed.' First, the ores in the north consist of roughly 25 percent magnetite ores and 75 percent hematite ores, while those in the south have the reverse of this concentration. This is an important difference because magnetite ores can be separated by magnetic means while hematite ores must be separated by flotation. The yield of concentrated ore is about 10 percent greater from magnetic separation than from flotation. A second characteristic considered here is the percentage of iron in the ore. The content is about 5 percent lower in the ore from Las Truchas than that from the other mines. The result of these two characteristics is that mining activities are separated into (1) mining in the north, (2) mining in the south (except at Las Truchas), and (3) mining at Las Truchas. It is necessary to use only two activities for magnetic and flotation concentration, however, since the yield of the northern and southern ores (except Las Truchas) is roughly the same. Among the activities for ore preparation and coke production only the two for coke production require any special discussion. The AHMSA and 1. We are indebted to Alejandro Reyes of SIDERMEX for suggesting this specification of mining and concentration activities. A LARGE STATIC MODEL 109 Table 6-2. Subsets of Production Processes in the Large Static Model Processes at mines (PM) Processes at steel mills (PS) (contd) Mining unwashed coal Steel production in BOFS with high pig Washing coal iron charge Mining in northern mines Steel production in BOFS with high scrap Mining in southern mines charge Mining at Las Truchas Steel production in electric furnace with Concentration of northern ores high sponge iron charge Concentration of southern ores Steel production in electric tutnace with Concentration of Las Truchas ores high scrap charge Processes at raw material processing plants Slabs production by continuous casting (PR) Billet production by continuous casting Pellet production with concentrated ore Ingot casting Coke production with domestic coal Slab production by rolling Processes at steel mills (PS) Rolling of blooms from ingots Pellet production using concentrated ore Billet production by rolling blooms Sinter production Coke production with domestic coal P le production Coke production with high input of Pocled coil production imported coal Ckled coil production Pig iron production with lump ore Annealed coil production Pig iron production with high sinter Tempered coil production charge Tin production Pig iron production with high pellets Rolling of heavy shapes charge Pig iron production with coke from imported coal Roughing mill for nonflat products Sponge iron production Rolling of bars Rolling of large-diameter reinforcing Steel production in open hearths with rods and bars high pig iron Rolling of small-diameter reinforcing Steel production in open hearths with rods and bars high scrap charge Rolling of wire rods Steel production in open hearths with Rolling of seamless pipes highest scrap charge Fundidora plants near the coal mines in the northern part of Mexico use only domestic coal. In contrast, the SICARTSA plant on the Pacific coast uses imported coal for coke production. In fact, coke is frequently produced from a mix of several types of coal, some domestic and some imported. Furthermore, the mix of inputs changes as the relative prices and availability of different types of coal change. This model captures only a small part of this complexity by using the two different activities for producing coke. 110 MEXICAN CASE STUDY The model includes six different activities for pig iron production and only one for sponge iron production. The explanation is that the national steel company, SIDERMEX, which owned all three of the plants using blast furnaces, was more actively involved in this study at an early stage than were the private companies which owned the plants using sponge iron production methods. Two of the six alternative activities for pig iron production reflect experimental efforts to use different mixes of sponge iron and sinter to produce pig iron at AHMSA. The other four activities reflect different mixes of lump ore, sinter, and pellets in the metal charge and different types of coke. Not all of these activities are used in the model at each plant. For example, AHMSA has a sinter plant but the other steel mills do not, so the activity for pig iron production using sinter as a part of the charge is included at AHMSA but not at SICARTSA or Fundidora. This will become clearer later when the production activity matrices are displayed. The production activities for steel may be divided into three groups according to the type of furnace used: open hearths, basic oxygen furnaces (BoFs), and electric arc furnaces. For each type of furnace there are two or three alternative activities reflecting different percentages of scrap in the charge. The open hearths and electric arc furnaces can operate efficiently with a wider variation in the percentage of scrap in the total metal charge than can the BOFS. A large group of activities in steel production are those for ingot casting and alternatively for slab and billet production by continuous casting methods. AHMSA, Fundidora, and HYLSA still use ingot casting, but this method is increasingly giving way to continuous casting both within these plants and in the newer plants, which use continuous casting exclusively. Among the rolling activities, the first three are used in plants that do ingot casting. Either slabs or blooms can be rolled from ingots and the blooms can in turn be rolled into billets. The rest of the flat product rolling activities may be thought of as a continuous stream of activities with various products leaving the stream along the way: slabs to hot rolled coils to cold rolled coils to tin. The rolling of shapes is rather more complicated. There is a profusion of different mills for rolling shapes. For large structural shapes, blooms are rolled into heavy shapes. For lighter shapes, billets are used as the input to the rolling processes. At SICARTSA billets are the input to different rolling mills to produce either large-diameter or small-diameter reinforc- ing rods and bars. At the HYLSA plant in Puebla bar and wire rolling mills A LARGE STATIC MODEL III also use billets as the input, and at TAMSA in Veracruz there is a mill used for rolling seamless pipe. Commodities The last major set to be considered is commodities. Although there were only eight commodities with three subsets (raw material, in- termediate products, and final products) in the small model, there are fifty commodities with eleven subsets in this more disaggregated static model. Furthermore, the subset of commodities in the small model provided a partition of the set (each commodity in one and only one subset), but the subsets in this larger model do not provide a partition. The set of commodities used in steel mills is the most comprehensive. These commodities are listed in table 6-3 with raw material first, intermediate products in the middle, and final products near the end. Table 6-3. Sets of All Commodities (CS) Used at Steel Mills Iron ore from the north, high in sulphur Liquid steel and phosphorus, 59 percent iron Ingot steel Iron ore from the south, no phosphorus, Slabs 60 percent iron Plates Iron ore from Las Truchas, no Hot strip and sheet phosphorus, 55 percent iron Pickled strip and sheet Iron ore, concentrated Cold strip and sheet Pellets Annealed strip and sheet Sinter Tempered strip and sheet Coal, raw unwashed Tin Coal, washed domestic Blooms Coal, imported Billets Coke produced with domestic coal Heavy shapes Coke produced with imported coal Light shapes Fuel oil Bars Limestone Large-diameter reinforcing rods Pig iron (hot metal) Small-diameter reinforcing rods Natural gas Wire rods Sponge iron Seamless pipes Steel scrap Electricity Ferroalloys Water Refractories Dolomite Rails Lime Steel blooms for seamless pipes Electrodes 112 MEXICAN CASE STUDY However, this is only a rough breakdown. For example, hot strip and sheet is both a final product that can be shipped to markets and an intermediate product used to produce another intermediate product, pickled strip. For this reason, a subset of intermediate products is defined, not explicitly, but rather implicitly by the input-output matrices. There are several new subsets in table 6-4 that did not appear in the small model. The first of these, CRAW is the subset of raw material used in the plants. The next two subsets, CM and CR, commodities at the mines and at the raw material processing plants, are defined to complement the set of production processes at these sites. A relatively small subset, CRV, includes raw material and intermediate products that are likely to be imported. The next four sets are all for shipments of intermediate material: from mines to raw material processing plants (CMR), from Table 6-4. Subsets of Commodities in the Large Static Model CRAW= domestic raw material = fuel oil, limestone, natural gas, scrap, ferroalloys, refractories, dolomite, lime, electrodes, water, electricity} CM = commodities at mines = {iron ore from the north, iron ore from the south, iron ore from Las Truchas, raw unwashed coal, domestic washed coal, concentrated iron ore} CR = commodities at raw material processing plants = {iron ore from the north, iron ore from the south, iron ore from Las Truchas, raw unwashed coal, domestic washed coal, concentrated iron ore, pellets, coke produced with domestic ores, electricity} CRV = imported raw material and intermediate products = {imported coal, pellets, steel scrap, cokel CMR = commodities shipped from mines to raw material sites = {concentrated iron ore, washed domestic coal} CMS =commodities shipped from mines to steel plants = {iron ore from the north, iron ore from the south, iron ore from Las Truchas, concentrated iron ore, washed domestic coal} CRS = commodities shipped from raw material sites to steel mills = (pellets, coke produced with domestic coal} CSS = commodities for interplant shipment between steel mills = {sponge iron, pellets, coke produced with domestic coal} CF = final products = lplate, hot strip and sheet, tempered strip and sheet, tin, heavy shapes, light shapes, bars, large-diameter reinforcing rods, small-diameter reinforcing rods, wire rod, seamless pipe, rails) CE = commodities for export = CF CFV = imported final products =CF A LARGE STATIC MODEL 113 mines to steel mills (CMS), from raw material processing plants to steel mills (CRS), and from steel mills to steel mills (CSS). The subset of final products, CF, can be divided into two groups: flat and nonflat products. Flat products include plate, hot sheet and strip, tempered sheet and strip, and tin. Nonflat products include shapes such as I beams and angles which are included in CF as heavy shapes and light shapes, depending on size. Next among nonflat products come bars, reinforcing rods and wire rods, and special shapes such as seamless pipe and rails. Two other subsets specified in table 6-4 are exported commodities and imports of final products. For the present version of the model, exports are restricted to final products only. For other versions, it might be useful to permit the export of selected intermediate products, perhaps those in the subsets of commodities which can be shipped between plants. Three subsets are used to specify ownership constraints. These constraints arise because two of the pellet plants are owned by consortia of the plants, and fixed percentages of the capacity of these plants are assigned to each set of owners. These relationships are specified in the model with the following three subsets: 0 = owner numbers = {1, 2, 3, 4, 5} O WN = owner groups = (1 (SICARTSA), 2 (AHMSA), 3 (Fundidora), 4 (1HYLSA, HYLSAP), 5 (TAMSA) } ISEX = companies excluded from shipments from Alzada = (SICARTSA, AHMSA, Fundidora, TAMSAJ Because of an error in typing, the HYLSA name read "-HyLs" in the owner groups of the GAMS input, which thus permitted shipment of pellets from Pefla Colorado to HYLSAP but not to HYLSA. When the error was discovered the base solution was recomputed with the correction. Only one minor change in raw material flows occurred, however, and this was not deemed large enough to merit resolving all the runs. The domain-checking procedures added to the GAMS language after the solutions of this model would have caught this error. This is yet another argument for the use of modeling languages in general and in particular for the implementation of domain-checking capabilities in those lan- guages. For example, in the present case the modeling language would have given an error message to indicate that HYLS was being used in the set of plants when it had not been included in the original set at the top of the GAMS listing. 114 MEXICAN CASE STUDY The GAMS listing at the end of the chapter shows the corrected input. If one wishes to replicate the solution reported in the next chapter, the spelling OfHYLSA in line 310 of the GAMs input should be changed to HYLS. A large part of the total modeling effort must be devoted to set specification. In fact, the choice of sets and elements ofthe sets are the key decisions in determining the usefulness of the model. A model should be disaggregated enough to capture the central economic problems of the industry and aggregated enough to permit a relatively quick and cheap solution. Once the sets are selected the next step is to choose the variables. Variables The principal variables for this model are the same as for the small model: z process levels (production levels) x = shipments u domestic purchases e= exports v = imports. Superscripts are added to some of these basic variables, however, to specialize them for use in this more disaggregated model. For example, the process levels are now specified as: z' = process levels in mines Z = process levels at raw material preparation plants z' = process levels at steel mills. In addition, the shipment activities are separated into four groups: x- = shipments of intermediate products from mines Xr = shipments of intermediate products from raw material preparation plants x8 = shipments of intermediate products between steel mills xf = shipments of final products. Similarly, domestic purchases are separated into two groups: ur = purchases of domestic products at raw material plants us = purchases of domestic products at steel mills. Exports are in one group of products, but imports are separated into two A LARGE STATIC MODEL 115 groups to allow imports of intermediate as well as final products: e = exports vs = imports of raw material and intermediate products to steel mills V = imports of final products to markets Finally, there is a group of variables used to define total cost and its various components: total cost less domestic by-product revenues and export revenues = cost groups = recurrent cost = transport cost = import cost = export revenues. Constraints The constraints for the model are divided into five principal groups: material balance constraints, capacity constraints, market requirement constraints, export bounds, and ownership constraints. Basically, these five sets of constraints require that (1) no more material can be used than is purchased or produced, (2) production cannot exceed capacity, (3) market requirements must be met, (4) export upper bounds cannot be exceeded, and (5) ownership constraints on pellet shipments cannot be violated. The detailed specification of the constraints follows. MATERIAL BALANCE CONSTRAINTS FOR MINES (6.1) a'z" z xz'. + x" . ce CM pePM 'eIR ceCMR 'eIS cECMS zEIM Shipment of Use of ores and intermediate prod- Shipments of inter- output of inter- ucts from mine i mediate products mediate products - to raw material from mine i to at mine i preparation plants steel mills i'elS i I'elR L This constraint requires that the ores which are mined must exceed their use in the concentration process and that the concentrated ores produced at each mine must exceed the shipment of those ores to raw 116 MEXICAN CASE STUDY material plants and to steel mills. It also requires that coal production and usage be balanced. The notation of the type ceCMR is unusual and deserves comment. Consider the simpler case of the use of the variable xc,, to represent the shipment of commodity c from plant i to marketj. It may be desirable to restrict the model so that only a subset of commodities (say, CS) can be shipped from itoj while the equation holds for all intermediate commodities CI. This could be written then as xes; ceCI For example, both coke and hot metal (molten pig iron) might be intermediate products in the set CI. Hot metal cannot be shipped since it will cool, but coke can be; therefore the shipment activity will be restricted to the subset of commodities CS, which includes coke but not hot metal. Now consider the particular case at hand, the variable xceCM ciCMR. The set CM contains ores, but the pellet plants in the set IR use only concentrate and not lump ore. The shipments from the mines to raw material plants should therefore be only for the commodities that can be supplied by the mines and used by the raw material plants. In this case, it is the set CMR (concentrated iron ore and washed domestic coal) that can be shipped from mines to raw material plants. This undoubtedly seems like a very elaborate notational procedure, but its use can greatly reduce the number of variables in the model through the simple device of proper set specification. MATERIAL BALANCE CONSTRAINTS FOR RAW MATERIAL PROCESSING PLANTS (6.2) a-Pz'1 y+ x"!, pe PR c i'elM Ce CMR Use and production of Receipts from all commodity c at raw mines of commodity c material processing at raw material pro- plant i [ cessing plant i +Ur yXr ceCR ceCRAW i'elS CeCRSi A LARGE STATIC MODEL 117 Shipment of inter- Purchases of raw material mediate product c + of type c at raw material 2 from raw material processing plant i processing plant i to all steel mills This constraint requires that the amount of each commodity used or produced plus the amount received from mines plus the amount purchased must exceed the amount shipped to steel mills. MATERIAL BALANCE CONSTRAINTS FOR STEEL MILLS (6.3) Y as Pzs + x" pePS i'eIM ceCMs Use of domestic raw material Shipment of intermediate and labor and output of inter roductsfrom all mines I mediate and final products at teel mines to steel mill i i'eIR ceCRS ielS cECSS Shipment of intermediate Shipment of intermediate material processing steel mills to steel plants to steel mill i mill i Purchase of local raw]+ Pucaeoimrtd F]+Purchase of imported + mraseo al raw material and material [intermediate products] x ,, + Y. x{ +ec ceCS ielS ceCSS jeJ cCF ceCE ieIS Shipment of inter- Shipment offinal mediate products pmentso Exports of 2: from steel mill i + products from + products from to all other steel market plant i mills This constraint requires that for each commodity c and each steel mill i the production and receipt of material must exceed the uses and shipments. Production and use are both in the first term of the inequality since the as , coefficients can be either negative or positive depending on 118 MEXICAN CASE STUDY whether the commodity c is an input or is produced as an output. Receipts come from five sources: mines, raw material plants, other steel mills, local purchases, and imports. Shipments go out to other steel mills, markets, and exports. The factor 2 represents the fact that coke tends to crumble somewhat during transport so that there is some product loss. Thus, 2 is the percentage of the shipment that arrives at the receiving steel mill. CAPACITY CONSTRAINTS FOR MINES (6.4) bmpz- < k- meMM pepm iEIM ~Initial capacity Capacity required] Iiilcpct at mine i Note that m is used both as a superscript and a subscript here and has different meanings in the two positions. As a superscript, it denotes mines and as a subscript it denotes machines. CAPACITY CONSTRAINTS FOR RAW MATERIAL PROCESSING PLANTS (6.5) br 'r. kr, meM pePR icIR Capacty required] r Initial capacity at CAPACITY CONSTRAINTS FOR STEEL MILLS (6.6) b b,sz- . dcj ccC e0s C Ci-jej product c from final prod- I for product Shipment of final [Imports of] Requirements] all steel mills + uct c to ;_ c at market J to market j market I A LARGE STATIC MODEL 119 EXPORT CONSTRAINTS ON COMMODITIES (6.8) Yec ec ceCE ielS TOTAL EXPORTS CONSTRAINT (6.8a) ec 250 ceCE ie[S OWNERSHIP CONSTRAINTS ON PELLET SHIPMENTS (6.9) x, x C,kr ce{pellets} PeOWN, oeO ief{Pefia Colorado} Shipment of pellets rom Peia Colorado hare i to all steel mills group o in ownership group o This constraint requires that the total amount of pellets shipped from the Pefia Colorado raw material plant to the steel mills in each ownership group must be less than or equal to the percentage ownership by group o times the capacity of the Pefia Colorado pellet plant. (6.10) r -0ce{Pellets} i'eISEX ie{Alzada} Shipments of pellets to plants = 0 not in the HYLSA group t This ownership constraint requires that none of the pellets from the Alzada plant should be shipped to AHMSA, Fundidora, SICARTSA, and TAMSA, the plants that are not in the HYLSA group. Or specified in a positive way, it requires that all the pellets from the Alzada raw material plant be shipped to HYLSA or HYLSAP. NONNEGATIVITY CONSTRAINTS z 0 pePM, isIM zpi 0 pePR, ilIR zS >0 pePS, isIS xc'i 0 ccCM, I'eIM, icISuIR xr,,, 0 ceCRS, i'elR, ielS 120 MEXICAN CASE STUDY x!il >0 ceCSS, ielS, i'eIS, with i i' x4 >0 ceCf, ieIS, jeJ uC 0 ceCR, ieIR us >0 cceCRAW, ieIS ec >0 ceCE, ieIS vs. >0 ceCRV, ieIS v6 >0 ceCF, jeJ Objective Function The constraints above must be satisfied while the analyst seeks to minimize the sum of production cost, transport cost, and import cost less revenues from exports and by-products. (6.11) = 0 + 0' + p(01 - 00 [Total F Recurrent cost of Transport cost ~raw materialof+ cs 1=L and labor I cos + Exchange Import Export I rate A cost H revenues]) where (6.12) 4P= Z pd ci pePM iWlM ceCRAW ielR Recurrent cost of Cost of mining Price times quantity-1 raw material + purchased at and labor I operatio L raw material plants + y pdusC ccCRAW ielS [Domestic price times quantity] purchased of raw material and labor at steel mills J (6.13) 0 = Y 474'" ceCMR iclM i'eIR Cost of shipping intermediate Transport _ products between mines cost and raw material processing LT I I plants A LARGE STATIC MODEL 121 ceCMS ieIM 'elS ceCRS ielR 'elS Cost of shipping intermediate Cost of shipping intermediate stee mils j procsn plansom all smteeil products from all mines to all +productsfrom all raw material steel mills processing plants to all steel mills ceCSS iels elS ceCF IS jeJ + Cost of shipping intermediate ] Cost of shipping final products products between steel mills from steel plants to markets + Y_ Y_ f'eiP c + Y Y JJisrV)s ceCE lelS ceCRV ijlS [Cost of shipping final products] F Cost of shipping imported for export from steel mills ]+ intermediate products from nearest to nearest port port to steel mills t ceCF jeJ " Cost of shipping imported final products from nearest port to markets (6.14) -= pV0, ceCRV jelS [ Import Cost of intermediate products cost L imported to steel mills ceCFV jeJ " [Cost of final products imported to markets (6.15) y =yp e, ceCE ieIS Export Price times quantity of exports Erevenues] [ofeprs Parameters Table 6-5 provides a summary of the parameters used in the model. They are separated into five groups: production, capacity, demand, 122 MEXICAN CASE STUDY Table 6-5. Parameters in the Large Static Model Production am Process inputs ( -) or outputs (+) at mines a' Process inputs (-) or outputs (+) at raw material plants as Process inputs (-) or outputs (+) at steel mills b. Capacity utilization in mines b' Capacity utilization in raw material plants bl Capacity utilization in steel mills Capacity k' Capacity at mines k' Capacity at raw material plants k' Capacity at steel mills Demand d Market requirements e Export upper bound Prices and cost p Exchange rate (pesos per dollar) me Cost of production of mines p" Prices at raw material plants and steel mills pe Prices of exports pv Prices of imports Unit transport cost ,r Intermediate products shipped from mines to raw material plants p Intermediate products shipped from mines to steel mills p5 Intermediate products shipped from raw material plants to steel mills p" Intermediate products shipped between steel mills p' Imports shipped from ports to steel mills of raw material pi Final products shipped from steel mills to markets fPf Exports of final products shipped from steel mills to ports te Imports shipped from ports to markets prices, and unit transport cost. Since all the parameters are contained in the GAMs listing in appendix B to this chapter, this section will not list every parameter, but a selection will illustrate the method employed and help the reader interpret the data in the GAMS listing. Production The principal set of production parameters are the input-output coefficients am for the mines, ar for the raw material plants, and as for the steel mills. As an example, consider a' by looking at the input-output table for a single plant, SICARTSA. Table 6-6 gives a portion ofsuch a table, the input-output matrix for processes for producing pellets, coke, and pig iron. In the pellet production process, 0.99 metric ton of concentrated ore is used to produce a ton of pellets. In the coke process, 1.38 tons of A LARGE STATIC MODEL 123 Table 6-6. Input-Output Matrix for SICARTSA: Pellets to Pig Iron (metric tons unless otherwise specified) Inputs and outputs Pellets Coke Pig Iron Ore, Las Truchas -- - 0.2 Ore, concentrated - 0.99 -- Pellets 1.0 - - 1.384 Coal, imported - - 1.38 -0.6 Coke from imported coal - 1.0 - Fuel oil (1,000 liters) - - --0.045 Limestone - - -0.081 Dolomite - - -0.049 Electricity (megawatt-hours) - - -0.090 Pig iron - - 1.0 -Not applicable. imported coal are used to produce 1.0 ton of coke. Finally, 0.2 ton of lump ore from the Las Truchas mine and 1.384 tons of pellets are combined with 0.6 ton of coke, 45 liters of fuel oil, 0.081 ton of limestone, 0.049 ton of dolomite, and 90 kilowatt-hours (kwh) of electricity to produce a ton of pig iron. One of the reasons that both lump ore and pellets are charged to the blast furnace is that the Las Truchas mines near SICARTSA yield both magnetite and hematite ores. The magnetite ores are separated magnetically and then shipped to the SICARTSA plant in a slurry pipeline. The hematite ores would require a flotation process if they were Table 6-7. Input-Output Matrix for SICARTSA: Steel and Billets (metric tons unless otherwise specified) Steel in Steel in Billets, Inputs and BOF with BOF with continuous outputs high pig iron high scrap casting Pig iron - 0.944 - 0.833 - Scrap -0.166 -0.180 0.04 Ferroalloys -0.033 - 0.033 - Refractories - 0.006 - 0.006 - Dolomite - 0.06 - 0.06 - Lime - 0.09 -0.09 - Electricity (megawatt-hours) - 0.068 - 0.068 - Steel 1.0 1.0 - 1.05 Billets - - 1.00 -Not applicable. 124 MEXICAN CASE STUDY to be concentrated, but since that process is not available at Las Truchas, they are charged directly to the blast furnace. Table 6-7 continues the illustration of the production processes by displaying those for steel and billet production. Two alternative processes for steel production in the BOF furnaces at SICARTSA are shown. One has a relatively high pig iron charge and the other has a relatively high scrap iron charge: the first process uses 0.944 metric ton of pig iron and 0.166 ton of scrap to produce a ton of steel, while the second uses 0.833 ton of pig iron and 0.180 ton of scrap. Which process is used in the model solution will depend on the relative cost and availability of pig iron and scrap at SICARTSA. The billet production process in table 6-7 shows a case in which a single input (steel) is used to produce two outputs (scrap and billets). The scrap is then recycled and used as an input to the BOFS. Table 6-8 gives the input-output information for the rolling of shapes at SICARTSA. Light shapes are typically angles and tees an inch or two in width. Reinforcing rods are used to reinforce concrete in structures. The four activities are very similar. The input in every case is billets, and the product is rolled to completion without becoming a named intermediate product. This pattern contrasts with the rolling of flat products, which can be sold as final products at several stages or treated as intermediate products and rolled into a different final product. This is illustrated in table 6-9 which shows a portion of the input-output matrix for AHMSA. Table 6-8. Input-Output Matrix for SICARTSA: Shapes (metric tons unless otherwise specified) Reinforcing rods Inputs and Light Large- Small- outputs shapes diameter diameter Wire Scrap 0.03 0.03 0.03 0.02 Billets - 1.06 - 1.06 - 1.06 - 1.05 Light shapes 1.0 - - - Reinforcing rods Large-diameter - 1.0 - Small-diameter - 1.0 - Wire - - - 1.0 Electricity (megawatt-hours) - 0.08 - 0.08 -0.08 -0.08 Water (1,000 cubic meters) -0.01 - 0.01 -0.01 -0.01 -Not applicable. A LARGE STATIC MODEL 125 Table 6-9. Input-Output Matrix for AHMSA Some Flat Products (metric tons) Continuous Inputs and casting of Hot strip Pickled strip outputs slabs Plate and sheet and sheet Scrap 0.02 0.02 0.03 - Steel, liquid - 1.04 - - Slabs 1.0 -1.04 -1.05 - Plate - 1.0 - - Hot strip - - 1.0 -1.0 Pickled strip - - 1.0 Cold strip and sheet Annealed Tempered Tin Scrap 0.13 - Pickled strip -1.17 - - Cold strip 1.0 -1.0 -- Annealed strip - 1.0 - 1.0 - Tempered strip - - 1.0 - 1.02 Tin - - 1.0 -Not applicable. The input-output structure for flat products in table 6-9 has a stair- step shape. This is caused by the fact that hot strip is used to produce pickled strip which is used to produce cold strip, and so on. There are normally electricity inputs for these processes, but these data were not obtained for AHMSA. The capital inputs are not included in the production relationships in the input-output matrices, but are contained separately in the capital utilization matrix, which provides a relationship between productive units and processes. An entry of "1" indicates that the productive unit is used by a particular process, and a blank entry indicates that it is not used. A portion of the capital utilization matrix is shown below: Coke from Coke from Pig iron Pig iron Pig iron domestic imported from from from coal coal ore sinter pellets Coke oven 1 1 - - Blast furnace - - 1 1 0.96 Each of the alternative processes for producing coke uses the coke ovens but not the blast furnaces, so there are entries of I in the coke oven 126 MEXICAN CASE STUDY row and blanks in the blast furnace row. A similar structure for three alternative ways of producing pig iron in blast furnaces is also shown in the table. The last process illustrates that the entries in the capital utilization matrix need not always be blank or 1. The capacity of the blast furnace in this case was determined with a lump ore charge. When pellets are used in the charge, however, the capacity of the furnace rises to 104 percent of the original capacity, and therefore only 1/1.04 = 0.96 as much capacity is required per ton of pig iron produced. Capacity The capacity of the iron ore mines in 1979 is shown in table 6-10. It is divided into three types of productive units: (1) trucks, draglines, drills, and crushers; (2) magnetic concentrators for magnetite ores; and (3) flotation concentrators for hematite ores. According to the availability of magnetite and hematite ores, magnetic concentrators are located in the southern mines (Pefia Colorado, Las Truchas, and El Encino), and flotation concentrators are located at the northern mines (La Perla and Cerro Mercado; see map 3). Two kinds of productive units, pellet plants and coke ovens, are footloose, in the sense that they are sometimes located near mines and sometimes located at steel mills. The advantage of locating them near mines is that there is some weight loss in this process. The disadvantage is that coke, and to a lesser extent pellets, may crumble somewhat while being transported. In Mexico three of the pellet plants and one of the coke plants are located at the mines. The capacity of the productive units at these plants (in thousands of tons a year) is: PeiRa La Las Colorado Perla Alzada Esperanzas Pellet plant 3,000 600 1,500 - Coke ovens - - - 684 The capacity of the productive units in the steel mills in 1979 is shown in table 6-11. The structure of capacity in the Mexican steel industry in that year is apparent. The three government-owned plants which belonged to SIDERMEX (SICARTSA, AHMSA, and Fundidora) used blast furnaces, open hearths, and basic oxygen furnaces to produce pig iron and steel; the three private plants (HYLSA in Monterrey, HYLSAP in Puebla, and TAMSA in Veracruz) employed direct reduction and electric are furnaces to produce sponge iron and steel. Table 6-10. Capacity of Iron Ore Mines and Coal Mines (thousand tons a year) Pefia Las La Cerro de La El Productive unit Colorado Truchas Perla Mercado Hercules Chula Encino Coahuila Mining equipment for iron ore Trucks and crushers 4,000 2,700 1,000 3,000 1,000 500 3,000 - Magnetic concentrator 4,000 1,500 - - - 3,000 - Flotation concentrator - - 1,000 3,000 __ Mining equipment for coal mines _ - 7,000 -Not applicable. 128 MEXICAN CASE STUDY Table 6-11. Capacity of Productive Units in Steel Mills, 1979 (thousand metric tons a year) Productive unit SICARTSA AHMSA Fundidora HYLSA HYLSAP TAMSA Pellet plant 1,850 - 750 - Sinter plant - 1,500 - - - Coke oven 660 2,100 - - Blast furnace 1,100 3,247 1,400 Direct reduction - - - 660 1,000 270 Open hearth - 1,500 850 - - Basic oxygen furnace 1,300 2,070 1,500 - - - Electric arc furnace - - - 1,000 560 450 Continuous caster of slabs - 710 - - - Continuous caster of billets 1,300 - - - 560 - Ingot casting - 2,600 2,000 1,000 - 420 Primary mill for flats - 1,850 1,450 1,000 - - Primary mill for nonflats - 1,200 - - - - Plate mill - 960 250 - Hot strip mill - 1,600 870 900 - - Pickling line - 1,600 575 650 - - Cold strip mill - 1,495 500 600 - - Annealing furnaces - 1,348 420 450 - - Temper mill - 1,225 520 450 - - Tinning line - 315 - 70 - - Billet mill - 1,000 200 - - Heavy shapes mill - 200 - - - - Bar mill 600 135 - - 430 80 Wire mill 600 270 - - 200 - Seamless pipe mill - - - - 280 -Not applicable. In contrast, the separation in rolling mills was divided not along government and private lines but along plant lines. One government plant (SICARTSA) produced shapes, one (Fundidora) produced primarily flat products, and one (AHMSA) produced both shapes and flat products. Similarly, one private plant (HYLSAP) produced shapes and one (HYLSA) produced flat products. Finally, a private plant (TAMSA) produced almost exclusively seamless pipe. Table 6-11 also shows some of the imbalances in capacity which result from economies of scale and technology changes in some productive units. Fundidora had excess capacity in steel production in its open hearths (850,000 tons) and basic oxygen furnaces (1.5 million tons) relative to its pig iron producing capacity (1.4 million tons) in the A LARGE STATIC MODEL 129 blast furnaces. HYLSAP had a sponge iron producing capacity of 1 million tons in its direct reduction units while its continuous caster had a capacity of only 560,000 tons. These imbalances presented interesting opportunities for interplant shipments of intermediate products. Some of these opportunities are exploited in the solutions presented in chapter 7. Demand Two components of demand, domestic and export, are treated in the model. Domestic demand is considered first. The demand projections used in this study are from a study by the Coordinating Commission for the Steel Industry (1978), which is located in Mexico City and has responsibility for overseeing the entire Mexican steel industry, both private and public. In this version of the static model an attempt was made to replicate the situation in the industry for 1979. The projections for that year are shown in table 6-12. These projections include the demand for some shapes that is satisfied by the small-scale rerolling industry. To obtain the demand for products produced by the integrated steel plants, which are the focus of this study, it is therefore necessary to subtract the part of demand met by the semi- integrated companies and the rerollers. In 1979 it was estimated that this Table 6-12. Domestic Demand Projections for 1979 (thousand metric tons) Seni-inte- Product Total grated' Net Plate 1,050 - 1,050 Hot sheet and strip 600 - 600 Cold sheet and strip (tempered) 1,250 - 1,250 Tin 400 - 400 Heavy shapes 300 130 170 Light shapes 310 160 150 Bars 340 155 185 Reinforcing rods 1,150 395 755 Wire rod 600 190 410 Seamless pipe 800 - 800 Rails 110 - 110 -Not applicable a. We are indebted to Alejandro Reyes for these estimates. Source: Based on results in Coordinating Commission for the Steel Industry (1978). 130 MEXICAN CASE STUDY Table 6-13. Demand for Steel Products from Integrated Steel Mills, 1979 (thousand metric tons) Steel product Demand Plate 1,050 Hot sheet and strip 600 Cold sheet and strip (tempered) 1,250 Tin 400 Heavy shapes 170 Light shapes 150 Bars 185 Reinforcing rods, large-diameter 453 Reinforcing rods, small-diameter 302 Wire rod 410 Seamless pipe 800 Rails 110 part of the industry supplied the amounts listed under semi-integrated in table 6-12. These figures are subtracted from the total figures to obtain the net domestic demand used in the model. One other modification of the data is necessary. Since some of the plants use different productive units for different sizes of reinforcing rods, demand for large-diameter is separated from that for small-diameter reinforcing rods. It is assumed that six-tenths of the demand for reinforcing rods is for large-diameter rods and the remaining four-tenths is for small-diameter rods. Thus, the demand for large-diameter reinforcing rods is (0.6) (755) = 453, and the demand for small-diameter reinforcing rods is (0.4) (755) = 302. After these changes, the demand for steel products from the integrated steel mills is as shown in table 6-13. Next, it is necessary to distribute the demand for steel products among the nine regional markets used in the study (see table 6-14). For example, it is assumed that 87.6 percent of the total demand for tin is in Mexico City but only 10.5 percent of the demand for seamless pipes. Coatzacoalcos, in the center of the new gas fields, has a negligible percentage of the demand for tin but 39 percent of the demand for seamless pipe. The results of multiplying the national demand times the regional percentages is given in table 6-15. This gives the demand in eight regional market centers for twelve categories of final products of the integrated steel industry in 1979 as projected from data available through 1977. Table 6-14. Percentage of Demand for Steel Products in Each Market Area, 1979 Mexico Quere- San Luis Guadala- Lazaro Coatza- Product City Puebla taro Potosi Monterrey jara Cardenas coalcos Plate 63.5 0.2 0.3 0.3 31.0 4.5 0.1 0.1 Hot strip 41.9 2.8 1.6 2.8 36.2 12.6 0.5 1.6 Tempered strip 45.1 2.5 4.5 1.1 41.7 4.3 0.4 0.4 Tin 87.6 0.3 0 0 9.4 2.7 0 0 Heavy shapes 36.6 2.2 3.2 0.8 12.9 42.6 1.4 0.3 Light shapes 74.4 2.5 1.9 1.8 8.1 8.9 1.6 0.8 Bars 46.6 4.2 23.5 2.2 11.2 11.8 0.4 0.1 Reinforcing rods Large-diameter 46.7 10.3 4.0 3.4 12.8 11.8 6.1 4.9 Small-diameter 46.7 10.3 4.0 3.4 12.8 11.8 6.1 4.9 Wire rod 61.2 5.3 3.9 3.7 12.2 9.8 1.9 2.0 Seamless pipe 10.5 28.0 0.4 0.2 18.4 1.8 1.7 39.0 Rails 40.0 5.0 5.0 10.0 20.0 10.0 5.0 5.0 Table 6-15. Regional Demand for Final Products from the Integrated Steel Industry, 1979 (thousand metric tons) Mexico Quer- San Luis Guadala- Izaro Coatza- Product City Puebla taro Potosi Monterrey jara C6rdenas coalcos Total Plate 667 2 3 3 325 47 1 1 1,050 Hot strip 251 17 10 17 217 76 3 10 600 Tempered strip 564 31 56 14 521 54 5 5 1,250 Tin 350 0 1 0 38 11 0 0 400 Heavy shapes 62 4 5 1 22 72 2 1 170 Light shapes 111 4 3 3 12 13 2 1 150 Bars 86 8 44 4 21 22 1 0 185 Reinforcing rods Large-diameter 211 47 18 15 57 53 27 22 453 Small-diameter 141 31 12 10 38 35 18 15 302 Wire rod 250 22 16 15 50 40 8 8 410 Seamless pipe 84 224 3 2 147 14 14 312 800 Rails 44 6 6 11 22 11 6 6 110 Total 2,823 394 176 95 1,472 450 87 380 5,880 Note: Row and column totals may be off slightly because of rounding errors. A LARGE STATIC MODEL 133 Prices The prices used in the model are shown in table 6-16. Domestic prices are in 1979 pesos and international prices are in 1979 dollars. The exchange rate used in the model is 25 pesos per dollar. One set of cost terms and three sets of prices play a role in the model: mc= cost of production at mines pd = prices at raw material plants and steel mills pe = prices of exports pV = prices of imports. Each of these sets of costs and prices will be discussed in turn. The domestic costs at mines used in the model are 250 pesos a ton for raw, unwashed coal and 100 pesos a ton for ore. This price for ore applies to the three types used in the model: northern, southern, and Las Truchas ores. Domestic prices at raw material plants and steel mills are given in the first column of table 6-16. The prices of natural gas, electricity, and coal have been changing very rapidly in recent years and are important in determining the relative efficiency of direct reduction-electric arc processes and blast furnace-BoF processes. The price given in table 6-16 for natural gas is 322 pesos per thousand cubic meters, equivalent to $0.36 per thousand cubic feet.2 Similarly, the international price for natural gas given in table 6-16 is $152 per thousand cubic meters which is equal to $4.30 per thousand cubic feet.3 There is therefore a large disparity between the domestic and the international price. This is an accurate description of the situation in 1979. Natural gas was sold in Mexico for a substantially lower price than in other countries. Electricity is priced in the model at 552 pesos per thousand kilowatt- hours, equivalent to roughly 2 cents per kilowatt-hour, which can be compared to prices in the United States in 1979 of 4 to 5 cents per kilowatt-hour. The prices for imports of final products are shown in the second 2. There are 0.0283 cubic meters per cubic foot and 25 pesos per dollar so 0.36 per thousand cubic feet = (322 pesos per thousand cubic meters) (0.0283 cubic meters per cubic foot) (1/25 dollars per peso). 3. $4.30 per thousand cubic feet = (S 152 per thousand cubic meters) (0.0283 cubic meters per cubic foot). 134 MEXICAN CASE STUDY Table 6-16. Domestic and International Prices Used in the Large Static Model (pesos or dollars per metric ton unless otherwise noted) Domestic International price price Commodity (1979 pesos) (1979 dollars) Ore, concentrated - 28 Pellets 430 45 Coal, domestic 880 - Coal, imported - 63 Coke 1,200 100 Fuel Oil (1,000 liters) 1,000 - Limestone 120 - Natural gas (1,000 cubic meters) 322 152 Scrap 3,050 120 Ferroalloys 16,000 - Refractories 50,000 - Dolomite 800 - Lime 690 - Electrodes 48,000 - Electricity (megawatt-hours) 552 - Plate - 347 Hot sheet and strip - 393 Cold sheet and strip (tempered) - 373 Tin - 393 Billets - 300 Heavy shapes - 338 Light shapes - 364 Bars - 350 Reinforcing rods, large-diameter - 347 Reinforcing rods, small-diameter - 368 Wire rods - 434 Seamless pipes - 455 Rails - 345 -Not applicable. A LARGE STATIC MODEL 135 column of table 6-16. These prices are assumed to hold at the port of entry. Additional costs are incurred in the model in transporting the imported raw material from the ports to the plants and the imported final products from the ports to the markets. Export prices are assumed to be only 80 percent of the international price. This is a relatively arbitrary estimate of the difference between f.o.b. and c.i.f. prices for products in the steel industry. Transport Cost Transport costs are differentiated in the model according to the kind of commodities being shipped. This difference is embodied in the relationship used to calculate unit transport cost. The expressions used for calculating transport cost are: mr' = ±' r#'l' ielM i'elR Ith, = U+,b ic-lM,i'elS pS = rLr5r ielR,i'elS Pi, = iefiy8 ieIS rs= (r + ielS,jeJ spf r + #r6s 4-~ flf65P8-S,c- gpf = CXf~ 6 +jpeiJI where a' = loading and unloading cost per ton for raw material pr = proportional cost per ton-kilometer for raw material af = loading and unloading cost per ton for final products fif = proportional cost per ton kilometer for final products 6-r = distance in kilometers from mines to raw material plants. All other distances are similarly defined with the superscripts defined as: m = mines r = raw material plants s = steel mills p = ports j = markets. 136 MEXICAN CASE STUDY For this model the parameter values used are: ,r= 30 cf = 60 'r= 0.11 flf = 0.19 The distances 6 are given in the GAMS statement of the model in appendix B to this chapter. The final parameter used in the model is a transport loss function for coke. It is used to represent the fact that coke tends to crumble somewhat when transported. It is assumed here that there is a 10 percent loss rate so this factor was set at 0.9 for coke and at 1.0 for all other commodities: A= 0.9 for ce{coke} A4 = 1.0 for all other ce-CS Appendix A. Notational Equivalence This appendix contains a list of equivalences between the mathemati- cal and GAMS terms. For a discussion of the model size and of the procedures used to reduce the model size, see Meeraus and Kendrick (1982). That paper provides a motivation for the use of the productive unit, process, and commodity possibility sets such as MMPOS, PMPOS, and CMPOSN. These sets are used to do the model reduction and can be ignored on a first reading of the GAMs statement for the large static model. The notational equivalence between the mathematical and the GAMS versions of the large static Mexican steel model follows. Equations Mathe- matical GAMS Material balance constraints for mines (6.1) MBM Material balance constraints for raw material processing plants (6.2) MBR Material balance constraints for steel mills (6.3) MBS Capacity constraints for mines (6.4) CCM Capacity constraints for raw material processing plants (6.5) CCR Capacity constraints for steel mills (6.6) CCS Market requirements (6.7) MREQ A LARGE STATIC MODEL 137 Export constraints on commodities (6.8) ME Total exports constraint (6.8a) ME2 Ownership constraints on pellet (6.9) PELPC shipments and and (6.10) PELAL Accounting cost, total (6.11) ACOST Accounting cost, recurrent (6.12) AREC Accounting cost, transport (6.13) ATRANS Accounting cost, imports (6.14) AIMP Accounting revenues, exports (6.15) AEXP Sets The mathematical and GAMs notations are identical. Variables Mathematical GAMS Mathematical GAMS zm ZM of VF zr ZR v VS zS ZS ur UR xm XM us us x' XR COST xe XS RECURRENT xf XF TRANSPORT e E IMPORT EXPORT Parameters Mathematical GAMS Mathematical GAMS am AM k' KS ar AR e EMAX as AS d D bm BM p PD br BR p m PM bs BS pV PV km KM pe PE k' KR ,mr MUMR (continued) 138 MEXICAN CASE STUDY Parameters (continued) Mathematical GAMS Mathematical GAMS " MUMS psr MUPSR yrs MURS It MUPJ p MUSS m MC ysi MUSJ p SH tI MUSPF C PCT A sampling of terms is given here to display the equivalence between mathematical notation and GAMS notation. Mathematical GAMS YaPm z'" ielM SUM(PM, AM(CM, PM)*ZM(PM, IM)) Use of domestic raw material and labor and output of inter- mediate products at mine i s ceCS US(CS, IS)$CRAW(CS) Purchase of] local raw material and labor The variable uci enters a set of equations defined over CS and IS but u enters only a subset CRAWof the set CS of commodity equations. Appendix B. GAMS Statement of the Large Static Model A GAMS statement of the large static model including the sets, data, equations, and reference map begins on the following page. GAMS 1.0 ME X I C S S T EE L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE SEE MARGIN 002-120 3 * REPERRNCRS - 6 * 1. SICARTSA, DSCRIPCION DI LOS PROEOS QUE SE REALICAN IN LAO 7 * PLANTAS DRL COMPLEJO SIDERORGRCO SICARTSA, 1978 5 8 9 2. ALTOS SORO, INFORMATIN GENERAL (BLUEPRINT), 1974 10 *1 3. ALTOS HORNOS, DIAGRAMIA DE PLUJO 3.75 NOT/A ANN 4.25 NOT/A 12 (BLEEPRINT$), 1978 13 IA 4 . CCIS, SITUATRON ACTEAL Y CRECIMIENTO PUTORO SE LA INDUSTRIA 15 SIDRRGICA, 1979 16 17 * 5. CCIS, REPORTS SE LA PR1EBA 1EL EMPLEO SE FIERRO ESPONJA 18 NIL EN EL ALTO HORRO 2, 1978 19 20 * 6. CCIS, ESTUIO BE PRE-PACTIRILIDAD PARA IRA PLANTA DE0 PIERRE 21 ESRPONJA PARA EXPORTACION CONVENIO MEXICO-RRASIL, 1979 22 23 * 7. CCIS, LAS MATERTAS PRIMAS Y OTROS NSU0MO EN LA IRSISTRIA 24 * SIRERURGICA, 1977 25 26 8. RESSEL ANN VA00HAN, STEEL PRODUCTIOR, 1976 27 28 9. SECETARIA SE LA PRECIDENCIA, LA INDUSTRIA SIDERURGICA 29 INETEGRADA SE MEXICO (VOL I AND 11), 1976 30 31 10. AIMSA, CAPACITY SORRY, 1978 32 33 *11. AHMSA, CAPACITY EXPANSION 1979 - 1902, 1978 34 305 12. PUNDIDORA, LA MODERNA PURDIDORA..197.. 36 37 * 13. SICARTSA, PRODUCTON Y CONSNO 38 39 * 1A. SICARTSA, INSUMOS PRINCIPALES, PECIOS SE PRESEPUESTO, 1979 40 * 41 * 15. NYLSA., THE NIL IRON ORI DIRECT REDUCTION PROCESS, 1973 42 * A3 * 16. PENDIDORA, COMPETER DATA DANK, 1978 44 * 43 * 17. PUNDIDORA, OPERTA Y DEMANDA, JOINT INDUSTRY PROJECTIONS, 1978 46 * 47 * 18. CCIS, TRANSPORT COST AND DISTANCES PSI MINERAL COAL 47 * 49 * 19. CCIS, TRANSPORT COST AND DISTANCES EON IRON ORE 50 * 51 20. CCII, SORTEST RAILROAD DIDTANCES BETWEEN MAJOR COTTER 52 3 * 21. CCI TRANSPORT COST ASS GETANCES POE RIMA STEEL PREDICTS GAMS 1.0 MEXIC 0 T E E L M 0 DE L FOR 1979 01/13/83 09.02.38. PAGE 2 54 * 55 * 22. IBRD, SICARTSA II, 1975 -A.. 56 * 0 57 * 23. CAPITAL COST. SICARTSA FIRST STAGE. 1973. REPORT BY S8 * INDUSTRIAL DEPARTMENT. 08RD. 59 * 60 * 24. PLAN DE DESARROLLO DE LA INDUSTRIA SIDERURGICA PARAESTATAL 61 * 1979-1990. SIDERMEX. CONFIDENTI4L DOCUMENT. NOT PUBLISHED YET 62 GAMS 1.0 M EX I C 0 S T E E L M 0 DE L FOR 1979 01/13/83 09.02.38. PAGE 3 SET DEFINITIONS 64 SET IM IRON ORE AND COAL MINES / 65 66 P-COLORADA PENA COLORADA COLIMA 67 LASTRUCHAS LAZARO CARDENAS MICHOACAN 68 LA-PERLA CAMARGO CHIHUAHUA 69 CERRO-MER CERRO DE MERCADO DURANGO 70 HERCULES SIERRA MOJADA COAHUILA 71 72 LA-CHULA MINATITLAN COLIMA 73 EL-ENCINO PIHUAMO JALISCO 74 COAHUILA COAL MINING REGION 75 76 IR RAW MATERIAL PLANTS / 77 78 PENACOL PENA COLORADA COLIMA 79 LAPERLA CAMARGO CHIHUAHUA 80 ALZADA COLIMA 81 ESPERANZAS COAHUILA 82 83 is STEEL MILLS / 84 85 SICARTSA LAS TRUCHAS 86 AHMSA MONCLOVA 87 FUNDIDORA MONTERREY 88 HYLSA MONTERREY 89 HYLSAP PUEBLA 90 TAMSA VERACRUZ / 91 92 J DOMESTIC MARKET AREAS / 93 94 MEXICO-DF MEXICO D.F. 95 PUEBLA PUEBLA 96 QUERETARO QUERETARO 97 SAN-LUIS SAN LUIS POTOSI 98 MONTERREY NUEVO LEON 99 100 GUADALAJA GUADALAJARA JALISCO 101 L-CARDENAS MICHOACAN 102 COATZACOAL VERACRUZ / 103 104 L EXPORT POINTS / 105 106 GULF 107 PACIFIC / 108 109 MM PRODUCTIVE UNITS AT MINES / 110 111 MINE-CO MINING EQUIPMENT FOR COAL MINES 112 MINE-EQ MINLNG EQUIPMENT: TRUCKS AND CRUSHERS 113 CONC-MAG RAGNETIC CONCENTRATOR 114 CONC-FLOT FLOTATION CONCENTRATOR / 115 GAMS 1.0 M E X I C 0 S T E E L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 4 SET DEFINITIONS 116 MR PRODUCTIVE UNITS AT RAW MATERIAL PLANTS / 117 118 PELLET PELLET PLANT 119 COKE-0VEN COKE OVEN AND BYPRODUCT UNITS / 120 121 MS PRODUCTIVE UNITS AT STEEL MILLS / 122 123 PELLET PELLET PLANT 124 SINTER SINTER PLANT 125 COKE-OVEN COKE OVENS AND BY-PRODUCT UNITS 126 BLAST-FURN BLAST FURNACES 127 DIRECT-RED DIRECT REDUCTION UNITS 128 129 OPENHEARTH OPEN HEARTH FURNACES 130 BOF BASIC OXYGEN CONVERTERS 131 ELEC-ARC ELECTRIC ARC FURNACES 132 CONCAS-SL CONTINUOUS CASTING UNIT FOR SLABS 133 CONCAS-BI CONTINUOUS CASTING UNIT FOR BILLETS 134 135 INGOT-CAST INGOT CASTING 136 PRIMARY-FL PRIMARY MILL AND SOAKING PITS - FLAT PRODUCTS 137 PRIMARY-NF PRIMARY MILLS AND SOAKING PITS - NON FLAT 138 PLATE-MILL PLATE MILL 139 HOT-MILL HOT STRIP MILL 140 141 PICKLELINE PICKLING LINE 142 COLD-MILL COLD STRIP MILL 143 ANNEAL ANNEALING UNITS 144 TEMPERMILL TEMPER MILL 145 TIN-LIME TINNING LINE 146 147 BILLET BILLET MILL 148 REAVYSMILL HEAVY SHAPES MILL 149 BAR-MILL INTEGRATED BAR MILL 150 WIRE-MILL INTEGRATED WIRE MILL 151 SEAML-MILL SEAMLESS PIPE MILL / 152 153 PM PRODUCTION PROCESSES AT MINES / 154 155 MIN-CO MINING UNWASHED COAL 156 WAS-CO WASHING OF COAL 157 MIN-N MINING IN THE NORTHERN MINES 158 MIN-S MINING IN THE SOUTHERN MINES 159 MIN-TR MINING IN LAS TRUCHAS MINE 160 161 CONC-N CONCENTRATION OF NORTHERN ORE 162 CONC-S CONCENTRATION OF SOUTHERN ORE 163 CONC-TR CONCENTRATION OF TRUCHAS ORE / 164 165 PR PRODUCTION PROCESSES AT RAN MATERIAL PLANTS / 166 167 PELT-C PELLET PRODUCTION USING CONC ORE RAMS 1.0 M E X I C 0 S T EE L M 0 D E L FOR 1979 01/13/83 09.02.38. PACE 5 SET DEFINITIONS 168 COKE-HD COKE PRODUCTION WITH DOMESTIC COAL / 169 170 PS PRODUCTION PROCESSES AT STEEL MILLS / 171 172 PELT-C PELLET PRODUCTION USING CONCENTRATED ORE 173 SINTER SINTER PRODUCTION 174 COKE-HD COKE PRODUCTION WITH HIGH DOMESTIC COAL INPUT 175 COKE-HI COKE PRODUCTION WITH HIGH IMPORT COAL INPUT 176 PIG-ORE PIG IRON ORE PRODUCTION WITH LUMP ORE 177 178 PIG-SIN PIG IRON PRODUCTION WITH HIG SINTER CHARGE 179 PIG-PEL PIG IRON PRODUCTION WITH HIGH PELLETS CHARGE 180 PIC-PEL-M PIG IRON PRODUCTION WITH COKE FROM IMPORTED COAL 181 SPONGE SPONCE IRON PRODUCTION 182 STL-OH-P STEEL PRODUCTION IN OPEN HEARTHS WITH HIGH PIG TSR 183 184 STL-OH-S STEEL PRODUCTION IN OPEN HEARTHS WITH HIGH SCRAP CHARGE 185 STL-0H-S STEEL PRODUCTION IN OPEN HEARTHS WITH HIGHEST SCRAP CHARGE 186 STL-BOF-P STEEL PRODUCTION IN BOF WITH HTGH PIG IRON CHARGE 187 STL-BOF-S STEEL PRODUCTION IN BOF WITH HIGH SCRAP CHARGE 188 STL-EAF-SP STEEL PRODUCTION IN ELECTRIC FUR. WITH HIGH SPONGE 189 190 STL-EAF-S STEEL PRODUCTION IN ELECTRIC FURNACE WITH HIGH SCRAP 191 SLABS-CC SLABS PRODUCTION By CONTINUOUS CASTING 192 BILLETS-CC BILLET PRODUCTION BY CONTINUOUS CASTING 193 INGOT INGOT CASTING 194 SLAB-ROLL SLAB PRODUCTION BY ROLLING 195 196 BLOOM-ROLL ROLLING OF BLOOMS FROM INGOTS 197 BILLET-ROL BILLET PRODUCTION BY ROLLING BLOOMS 198 PLATE PLATE PRODUCTION FROM SLABS 199 HOT-SHEET HOT ROLLED COIL PRODUCTION 200 PICKLED PICKLED COIL PRODUCTION 201 202 COLD-SHEET COLD OOLO COIL PRODUCTION 203 ANNEALED ANNEALED COIL PRODUCTION 204 TEMPERED TEMPERED COIL PRODUCTION 205 TINNING TIN PRODUCTION 206 HEAVYSHAPE HEAVY SHAPE ROLLING 207 208 LIGHTSHAPE ROLLING OF LIGHT SHAPES 209 ROUGH-NF ROUGHING MILE FOR NON-FLAT PRODUCTS 210 BAR-ROLL ROLLING OF BARS 211 REBARS-LD ROLLING OF LARGE DIAMETER RE-RODS AND BARS 212 REBARS-SD ROLLNG OF SMALL DIAMETER RE-RODS AND BARS 213 214 WIRE ROD ROLLING OF WIRE ROD 215 SEAM-ROL ROLLLING OF SEAMLESS PIPES / 216 217 CS COMMODITIES AT STEEL MILLS / 218 219 ORE-N IRON ORE FROM NORTH. HIGH S AND P. 59% FE. SASS 1.0 M E X I C 0 S S E L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 6 SET DEFINITIONS 220 ORE-S IRON ORE FROM SOUTH. NO P. 60% FE. 221 ORE-TRUCHA IRON ORE FROM SICARTSA. NO P. 55% FE. 222 ORE-CONC IRON ORE CONCENTRATED 223 PELLETS PELLETS 224 225 SINTER SINTER 226 COAL-D COAL-DOMESTIC: WASHED 227 COAL-I COAL-IMPORTED: WASHED 228 COAL-R RAW UNWASHED COAL 229 COKE COKE PRODUCED WITH DOMESTIC COAL 230 231 COKE-IMP-C COKE PRODUCED WITH IMPORTED COAL 232 FUEL-OIL FUEL OIL IN THOUSAND LITERS 233 LIMESTONE LIMESTONE 234 PIG-IRON PIG IRON (HOT METAL) 235 NAT-GAS NATURAL GAS IN 1000 M3 236 237 SPONGE SPONGE IRON 238 SCRAP STEEL SCRAP 239 FERRO-ALLO FERROALLOYS 240 REFRAC REFRACTORIES 241 DOLOMITE DOLOMITE 242 243 LIME LIME 244 ELECTRODES ELECTRODES (KG) 245 STEEL-LIQ LIQUID STEEL 246 STEEL-ING INGOT STEEL 247 SLABS SLABS 248 249 PLATE PLATE 250 HOT-STRIP HOT STRIP SHEET 251 PICK-STRIP PICKLED STRIP SHEET 252 COLD-STRIP COLD STRIP SHEET 253 ANL-STRIP ANNEALED STRIP SHEET 254 255 TEMP-STRIP TEMPERED STRIP SHEET 256 TIN TIN SHEET 257 BLOOMS BLOOMS 258 BILLETS BILLETS 259 HEAVYSHAPE HEAVY SHAPES 260 LIGHTSHAPE LIGHT SHAPES 261 BARS BARS 262 RE8BS REINFORCING RODS - DEMAND DATA IS AVAILABLE ONLY FOR AGGREGATE 263 REBARS-LD LARGE DIAMETER REINFORCING RODS 264 REBARS-SD SMALL DIAMETER REINFORCING RODS 265 WIRE WIRE ROD 266 267 SEAMLESS SEAMLESS PIPE 268 PESOS MEXICAN CURRENCY 269 ELECTRIC ELECTRICITY IN 1000 KWH 270 WATER WATER IN 1000 M3 271 ING-BLOOMS STEEL BLOOMS FOR SEAMLESS PIPE GAMS 1.0 ME X I C 0 ST 1E L M 0 DE L FOR 1979 01/13/83 09.02.38. PAGE 7 SET DEFINITIONS 272 RAILS RAILS - ONLY IMPOE 273 274 CRAW(CS) DOMESTIC RAW MATERIALS 275 276 FEEL-OIL, LIMESTONE, NAT-GAS, SCRAP, FERRO-ALLO, REPEAC 277 DOLONITE, LONE, ELECTNODES, WATER, ELECTRIC 278 279 CM(CS) COMMODITIES AT MIRES 280 281 ORE-N, ORE-I, ORE-TRUCRA, COAL-R, COAL-I, SEE-CONC 282 283 10(CS) COMMODIIES AT RAW MATERIAL PLANTS 284 285 ORE-N, ORE-S ORE-TRUCHA, COAL-E, COAL-I, ORE-CONC, FILLETS, COKE, ELECTRIC 286 287 CRV(CS) IMPONTED RAW MATERIALS AND INTERMEDIATE PRODUCTS / COAL-I, PELLETS, SCRAP, COKE 288 289 290 CMR(CS) CONMODITIES IPFED PEON MOSES TO RAW MATERIAL PLAITS / ORE-CONE, COAL-S 291 292 293 CMSC) COMMODITIES SNIPPED FROM MINES TO STEEL FLANTS / COAL-I, ORE-CISC, ORE-I, ONE-N, ORE-TRUCHA 294 295 296 CRS(CS) CONNODTIES SHEPPED FROM RAW MATERIAL PLANTS TO STEEL MILLS / PELLETS, COKE 297 298 299 CSS(CS) COMMODITIES FOE INTERPLANT SHIPMENT BETWEEN STEEL MILLS / SSEE, PELLETS, COKE 300 301 CF(CS) FINAL PRODUCTS / PLATE, ROT-STROP, TEMP-STROP, TIN , HEAVYSSAPE, LIGHTONiAFE 302 SARI , REBARS-LD, REBANS-S , WORE, SEAMLESS , RAILS 303 304 CE(CS) CONNODITES FOE EXPORTS 305 306 CFV(CS) IMPORTED FINAL PRODUCTS 307 308 0 OINER NDERS / 5 309 310 OWN(O,IS) OWNER GROEPS ISICARTSA, 2.AHMSA, 3.FERNDfORA, 4.(HYLS,HYLSAP), 5,TANSA 311 312 313 ISEX(IS) PLANTS ECLUDED FROM ALZADA IRKS SICARTSA, AHMS, FONDIDORA, TAMSA 314 315 RES(CC,IN) RESERVE TYPES AT LOCATIOS /ORE-S.P-COLORADA, ORE-TRUCHA.LASTRUCHAS, ORE-N.LA-PERLA 316 ORE-N.CNERRO-MER ,ORE-N.HRECULES ORE-S.LA-CHULA 317 ORE-S.EL-ENCINO COAL-.COAHUILA 318 319 CE(CF) YES 320 CFV(CF) TES 321 327 ALIAS(CS,ISP) GANS 1.0 E B X I C 0 S T EE L N 0 DE L FOR 1979 01/13183 09.02.38. PAGE 8 PRODUCTION 324 PARAMETER AS(CS,PS,IS) INPUT OUTPUT RELATIONS FOR STEEL MILLS 325 326 TABLE AM(CM,PM) A MATRIX FOR MINING PRODUCTS 327 328 NIN-N MIN-S MIN-TR CONC-N CONC-S CONC-TR MIN-CO WAS-CO 329 330 ORE-N 1. -1.42 331 ORE-S 1. -1.28 332 ORE-TRUCHA 1. -1.37 333 ORE-CONC 1. 1. 1. 334 COAL-R 1. -2.1 335 COAL-D 1. 336 337 338 TABLE AR(CS,PR) A MATRIX FOR RAN MATERIAL PLANTS 339 340 PELT-C CORE-ND 341 342 FUEL-OIL -.02 343 ORE-CONC -.99 344 PELLETS 1.0 345 COAL-D -1.50 346 COKE 1.0 347 ELECTRIC -.045 -.060 348 349 TABLE ASIC(CS,PS) A MATRIX FOR SICARTSA 350 351 PELT-C COKE-HI PIG-PEL-M STL-ROF-P STL-BOF-S 352 353 ORE-TRUCHA -.20 354 ORE-CONC -.99 355 PELLETS 1.0 -1.384 356 COAL-I -1.38 357 COKE-IMP-C 1.0 -.60 358 FUEL-OIL -.045 359 LIMESTONE -.081 360 PIG-IRON 1.0 -.944 -.833 361 SCRAP -.166 -.180 362 FERRO-ALLO -.033 -.033 363 REFRAC -.006 -.006 364 DOLOMITE -.049 -.06 -.06 365 LIME -.09 -.09 366 STEEL-LIQ 1.0 1.0 367 ELECTRIC -.045 -.060 -.090 -.068 -.068 368 369 CAMS 1.0 M E X I C 0 S T EE L M 0 DE L FOR 1979 01/13/83 09.02.38. PAGE 9 PRODUCTION 371 + BILLETS-CC LIGHTSHAPE HEBARS-LD REBAHS-S WIRE 372 373 SCRAP .04 .03 .03 .03 .02 374 STEEL-LIQ -1.05 375 BILLETS 1.0 -1.06 -1.06 -1.06 -1.05 376 LIGHTSHAPE 1.0 1 4 *ff#f1:k8 1.0 1.0 379 WIRE 1.0 380 ELECTRIC -.08 -.08 -.08 -.00 381 WATER -.01 -.01 -.01 -.01 382 383 D ATA SFORSPELT-COAND COKE-HI COME PROM PLANT VISIT. DATA POR PIG-PEL 384 AND STL- S0F-P CONES PROM (1 PAGE 83 AND 95). IDEALICED DATA RATHER 385 *THAN HISTORICAL YIELDS POE 1978 WERE USED FOR ROLLING MILLS. 386 387 388 TABLE AANM(CS,PS) A MATRIX FOR AHMSA 389 390 COKE-S NR PIC-PEL PIGSIN 391 392 ORE-N -1.1 -.64 393 COAL-S -1.50 394 SINTER 1.0 -1.03 N395 PELLETH -1.6 396 COKE 1.0 -.1 -.63 -.70 397 LIMEETONE -.17 -.10 398 OLONITE -.049 -.049 399 PIG-IRON 1.0 1.0 400 EAT-GAS -.05 -.05 401 SPONGE 402 ELECTEIC -.060 -.040 -.090 -.090 403 FERRO-ALLO -.065 -.065 404 405 + STL-OH-S STL-BSP-P OIL-HOP-H INGOT SLABS-CC SLAB-ROLL 406 407 ORE-N -.02 408 P10-IRON -.77 -1.07 -.74 409 SCRAP -.33 -.11 -.42 .02 .02 .13 410 NAT-GAS -.078 -.03 -.03 411 FUEL-OIL -.079 412 LINESTONE -.14 413 PERRO-ALLO -.011 -.011 -.11 414 REPRAC -.002 -.006 -.012 415 DOLOMITE -.10 -.06 416 LINE - 09 -.14 417 STEEL-LIQ 1.0 1.0 1.0 -1.04 -1.04 418 STEEL-INC 1.0 -1.17 419 SLABS 1.0 1.0 420 ELECTRIC -.040 -.068 -.068 421 422 + BLOS-ROLL BILLT-OL PLATE HOT-INET PICKLES CAMS 1.0 M E XI C 0 S T E F L M 0 DE L FOR 1979 01/13/83 09.02.38. PAGE 10 PROLUCTION 423 424 SCRAP .13 .13 .02 .03 425 STEEL-ING -1.17 426 SLABS -1.04 -1.05 427 PLATE 1.0 428 HOT-STRIP 1.10 -1.0 429 BLOOMS 1.0 -1.17 430 BILLETS 1.0 431 PICK-STRIP 1.0 432 433 + COLD-SHEET ANNEALED TEMPERED TINNING 434 435 SCRAP .13 436 PICK-STRIP -1.17 437 COLD-STRIP 1.0 -1.0 438 ANL-STRIP 1.0 -1.0 439 TEMP-STRIP 1.0 -1.02 440 TIN 1.0 441 442 + HEAVYISHAPE LIGHTSHAPE BAR-ROLL REBARS-LD REtARS-SD WIRE 443 BLOOMS -1.15 444 HEAVYSHAPE 1.0 445 BILLETS -1.14 -1.06 -1.06 -1.06 -1.0 446 LIGHTSHAPE 1.0 447 BARS 1.0 448 REBARS-LD 1.0 449 REBARS-SD 1.0 450 WIRE 1.0 451 SCRAP .05 .03 .04 .04 .04 .0 452 453 TABLE AFUND(CS,PS) A RATRIX FOR FUNDIDORA 454 455 PIG-PEL PIG-ORE PELT-C 456 457 ORE-N -.29 -1.38 458 ORE-CONC -.99 459 PELLETS -1.38 -.29 1.0 460 COKE -.69 -.75 461 LIMESTONE -.24 -.27 462 PIG-IRON 1.0 1.0 463 NAT-GAS -.051 -.029 464 ELECTRIC -.06 -.036 -.045 465 WATER -.003 -.001 466 PERRO-ALLO -.065 -.065 467 468 + STL-O-S STL-BOF-P STL-BOF-S STL-OH-S2 469 470 ORE-N -.02 -.02 471 FUEL-OIL -.079 -.079 472 PIG-IRON -.74 -.96 -.81 -.32 473 NAT-GAS -.078 -.078 474 SCRAP -.42 -.15 -.27 -.80 CAMS 1.0 M EX I C S S T EE L M 0 DE L FOR 1979 01/13/83 09.02.38. PACE 11 PRODUCTION 475 PERS-ALLO -.012 -.012 -.012 -.012 476 REPSAC -.012 -.006 -012 477 LIMO -14 -.14 478 STEEL-LIQ 1.0 1.0 1.0 1.0 479 ELECTRIC -.072 -.068 -068 -.072 480 481 + SHOOT SLAB-ROLL PLATE HOT-SHEET PICKLES COLD-SHET 482 483 SCRAP .01 .10 .10 .13 484 STEEL-LIQ -1.04 485 STOOL-ING 1.0 -0.04 486 SLABS 1.0 -1.12 -1.05 M KbMTRIP 10 1.0 -1.0 489 PECK-STEEP 1.0 -1.17 490 COLD-STROP 1.0 491 492 + ANNEALED TOMPOSES BLOOM-ROLL BILT-ROL LIGHTSAPE 493 484 SCRAP .10 495 STEEL-IN 496 COLD-STRIP -1.0 497 AWL-STRIP 0 498 TEMP-STROP 0 '4t) 499 BLOOMS 1.0 -1.03 500 BILLETS 1.0 -0.14 501 LIOHTSHAPE 1.0 502 503 + WIRE REBARS-SD 504 505 SCRAP .04 .04 506 BILLETS -1.06 -1.96 507 RERS-SD 1.0 508 WIRE 1.0 509 510 511 51 DATA FOR THE P10-ORE ASS PIG-PEL PROCESSES WIRE SERIED 912 F ROM BF No. 2 ABS SF HO. 3 DATA POE 1875 AS REPORTED IN 513 (9- VOL 3) TABLE 3.3.6 514 DATA FOR STL-OH-S ARE PROM 0A08 SOUREE TABLE 3.4.6 515 516 517 TABLE AHTL(CS,PS) A MATRIX POE HYLSA SB MONTERREY 518 5189 SPONGE STL-EAP-SP STL-EAF-S INGOT SLAB-ROLL 520 521 PELLETS -1.38 522 NAT_ORE -.470 -.05 523 5105CR 6.0 -1.09 -.60 524 SCRAP -.46 .05 525 FERRO-ALLO -.012 -.012 526 REFRAC -.006 -.006 GAMS 1.0 M E X I C 0 S T EE L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 12 PRODUCTION 527 ELECTRODES -.0052 -.0052 528 DOLOMITE -.009 -.009 529 LIME -.007 -.007 530 STEEL-LIQ 1.0 1.0 -1.02 531 STEEL-ING 1.0 -1.07 532 SLABS 1.0 533 ELECTRIC -.10 -.68 -.60 534 535 + HOT-SHEET PICKLED COLD-SHEET ANNEALED 536 537 SCRAP .05 .06 .02 538 SLABS -1.07 539 PLATE 540 HOT-STRIP 1.0 -1.06 541 PICK-STRIP 1.0 -1.05 542 COLD-STRIP 1.0 -1.0 543 ANL-STRIP 1.0 544 545 + TEMPERED TINNING 546 547 SCRAP .03 .01 548 ANL-STRIP -1.04 549 TEMP-STRIP 1.0 -1.02 550 TIN 1.0 551 552 * DATA FOR SAF FROM (15), ROLLING PROCESSES FROM (9 VOL II) 553 * VERIFY SCRAP GENERATION AND ELECTRICITY 554 555 556 TABLE AHYLP(CS,PS) A MATRIX FOR HYLSA IN PUEBLA 557 558 SPONGE STL-EAF-SP STL-EAF-S BILLETS-CC 559 560 PELLETS -1.38 561 NAT-GAS -.420 562 SPONGE 1.0 -1.09 563 SCRAP -1.06 564 FERRO-ALLO -.014 -.012 565 REFRAC -.006 -.006 566 ELECTRODES -.0052 -.0052 567 DOLOMITE -.009 -.009 568 LIME -.007 -.007 569 STEEL-LIQ 1.0 1.0 -1.06 570 BILLETS 1.0 571 ELECTRIC -.010 -.68 -.50 572 573 + LIGHTSHAPE BAR-ROLL REBARS-LD REBARS-SD WIRE 574 575 SCRAP .04 .04 .04 .03 .03 576 BILLETS -1.06 -1.06 -1.06 -1.05 -1.05 577 LIGHTSHAPE 1.0 578 BARS 1.0 CAMS 1.0 M E X I C 0 S T E E L m 0 DE L FOR 1979 01/13/83 09.02.38. PAGE 13 PRODUCTION 579 REBARS-LD 1.0 580 REBARS-SD 1.0 581 WIRE 1.0 582 ELECTRIC -.03 -.025 -.025 -.03 -.03 583 584 * ROLLING PROCESSES FROM (9-II), SPONGE AND ST-EAF FROM PLANT VISITS 585 * AND (15) 586 587 588 TABLE ATAM(CS,PS) A MATRIX FOR TAMSA 589 590 SPONGE STL-EAF-SP STL-EAF-S INGOT 591 592 PELLETS -1.38 593 NAT-GAS -.50 594 SPONGE 1.0 -1.09 595 SCRAP -1.06 596 FERRO-ALLO -.033 -.033 597 REFRAC -.006 -.006 598 ELECTRODES -.0052 -.0052 599 DOLOMITE -.009 -.009 600 LIME -.007 -.007 601 STEEL-LIQ 1.0 1.0 -1.06 602 ING-BLOOMS 1.0 603 ELECTRIC -.01 -.68 -.50 604 605 + BILLET-ROL LIGHTSHAPE BAR-ROLL SEAM-ROL 606 607 SCRAP .01 .04 .04 .35 608 ING-BLOOMS -1.03 -1.45 609 BILLETS 1.0 -1.06 -1.06 610 LIGHTSHAPE 1.0 611 BARS 1.0 612 SEAMLESS 1.0 613 614 615 AS(CS,FS,-SICARTSA") - ASIC(CS,PS); 616 AS(CS,PS,"AHMSA") - AAHM(CS,PS); 617 AS(CS,PS,-FUNDIDORA") - APUND(CS.PS); 618 AS(CS,PS,"HYLSA-) - AHYL(CS,PS); 619 AS(CS,PS,"HYLSAP") - ANYLP(CS,PS); 620 AS(CS,PS,"TAMSA") - ATAM(CS,PS); 621 622 623 TABLE BM(MM,PM) CAPACITY UTILIZATION MATRIX FOR MINES 624 625 MIN-N MIN-S MIN-TR CONC-S CONC-TR CONC-N MIN-CO 626 627 MINE-EQ 1 1 1 628 CONC-MAG I I 629 CONC-FLOT 630 MINE-CO OAMS 1.0 M E X I C 0 S T EE L M 0 DE L FOR 1979 01/13/83 09.02.38. PAGE 14 PRODUCTION 631 632 TABLE BR(MR,PR) CAPACITY UTILIZATION FOR RAW MATERIALS PLANTS 633 634 COKE-HD PELT-C 635 636 COKE-OVEN 1 637 PELLET 1 638 639 TABLE BS(MS,PS) CAPACITY UTILIZATION MATRIX FOR STEEL MILLS 640 641 COKE-HD COKE-HI PIG-ORE PIG-SIN PIG-PEL PIG-PEL-M 642 643 COKE-OVEN 1 1 644 BLAST-FURN 1 1 .96 1 645 646 + SPONGE STL-OH-P STL-OH-S STL-OH-S2 647 648 BLAST-FURN 649 DIRECT-RED 1 650 OPENHEARTH 1 1 1 651 652 + STL-BOF-P STL-BOF-S STL-EAF-SP STL-EAF-S 653 654 BOF 1 1 655 ELEC-ARC 1 I 656 657 + SLABS-CC BILLETS-CC INGOT SLAB-ROLL BLOOM-ROLL 658 659 CONCAS-SL 1 660 CONCAS-BI 1 661 INGOT-CAST 1 662 PRIMARY-FL 1 663 PRIMARY-NF 1 664 665 + BILLET-ROL PLATE HOT-SHEET PICKLED COLD-SHEET 666 667 PLATE-MILL 1 668 HOT-MILL 1 669 PICKLELINE 1 670 COLD-MILL 1 671 BILLET 1 672 673 + ANNEALED TEMPERED TINNING EAVYSHAPE LIGHTSHAPE 674 675 ANNEAL 1 676 TEMPERMILL 1 677 TIN-LINE 1 678 HEAVYSMILL 1 679 BAR-MILL 1 680 681 + BAR-ROLL REBARS-LD REBARS-SE WIRE SEAM-ROL 682 GAMS 1.0 m E x i c 0 S T E E L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 15 PRODUCTION 683 BAR-MILL 1 1 684 WIRE-MILL 685 SEAML-MILL U4 686 687 + PELT-C SINTER 688 689 PELLET 1 690 SINTER 691 GANS 1.0 H E X I C 0 S T E E L H 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 16 CAPACITY 693 TABLE KM(MM,IM) INITIAL CAPACITIES FOR MINES (1000 TPY) 694 695 P-COLORADA LASTRUCHAS LA-PERLA CERRO-MER HERCULES 696 697 MINE-EQ 4000 2700 1000 3000 1000 698 CONC-MAG 4000 1500 699 CONC-FLOT 1000 3000 700 701 702 + LA-CHULA EL-ENCINO COAHUILA 703 704 MINE-EQ 500 3000 705 CONC-MAG 3000 706 MINE-CO 7000 707 708 TABLE KR(MR,IR) INITIAL CAPACITIES FOR RAW MATERIAL PLANTS (1000 TPY) 709 710 PENACOL LAPERLA ALZADA ESPERANZAS 711 712 PELLET 3000 600 1500 713 COKE-OVEN 684 714 715 716 TABLE KS(MS,IS) INITIAL CAPACITIES FOR STEEL MILLS (1000 TPY) 717 718 SICARTSA AHMSA FUNDIDORA HYLSA HYLSAP TAMSA 719 720 PELLET 1850 750 721 SINTER 1500 722 COKE-OVEN 660 2100 723 BLAST-FURN 1100 3247 1400 724 DIRECT-RED 660 1000 270 725 OPENNEARTH 1500 850 726 BOF 1300 2070 1500 727 ELEC-ARC 1000 560 450 728 CONCAS-SL 710 729 CONCAS-BI 1300 560 730 INGOT-CAST 2600 2000 1000 420 731 PRIMARY-FL 1850 1450 1000 732 PRIMARY-NF 1200 733 PLATE-MILL 960 250 734 HOT-MILL 1600 870 900 735 PICKLELINE 1600 575 650 736 COLD-MILL 1495 500 600 737 ANNEAL 1348 420 450 738 TEMPERMILL 1225 520 450 739 TIN-LINE 315 70 740 BILLET 1000 200 741 HEAVYSMILL 200 742 BAR-HILL 600 135 430 80 743 WIRE-MILL 600 270 200 744 SEAML-MILL 280 GAMS 1.0 B K I S C 0 S T E E L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 17 CAPACITY 745 746 747 * SICARTSA 748 * 749 * 1. COKE-OVEN (1) 2200 T/DAY - 660 MT/A BASED ON STATED COAL MIX 750 * 2. BLAST-FURN (1) 3300 T/DAY WITH 330 DAYS/YEAR - 1100 MT/A 751 * 3. ALL CAPACITIES FROM (1) UNLESS OTHERWISE NOTED 752 * 753 * AHMSA 754 * 755 * 1. ALL CAPACITIES FROM (10) UNLESS OTHERWISE NOTED 756 * 757 * FUNDIDORA 758 * 759 * 1. COKE PLANT IS AT THE MINE 760 * 2. ALL CAPACITIES FROM (12) UNLESS OTHERWISE NOTED 761 * 3. OPEN HEARTH CAPACITY IS FOR STEELSHOP NO. 2 FROM (9 - VOL 1) 762 * TABLE 3.4.3 763 * 764 * HYLSA 765 * 766 * 1. ALL CAPACITIES FROM (9 - VOL 1) UNLESS OTHERWISE NOTED 767 * 2. ONLY ROUGH ESTIMATES FOR PICKLE, ANNEALING, AND TEMPER LINES 768 * 3. HONTERREY VISIT APRIL 1981 769 * 770 * HYLSAP 771 * 772 * 1. DATA OBTAINED DURING PLANT VISIT 773 * 774 * TAMSA 775 * 776 * 1. ALL CAPACITIES FROM(9 -VOL 1) 777 * 2. MONTERREY VISIT 1981 778 779 780 PARAMETER UT(IS) CAPACITY UTILIZATION / SICARTSA .5, (AHMSA,FUNDIDORA,TAMSA) .9, HYLSA 1, HYLSAP 1.1 / 781 782 KM(MM,IM) - .9*KM(MM,IK); 783 KR(MR,1R) - .9*KR(MR,IR); 784 KS(HS,ES) - UT(IS)*KS(MS,IS); 785 GAMS 1.0 M E K I C 0 ST E E L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 18 DEMAND DATA 787 SET OS DEMAND DATA COMPONENTS / DEMAND, SEMI-INT, ADJ-DEM / 788 789 TABLE HROD(CS,CS) MAP FOR DISAGGREGATING DEMAND FOR REINFORCED BARS TO LARGE AND SMALL DIAMETERS 790 791 REBARS-SD REBARS-LD 792 REBARS .4 .6 793 794 795 TABLE DENDAT(CS,DS) DEMAND AND SEMI-INTGRATED OUTPUT (1000 TPY) 796 797 DEMAND SEMI-INT 798 799 PLATE 1050 800 HOT-STRIP 600 801 TEMP-STRIP 1250 802 TIN 400 803 HEAVYSHAPE 300 130 804 LIGHTSHAPE 310 160 805 BARS 340 155 806 REBARS 1150 395 807 WIRE 600 190 808 SEAMLESS 800 809 RAILS 110 810 812 TABLE REGDEM(CS,J) REGIONAL DEMAND PER PRODUCT ( % OF TOTAL 813 814 MEXICO-DF PUEBLA QUERETARO SAN-LUIS MONTERREY 815 816 PLATE 63.5 0.2 0.3 0.3 31.0 817 HOT-STRIP 41.9 2.8 1.6 2.8 36.2 818 TEMP-STRIP 45.1 2.5 4.5 1.1 41.7 819 TIN 87.6 0.3 9.4 820 HEAVYSRAPE 36.6 2.2 3.2 0.8 12.9 821 LIGHTSHAPE 74.4 2.5 1.9 1.8 8.1 822 BARS 46.6 4.2 23.5 2.2 11.2 823 REBARS 46.7 10.3 4.0 3.4 12.8 824 WIRE 61.2 5.3 3.9 3.7 12.2 825 SEAMLESS 10.5 28.0 0.4 0.2 18.4 826 RAILS 40.0 5.0 5.0 10.0 20.0 827 828 + GJADALAJA L-CARDENAS COATZACOAL 829 830 PLATE 4.5 0.1 0.1 831 HOT-STRIP 12.6 0.5 1.6 832 TEMP-STRIP 4.3 0.4 0.4 833 TIN 2.7 834 HEAVYSHAPE 42.6 1.4 0.3 835 LIGHTSHAPE 8.9 1.6 0.8 836 BARS 11.8 0.4 0.1 837 REBARS 11.8 6.1 4.9 838 WIRE 9.8 1.9 2.0 W о д ы о о ы � � О W д "� д б U н • д � д i. .. - £ "� .-. w д У н U М 2 Н W £ •• 1 U W О • д О £ V О W U W и а v е ❑ - О а н а •. � £ г а д Н G и а н а а д о � нн о ы � о � оо н д р о w о о о .+ с� и а н о о о г е £ г w а � о .... о х i � w iд ti.. .. о н о о 3 д U � й V д .] пи Ч W и а £��U аН д U � О W^i � v W Ч � W д w � W у о У Н О д О д С] V W и ГL ыi д U а т г avU О б F £ д е д д А н б ... £ n О г д И SW £ О .е tWi £ V U д W U И� .] Х й •• W R1 д д д v v 41 д £ О 1£� д F � т w z � й г а да и е' н г °а н н н n о w х о о w а z д •� е н о w н н S О '£ у V д Ч. о т F т О F н р д £ v б W и .+О ио 1 1 Р F�е^ _ U •. .+ w ью ti 5 м д- W F д 6 £ д д д О О �а W Н д £ F и оН Фд W W д д6 Fd е£l � W 1 Ud у у U а А F Н д а д и Н н F Н £ Н �+ F F ,и F W Ч д W д 6 6 д N W 'а д W V х д ��-l д а � S � � w w_ а д х и£т �6 д о иа' 6 U- о и 6 S £д С W дддд О W и� ie # О .в ТО н Hf.1 И ЕDО�ОЧ N n W rnО.в NПО�П �{OV v дддИИИииЙииИИ•D�D�O�ee�O�O ФаDОра0Фа0ФФарФиФФсО W W щеЛарррtрарарФгGа0М � о 1S7 CAMS 1.0 M E X I C 0 S T E E L M 0 D E L FOR 1979 01/13/83 09.02.38. PACE 20 PRICES 867 SET SP DOMESTIC AND INTERNATIONAL PRICES / DOMESTIC, INTERNAT 868 869 870 PARAMETER MC(PM) MINING COST (PESOS PER TON) / MIN-CO 250, (MIN-S,ltIN-N,MIN-TR) 100 871 872 TABLE PRICES(CS,SP) DOMESTIC AND INTERNATIONAL PRICES OF COMMODITIES $73 874 DOMESTIC INTERNAT 875 (79 FESOS) (79 DOLLARS) NEW MARGIN 002-040 877 878 ORE-CONC 28 TONS 879 PELLETS 430 45 TONS 880 COAL-D 880 TONS 881 COAL-1 63 TONS 882 COKE 1200 100 TONS 883 FUEL-OIL 1000 TONS 100OLITERS 884 LIMESTONE 120 TONS 885 NAT-GAS 322 152 1000 M3 886 SCRAP 3050 120 TONS 887 FERRO-ALLO 16000 TONS 888 REFRAC 50000 TONS DOLOMITE 00 TONS ::9 LIME 9 0 TONS 0.1 891 ELECTRODES 48000 TONS 892 ELECTRIC 552 1000 KWH 893 PLATE 347 TONS 894 HOT-STRIP 393 TONS 895 TEMP-STRIP 373 TONS 896 TIN 393 TONS 897 BILLETS 300 TONS 898 HEAVYSHAPE 338 TONS 899 LIGHTSHAPE 364 TONS 900 BARS 350 TONS 901 REBARS-LD 347 TONS 902 REBARS-SD 368 TONS 903 WIRE 434 TONS 904 SEAMLESS 455 TONS 905 RAILS 345 TONS NEW MARGIN 002-120 907 DIFFERENT PRICES FOR LIMESTONE: AHMSA 90, FUNDIDORA 60, SICARTSA 120 908 PRICE OF NATURAL GAS FOR SICARTSA EXPANSIONS: 30% LOWER. 909 910 911 PARAMETER PD(CS) PRICES OF DOMESTIC PRODUCTS (1979 PESOS PER UNIT) 912 PV(CS) PRICES OF IMPORTS (1979 US $ PER TON) 913 PE(CS) EXPORT PRICES (1979 US $ PER TON) 914 SH SHADOW EXCHANGE RATE (1979 PESOS PER US$); 915 916 SH - 25.0 917 PD(CRAW) - PRICeS(CRAW,"DOMESTIC"); 918 PV(CRV) - PRICES(CRV,"INTERNAT"); '59 GAMS 1.0 M E X I C 0 S T E E L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 22 TRANSPORT DATA 922 TABLE RDSJ(IS,J) RAIL DISTANCES FROM STEEL MILLS TO MARKETS (KS) 923 924 MEKTGO-FPUENLA QUERETARO SAN-LOIS MONTERREY 925 926 SICARTSA 819 995 691 5 1305 927 AHMSA 1204 1300 949 592 218 928 FUNDIDORA 1017 1139 253 499 929 HYLSA 1017 1159 755 498 930 HYLSAP 185 410 667 1085 931 TAMSA 428 315 650 907 1330 932 933 + GUADALAJA L-CARDES COATZACOAL 934 935 SICARTSA 704 1638 936 AHMSA 1125 1416 180 937 FUNDIDORA 1030 1322 1756 938 NYLSA 1030 1322 1756 939 HYLSAP 260 995 671 940 TAMSA 1005 1239 550 941 942 * DATA PROM (20) AND (21) 943 * ONLY STEEL PLANTS INCLEDED, SINCE PELLET AND COKE PLANTS DO ROT 944 * SEED FINAL PRODECTS TO MARKETS 945 946 TAS3LE EDSS(IS,IS) RAIL DISTANCES BETWEEN STEEL PLANTS 947 948 SICARTSA ABMSA FENDIDORA SYLSA HYLSAP TANSA 949 950 AMA 1416 951 PUNDIDODA 1322 218 952 HYLSA 1322 21a 10 953 HYLSAP 995 1300 1159 1159 954 TASA 1239 1499 1405 1400 315 955 956 TARLE RR(IR,IS) SAIL DSTANCED FROM RAW MATERIAL PLANTS TO STEEL MILLS 957 958 SICARTSA ANMSA PUNDIORA HYLSA HYLSAP TAMSA 959 960 PENACOL 1037 1490 1396 1390 1116 1360 961 LAPERLA 1797 405 621 621 1595 1703 962 ALZADA 920 1360 1260 1260 990 1300 963 ESFERANCAS 1522 121 340 240 1422 1670 964 965 966 DATA PROM (19) AND(20) 967 968 TABLE RDMS(IM,I1) RAIL STANCES PROS MIMES TO STEEL PLANTS 969 970 SICAETSA AHMSA PUNIDORA BYLSA HYLSAP TAMSA 971 972 P-COLORADA 1037 1490 1396 1596 1116 1360 973 LASTRUCHAS 1416 1)22 1322 995 1239 CAMS 1.0 M E X I C 0 S T E E L M 0 DE L FOR 1979 01/13/83 09.02.38. PAGE 23 TRANSPORT DATA 974 LA-SERLA 1797 403 621 621 1595 1927 975 CR0-MER 1275 677 636 636 1245 1489 976 HERCULES 1613 219 563 563 1411 1655 977 LA-CHULA 1044 1480 1300 1300 1112 1356 978 EL-ENCINO 965 1401 1307 1307 1033 1277 979 COAHFILA 1500 170 400 400 1420 1700 980 981 TABLE RDMR(IM,IR) RAIL STANCES FROM HINES TO RAW MATERIAL PLANTS 982 983 PENACOL LAPERLA ALZADA ESPERANZAS 984 985 P-COLORADA 1803 70 986 LASTRUCHAS 1037 1797 920 987 LA-FERLA 1803 1800 988 ERS-MER 1100 400 1500 989 HERCULES 1616 400 1600 990 LA-CHOLA 90 1800 60 991 EL-ENCIO 90 1000 40 992 COAHUILA 15 993 994 DATA FROM (19) 995 DATA FROM (IS) 996 DISTANCES PEON COAL MES TO PELLET PLANTS ROT IHCLUDED FOE OBVIOU 997 998 TABLE RDPS(*,TS) RAIL DISTANCES PROM NEAREST PORT TO STOOL MILL 999 1000 SICASA AHM04 FUNDIDORA HYLSA SYLSAF TAMSA 1001 1002 GOLF 1239 739 521 521 35 1003 PACIFIC 1416 1372 1322 995 1239 1004 1005 1006 1007 DATA FROM (19) AND (20) 1008 DISTANCES ON THIS TA011 ARE FROM PLAIT TO NEAST FORT. 1009 FOE GOLF: ICARTSA,HYLSAP,TAMSA ASS SEW-N P0 VEACRUZ. 1010 ASA,FUNDIDORA,HYLSA,AW-TAMP TO TAMPICO. 1011 RIO-COAT TO COATZACOALCS. 1012 F00 PACIFIC: ALL PLAITS TO LAlAES CAR@ENAS AX.CPT I 1013 * HEW-HANT TO MANZANILLO 1014 1015 1016 1017 TABLE RDPJ(*,J) SAIL DISTANCES FROM NEAREST RT TO MARETS 1018 1019 011110-OF P1EBLA QUERTARO SAN-LUIS MONTERRE 1020 1021 GOLF 428 315 600 044 521 1022 PACIFIC 019 995 691 875 530o 1023 1024 + GUADATLAJA L-CARDENAS COATZACOAL 1025 GAMS 1.0 M EX I C 0 S T E E L N 0 D EL FOR 1979 01113/83 09.02.38. PAGE 24 TRANSPORT DATA 1026 GOLF 995 1239 1027 PACIFIC 300 1638 1028 1029 1030 . DATA BASE FROM (20) ANS (21) 1031 * NAREST FORTS FOR 1032 * GULF: VEACRUZ TO MEXICO-DF,FOEBLA,QOORETARO,TOLOCA,L-CARDENAS 1033 * TAMFICO TO SAN-LUIS,GUADALAJARA 1034 * MATAMOROS TO MONTERROY 1035 * COATZACOALCOS TO COATZACOAL 1036 * PACIFIC: ALL TO LAZARD CARDENAS, EXCEPT FOR MANZANILLO TO GUADALAJA 1037 1038 14INRO - IRON OR AND COAL MINUS 1039 PLANTS - RAW MATERIAL PLANTS 1040 MILLS - STEEL MILLS 0041 PARAMETER MUMR(IM,IR) TRANSPORT COST: MONES TO PLANTS (00$ PER TON) 1042 MUMS(IM,RS) TRANSPORT COST: MINES TR ROLLS (00$ FOR TOM) 1043 MS(UR,OD) TRANSPORT COST: PLANTR TO ROLLS (08$ PER TSR) 1044 MUSS(IS,ES) TRANSPORT COST: BETWREN MILLS (00$ PER TON) 1045 MUSJ(1S,J) TRANSPORT COOT: MILLS TO RARKETS (00$ FEE TON) 041046 HRPSE(1S) TRANSPORT COST: PORTS TO MILLRS RAW MATERIAL (00$ PER TON) K)1047 MUSPF(IS) TRANSPORT COST: MILLS TO POETS -FERAL PRODUCT ($ FOR TON) 1048 MOPS(S) TRANSPORT COOT: FORTS TO MARETS (00B$ FER TON); 1049 1050 RDPS(SMORT",IS> MIN(RDPS("GULF,IS) ,RDPS("ACIFIC",IS) 1051 EDSS(IS,ISP) MAX(R55S(IS,ISP),RDSS(ISP,IS)); 1052 RDPS(RNORT.I) MIN(RDPJ("GLF,J ),RDPS(PACIIC", ) 1053 1054 MUMR(IR,IR) - (35 + 1055 MR(IM.IR) - (35 + .RM M,RS))$RDMS(IM,IS); 1056 MURS(IR,IS) - (35 + .11*EDRS(IR.IS))$RDRS(IRjS); 1057 MtSS(IR,ISP) -(30 + .11*RDS(IS,ISP))$RDSS(US,ISP); 1008 RUPRR(Is) - (35 + .11*RDPS('S"ORT",0))$.DPR("SMOP.T,IS); 1059 MUSJ(OS,S) - (60 + .19*RDSJ(1S,J))$RRRJ(IS,J); 1060 HORPP(ES) - (60 + .19*RDPD(0SH0RT",IR3)$RDPS(SRORT",ID); 1061 MOPS(S) (60 + .19*RDPS'ORTS))$RDPJ(RSORT,J); 1062 1063 DATA BASE PROM (19) ANR (20) 1064 OLD FIGURES WERE 57.16 + .194 AND 17.46 + .106 1065 DISPLAY RUME, MOMS, RURS, NODS, MOSS, MUPSR, MRSFF, MOPS; 1066 1067 PARAMEOTER LOSS(CS) CORRECTION FACTOR FOR CORE LOSSES DURIRG UNTRMILL SHIPMENTS OP COKE 1068 PCT(O) SNARE OP PELLET SHIPRERTS FROM PENlA COLARADA RY OWNERSHIP 1 2 - .46, 3 .1, 4 -.26, 5 .18 I 1069 1070 LOSD(C) - 1; LOS(COKEA) A 0.91 CAMS 1.0 M E X I C 0 S T F E L M 0 DE L FOR 1979 01/13/83 09.02.38. PAGE 25 MODEL REDUCTION 1072 NET MMPO(MM,IM) PRODUCTIVE UNIT POSSIBILITY: MINES 1073 MRPOS(MR,ER) PRONUCTIVE UNIT PSSIBILITY: RAW MATERIAL PLANTS 1074 MSPOS(MS,IS) PRONUCTIVE UNIT POSSIBILITY: STEEL MILLS 1075 1076 PMPOS(PM,TM) PROCESS PSSIBILITY: MOSES 1077 PRPOS(PN,IR) PROCESS PSSIBILITY: RAW MATERIAL PLANTS 1078 PNPOS(PS,IS) PROCESS PSSIBILITY: NTEEL ROLLS 1079 1080 CMPOSP(CN,IS) COMMOITY PRODUCTIOU POSSIBILITY: MINES 1081 CRPOSP(CS,IR) COMMODITY PRODCTION POSSIBILITY: RAW MATERIAL PLANTS 1082 CSPOSP(CO,IS) COMMODITY PROUCTION PONSIDELITS: STEEL SELLS 1083 1084 CMPSN(CO,IM) COMMUNITY CONSUMPTION POSSIDILITY: MINES 1085 CRPOS(CS,IR) COMMODITY CONSUMPTEON POSSIDILITY: RAW MATERIAL PLANTS 1086 CSPOSN(CS,IS) COMMODETY CONSUMPTION POSSIDILETY: STEEL MILLS 1087 1088 MMPOS(MM,IM) - KM(MM,IM); 1089 MRPOS(MR,IR) KR(MR,IR); 1090 MSPON(MN,IS) KS(MEIO); 1091 1092 PMPOS(PM,NM)$SUM(CM, AM(CM,PM)$RES(CM,UM) NE U 1093 SUM(MM$(NOT MMPOS(MM,IM)), BM(MM,PM) NE U) EQ 1094 PRPOS(PR,IR)$SUM(CR, AR(CR,PR) NE 0 1095 DUM(MR$(NOT MRPOS(MR,SR)), BR(MR,PR) NE N) EQ 1096 PSPOS(PS,IS)$SEM(CS, AS(CS,PS.IS) NE 0 1097 SUM(MS$(NOT MSPON(MS,IS)), BN(MS,PS) NE 5) EQ 0 1098 1099 CMPOSP(CM,SM) DUM(PM$PMPOS(PM,IM), AM(C4,PM) CT 0) 1100 CRPOSP(CR,NR) - SUM(PR$PRPOS(PR,tR), AR(CR,PR) CT 0) 1101 CSPOSP(CS,IN) - SUM(PS$PSPOS(PS,IS), AS(CS,PS,US) ST 0) 1102 1103 CMPOSN(CM,IM) - SUM(PM$PMPOS(PM,IM), AM(CM,PM) LT U) 1104 CRPOEN(CR,IR) SUM(PR$PRPO(PR,IR), AR(CR,PR) LT 0); 1105 CSPODN(CN,IS) SUM(PN$PSPOS(PE,IS), AS(CS,PS,IE) LT 0); 1106 1107 DISPLAY MMPOS, MRPOS, MSPOS, PMPOS, PRPOS, PSPOS, CMPOSP, CRPSP, 1108 COP, CMP0S8, CRP009, CSPOON 1109 1110 DRT IMRRS(IM) RESTRICTRD MINES / LASTRUCHAS 1111 IMFRRR(IM) PE MINES 1112 XMPOS(CS.IM,*) POSSIBLE SHIPMENTS OP MINENO PRODUCTS TO RAW MAT PLANTS; 1113 1114 IMFREE(IM) - YRO - IMRES(RM) 1115 1116 YMPS("COAL-D,'COAHUILA",'ESPERANZAS') YEN; 1117 XMPOD(ORRCONC',"PCOLORADA",PRNACOL) YER; 1118 XMPOS(OR-CONC",LA-PERLA"LAPERLA) TED; 1119 XMPOS(ORE-CONC,EL-ENCINO,ALZAOA) YES; 1120 KMPON(CM,LADTRDCMA8 *NECARTSA') TEN; 1121 xMPOg( CM ,IMIPREE,IS) YEN; 1122 GAMS 1.0 M E XI C 0 S T E U L M 0 D E L FOR 1979 01/13/83 09.02.38. PASS 26 EQUATIONS 1124 EQUATIONS 1125 1126 MBM(CM,IM) MATERIAL BALANCE: MINES (1000 TPY) 1127 MBR(CR,IR) MATERIAL BALANCE: RAW MATERIAL PLANTS (1000 UNITS TOY) 1128 MBS(CS,IS) MATERIAL BALANCE: STEEL MILLS (1000 UNITS TPY) 1129 1130 CCM(MM,IM) CAPACITY CONSTRAINT: MINES (1000 TPY) 1131 CCR(MR,IR) CAPACITY CONSTRAINT: RAW MATERIAL PLANTS (1000 TPY) 1132 CCS(MS,IS) CAPACITY CONSTRAINT: STEEL MILLS (1000 TPY) 1133 1134 MREQ(CF,J) MARKET REQUIREMENTS (1000 TPY) 1135 ME(CF) EXPORT BOUNDS (1000 TPY) 1136 ME2 TOTAL EXPORTS (1000 TPY) 1137 1138 PELPC(0) PELLET SHIPMENTS FROM PENA COLARADA (1000 TPY) 1139 PELAL PELLET SHIPMENTS FROM ALZADA (1000 TPY) 1140 1141 ACOST ACCOUNTING: TOTAL COST (MILL US$) 1142 AREC ACCOUNTING: RECURRENT COST (MILL 0S$) 1143 ATRANS ACCOUNTING: TRANSPORT COST (HILL US$) 1144 AIMP ACCOUNTING: IMPORT COST (MILL US$) 1145 AEXP ACCOUNTING: EXPORT REVENUE (MILL 01$) 1146 1147 VARIABLES 1148 1149 ZM(PM,IM) PROCESS LEVEL: MINES (1000 TPY) 1100 ZR(PR,IR) PROCESS LEVEL: RAW MATERIAL PLANTS (1000 TPY) 1151 ES(PS,IS) PROCESS LEVEL: STEEL MILLS (1000 TPY) 1152 1103 KM(CS,IH,*) SHIPMENTS: MINE PRODUCTS (1000 TPY) 1154 XR(CS,IR,IS) SHIPMENTS: FROM RAW MATERIAL PLANTS (1000 TPY) 1155 RS(CS,IS,ISP) SHIPMENTS: INTERPLANT (1000 TPY) 1156 XF(CS,IS,J) SHIPMENTS: FINAL PRODUCTS (1000 TPY) 1107 1158 UR(CS,IR) DOMESTIC PRODUCTS PURCHASE: RAW MAT. PLANTS (1000 UNITS TPY) 1159 US(CS,IS) DOMESTIC PRODUCTS PURCHASE: STEEL MILLS (1000 UNITS TPY) 1160 1161 E(CS,IS) EXPORTS (1000 TPY) 1162 VS(CS,IS) IMPORTS TO STEEL SILLS (1000 TPY) 1163 VF(CS,J) IMPORT OF FINAL PRODUCTS (1000 TPY) 1164 1165 COST TOTAL COST (MILL US) 1166 RECURRENT COST (MILL US$) 1167 TRANSPORT COST (MILL USS) 1168 IMPORT COST (MILL US$) 1169 EXPORT COST (MILL US$) 1170 1171 POSITIVE VARIABLES ZM, ZR. ZS, XM, XR, ES, XF, OR, US, E, VS, VF; £9' * É Én Én I Én Én É Én É Én Én É + + •n É Én Én• t I Én É n n É Én n nÉ É É É Én Én Én É n É Én É Én Én Én Én Én Én Én Én Én Éncc - c GAMS 1.0 M E X I C 0 5 T EE L m 0 DE L FOR 1979 01/13/83 09.02.38. PAGE 28 EQUATIONS 1200 ME2.. SUl((CP,Io)$CSPOSP(CF,IS), E(CF,IS)) -L- ETOT 1201 1202 PELPC(O).. SUMCIS$(OWN(O,IS)*CSPOSN(PELLETS',TS)), XRCPELLETS,PENACOL,IS)) L- PCT(O)*KR('PNLLET,PNACOL); 1203 1204 PELAL.. SUM(ISEX$CSPOSN(PELLETS',ISE), XR(PSLLSO'ALZAA,ISEX)) -- 0; 1205 1206 ACOST.. COST - RECURNENT + TRANSPORT + SH*(IMPOEXPORT) 1207 1208 AREC.. RECUNRENT -E- ( SUM((PN.TM)$PMPOO(PM,TM), MC(PM)*ZM(PN,IM)) 1209 + SUMUCRAW,I)$CRPON(CRA,IR), PD(CRAW)-UR(CRAM,1R)) 1210 + SM((CRAW,TS)$CSPOSN(CRAW,1S), PD(CRAW)*US(CNAW,IS)) )/1000; 1211 1212 ATRANS.. TRANSPORT - ( SSM((CMR,TM,IR)O(CNPOSP(CNR,IM)*XMPOO(CMR,IM,IR)*CRP0SNCMR,IR)) 1213 1214 + SUN(CN,IM,IS)$(CNPOSP(CNS.TM)*CSPOON(CMS.IO)*XNPOO(CM,I,1S)), 1215 mttms(15,IS)*RM(CMS,SM,IT)) 1216 + SUM((CRS,IR,IS)$(CRPOSP(CRS,IR)*CSPOSN(CRS,1S)), MORS(IR,IS)*XR(CRS,IR,IS)) 1217 + sUM((Css,ls,isp)$(Csposp(CSS,1s)*CIPOIN(Css,Isp)), M1uSS(CS,ISP)*XS(CSS,IS.ISP)) 1218 + SUM((CF,1S,J)$CSPOSP(CF,IS), MUSJ(IS,J)*XF(CF,TO,J)) 1219 + SM((CRV,IS)$CSPOSN(CRV,IS), MUPSR(TS)*VS(CRV,ES)) 1220 + SUM((CF,Ig)$CSPOSP(CF,IO), MUSPF(IS)*E(CF,IS)) + SOM((CF,J), MUPJ(J)*VF(CF.J)) )/1000; 12l1 1222 AIMP.. IMPORT -E- SUM((CRV,1I)$CSPOSN(CRV,IS), PV(CRV)*VS(CRV,IS)) + SUM((CFV,J), PV(CFV)*VF(CFV,J)) )/1000; 1223 1224 AEP.. EXPORT E- SUMCE,IS)$CSPOSP(CE,bS), PE(CE)*E(CE.IS)) )/1000; 1225 CAMS 1.0 M E K I C O S T E E L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 29 EQUATIONS 1226 MODEL ONE /ALL/ ; 1227 1228 * DEVINE RUN 1 1229 1230 VS.UP("COKE",IS) - 0; US.UP("SCRAP",IS) - 0: 1231 1232 KS(MS,"AHMSA") = KS(MS,"AHMSA")*0.9; L233 KS(MS,"FUNDIDORA") - KS(MS,"FUNDIDORA")*0.95; 1234 DISPLAY KS; 1235 1236 SOLVE ONE MINIMIZING COST USING LP ; GAMS 1.0 N E X I C 0 ST E E L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 30 REFERENCE MAP OF VARIABLES VARIABLES TYPE REFERENCES AAHM PARAM4 REF 616 DEFINED 388 DCL 388 ACoST EQU DEFINED 1206 DCL 1141 AEXP EQU DEFINED 1224 DCL 1145 AFUND PARAM REF 617 DEFINED 453 DCL 453 AHYL PARAM REF 618 DEFINED 517 DCL 517 AHYLP PARAM REF 619 DEFINED 556 DCL 556 AIMP EQU DEFINED 1222 DCL 1144 AM PARAM REF 1092 1099 1103 1174 DEFINED 326 DCL 326 AR PARAM REF 1094 1100 1104 1178 DEFINED 338 DCL 338 AREC EQU DEFINED 1208 DCL 1142 AS PARAM4 REF 1096 1101 1105 1182 DEFINED 615 616 617 618 619 620 DCL 324 ASIC PARAM REF 615 DEFINED 349 DCL 349 ATAM PARAM REF 620 DEFINED 588 DCL 588 ATRANS EQU DEFINED 1212 DCL 1143 BM PARAM REF 1093 1190 DEFINED 623 DCL 623 DR PARAM4 REF 1095 1192 DEFINED 632 DCL 632 BS PARAM REF 1097 1194 DEFINED 639 DCL 639 CCM EQU DEFINED 1190 DCL 1130 CCR EQU DEFINED 1192 DCL 1131 CS EQU DEFINED 1194 DCL 1132 CE SET REF 920 1188 3*1224 DEFINED 319 CONTROL 920 1224 DCL 304 CF SET REF 2*848 2*850 2*854 855 856 857 862 1134 1135 1188 4*1196 3*1198 2*1200 2*1218 3*1220 DEFINED 301 CONTROL 319 320 848 850 854 855 856 857 865 1196 1198 1200 1218 2*1220 DCL 301 CFV SET REF 919 2*1222 DEFINED 320 CONTROL 919 1222 DCL 306 CA SET REF 315 326 2*1092 1099 1103 1126 1174 3*1175 4*1176 DEFINED 279 CONTROL 1092 1099 1103 1120 1121 1174 DCL 279 CMPOSN SET REF 1108 DEFINED 1103 DCL 1084 CKPOSP SET REF 1107 1176 1179 1183 1212 1214 DEFINED 1099 DCL 1080 CMR SET REF 1179 3*1212 1213 DEFINED 290 CONTROL 1212 DCL 290 CMS SET REF 1183 3*1214 1215 DEFINED 293 CONTROL 1214 DCL 293 COST VAR REF 1206 1236 DCL 1165 CR SET REF 1094 1100 1104 1127 1178 7*1179 4*1180 DEFINED 283 CONTROL 1094 1100 1104 1178 DCL 283 CRAW SET REF 917 1179 1186 3*1209 3*1210 DEFINED 274 CONTROL 917 1209 1210 DCL 274 CRPOSN SET REF 1108 1175 1179 1209 1212 DEFINED 1104 DCL 1085 CRPOSP SET REF 1107 1180 1184 1216 DEFINED 1100 DCL 1081 CRS SET REF 1180 1184 3*1216 DEFINED 296 CONTROL 1216 DCL 296 CRV SET REF 918 1186 2*1219 3*1222 DEFINED 287 CONTROL 918 1219 1222 DCL 287 CS SET REF 274 279 283 Z87 290 293 296 299 301 304 306 324 338 349 388 453 517 556 588 615 616 617 618 619 620 2*789 795 812 2*846 3*848 3*850 872 911 912 913 1067 1080 1081 1082 CAMS 1.0 M E X I C 0 S T EE L M 0 DE L FOR 1979 01/13/83 09.02.38. PAGE 31 REFERENCE MAP OF VARIABLES VARIABLES TYPE REFERENCES 1084 1085 1086 1096 1101 1105 1112 1128 1153 1154 1155 1156 1158 1159 1161 1162 1163 1182 4*1183 4*1184 4*1185 5*1186 3*1187 5*1188 DEFINED 217 CONTROL 615 616 617 618 619 620 846 2*848 2*850 1070 1096 1101 1105 1182 DCL 217 CSPOSN SET REF 1108 1176 1180 1186 1187 1202 1204 1210 1214 1216 1217 1219 1222 DEFINED 1105 DCL 1086 CSPOSP SET REF 1108 1185 1188 1196 1198 1200 1217 1218 1220 1224 DEFINED 1101 DCL 1082 Css SET REF 1185 1187 3*1217 DEFINED 299 CONTROL 1217 DCL 299 D PARAM REF 855 856 857 859 1196 DEFINED 854 855 856 857 DCL 852 DEMDAT PARAM REF 2*846 848 854 859 DEFINED 795 846 848 DCL 795 DS SET REF 795 DEFINED 787 DCL 787 E VAR REF 1171 1188 1198 1200 1220 1224 DCL 1161 EMAX PARAM REF 1198 DEFINED 865 DCL 862 ETOT PARAM REP 1200 DEFINED 865 DCL 863 EXPORT VAR REF 1206 1224 DCL 1169 IM SET REP 315 693 782 968 981 1041 1042 2*1054 2*1055 1072 1076 1080 1084 1088 1092 1093 1099 1103 1110 1111 1112 1414 1126 1130 1149 1153 2*1174 2*1175 3*1176 3*1179 3*1183 4*1190 2*1208 2*1212 2*1213 2*1214 2*1215 DEFINED 64 CONTROL 782 1054 1055 1088 1092 1099 1103 1114 1174 1179 1183 1190 1208 1212 1214 DCL 64 IMFREE SET DEFINED 1114 CONTROL 1121 DCL 1111 IMPORT VAR REF 1206 1222 DCL 1168 CORES SET REF 1114 DEFINED 1110 DCL 1110 IR SET REP 708 783 956 981 1041 1043 2*1054 2*1056 1073 1077 1081 1085 1089 1095 1100 1104 1127 1131 1150 1154 1158 3*1175 2*1178 4*1179 2*1180 2*1184 4*1192 2*1209 2*1212 2*1213 3*1216 DEFINED 76 CONTROL 783 1054 1056 1089 1094 1100 1104 1175 1178 1184 1192 1209 1212 1216 DCL 76 iS SET REP 310 313 322 324 716 780 2*784 922 2*946 956 968 998 1042 1043 2*1044 1045 1046 1047 2*1050 2*1051 2*1055 2*1056 2*1057 2*1058 2*1059 2*1060 1074 1078 1082 1086 1090 1096 1097 2*1101 2*1105 1028 1132 1151 1154 1155 1156 1159 1161 1162 3*1176 2*1180 3*1182 2*1183 1184 IL85 3*1186 1187 3*1188 4*1194 2*1196 2*1198 2*1200 3*1202 2*L210 2*1214 2*1215 3*1216 3*1217 3*1218 3*1219 3*1220 2*1222 2*1224 DEFINED 83 CONTROL 784 1050 1051 1055 1056 1057 1058 1059 1060 1090 1096 1101 1105 1121 1176 1180 1182 1194 1196 1198 1200 1202 1210 1214 1216 1217 1218 1219 1220 1222 1224 2*1230 DCL 83 ISEX SET REF 2*1204 DEFINED 313 CONTROL 1204 DCL 313 ISP SET REF 2*1051 2*1057 1155 2*1185 2*1187 3*1217 CONTROL 1051 1057 1185 1187 1217 DCL 322 J SET REF 812 850 854 855 856 922 1017 1045 1048 2*1052 2*1059 2*1061 1134 1156 1163 1188 3*1196 2*1218 2*1220 GAMS 1.0 M F X I C 0 S T E E L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 32 REFERENCE MAP OF VARIABLES VARIABLES TYPE REFERENCES 1222 DEFINED 92 CONTROL 850 854 855 856 1052 1059 1061 1188 1196 1218 1220 1222 DCL 92 KM PARAM REF 782 1088 1190 DEFINED 693 782 DCL 693 KR PARAM REF 783 1089 1192 1202 DEFINED 708 783 DCL 708 KS PARAM REF 784 1090 1194 1232 1233 1234 DEFINED 716 784 1232 1233 DCL 716 L SET DEFINED 104 DCL 104 LOSS PARAM REF 1184 1185 DEFINED 2*1070 DCL 1067 MAX FUNCT REF 1051 MBM EQU DEFINED 1174 DCL 1126 MBR EQU DEFINED 1178 DCL 1127 MBS EQU DEFINED 1182 DCL 1128 MC PARAM REP 1208 DEFINED 870 DCL 870 ME EQU DEFINED 1198 DCL 1135 ME2 EQU DEFINED 1200 DCL 1136 MIN FUNCT REF 1050 1052 MM SET REF 623 693 782 1072 1088 2*1093 1130 3*1190 DEFINED 109 CONTROL 782 1088 1093 1190 DCL 109 MmPOS SET REF 1093 1107 1190 DEFINED 1088 DCL 1072 MR SET REF 632 708 783 1073 1089 2*1095 1131 3*1192 DEFINED 116 CONTROL 783 1089 1095 1192 DCL 116 MREQ EQU DEFINED 1196 DCL 1134 MROD PARAM REF 2*848 2*850 DEFINED 789 DCL 789 MRPOS SET REF 1095 1107 1192 DEFINED 1089 DCL 1073 MS SET REF 639 716 784 1074 1090 2*1097 1132 3*1194 1232 1233 DEFINED 121 CONTROL 784 1090 1097 1194 1232 1233 DCL 121 MSPOS SET REF 1097 1107 1194 DEFINED 1090 DCL 1074 MUMR PARAM REF 1065 1213 DEFINED 1054 DCL 1041 Mums PARAM REF 1065 1215 DEFINED 1055 DCL 1042 MUPJ PARAM REP 1065 1220 DEFINED 1061 DCL 1048 MUPSR PARAM REF 1065 1219 DEFINED 1058 DCL 1046 MURS PARAM REF 1065 1216 DEFINED 1056 DCL 1043 MSJ PARAM REP 1065 1218 DEFINED 1059 DCL 1045 MUSPF PARAM REF 1065 1220 DEFINED 1060 DCL 1047 muSS PARAM REF 1065 1217 DEFINED 1057 DCL 1044 0 SET REP 310 1068 1138 2*1202 DEFINED 308 CONTROL 1202 DCL 308 ONE MODEL REF 1236 DEFINED 1226 DCL 1226 OWN SET REF 1202 DEFINED 310 DCL 310 PCT PARAM REF 1202 DEFINED 1068 DCL 1068 PD PARAM REP 1209 1210 DEFINED 917 DCL 911 PE PARAM REF 1224 DEFINED 920 DCL 913 PELAL EQU DEFINED 1204 DCL 1139 PELPC EQU DEFINED 1202 DCL 1138 PM SET REF 326 623 870 1076 1092 1093 2*1099 2*1103 1149 3*1174 3*1190 3*1208 DEFINED 153 CONTROL 1092 1099 1103 1174 1190 1208 DCL 153 PMPOS SET REP 1099 1103 1107 1174 1190 1208 DEFINED 1092 DCL 1076 GAMS 1.0 H E X I C 0 S T E E L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 33 REFERENCE MAP OF VARIABLES VARIABLES TYPE REFERENCES PR SET REF 338 632 1077 1094 1095 2*1100 2*1104 1150 3*1178 3*1192 DEFINED 165 CONTROL 1094 1100 1104 1178 1192 DCL 165 PRICES PARAM REF 917 918 919 920 DEFINED 872 DCL 872 PRPOS SET REF 1100 1104 1107 1178 1192 DEFINED 1094 DCL 1077 PS SET REF 324 349 388 453 517 556 588 615 616 617 618 619 620 639 1078 1096 1097 2*1101 2*1105 1151 3*1182 3*1194 DEFINED 170 CONTROL 615 616 617 618 619 620 1096 1101 1105 1182 1194 DCL 170 PSPOS SET REF 1101 1105 1107 1182 1194 DEFINED 1096 DCL 1078 PV PARAM REF 2*1222 DEFINED 918 919 DCL 912 RDER PARAM REF 2*1054 DEFINED 981 DCL 981 EONS PARAM REF 2*1055 DEFINED 968 DCL 968 RDFJ PARAM REF 2*1052 2*1061 DEFINED 1017 1052 DCL 1017 RDPS PARAM REF 2*1050 2*1058 2*1060 DEFINED 998 1050 DCL 998 RRES PARAM REF 2*1056 DEFINED 956 DCL 956 RDSJ PARAM REF 2*1059 DEFINED 922 DCL 922 RDSS PARAM REF 2*1051 2*1057 DEFINED 946 1051 DCL 946 RECURRENT VAR REF 1206 1208 DCL 1166 REGDEM PARAM REF 850 854 859 DEFINED 812 850 DCL 812 RES SET REF 1092 DEFINED 315 DCL 315 Ski PARAM REF 1206 DEFINED 916 DCL 914 SP SET REF 872 DEFINED 867 DCL 867 TRANSPORT VAR REF 1206 1212 DCL 1167 UR VAR REF 1171 1179 1209 DCL 1158 us VAR REF 1171 1186 1210 DEFINED 1230 DCL 1159 UT PARAM REF 784 DEFINED 780 DCL 780 VF VAR REF 1171 1196 1220 1222 DCL 1163 VS VAR REF 1171 1186 1219 1222 DEFINED 1230 DCL 1162 XF VAR REF 1171 1188 1196 1218 DCL 1156 IM VAR REF 1171 1175 1176 1179 1183 1213 1215 DCL 1153 XMPOS SET REF 1175 1176 1179 1183 1212 1214 DEFINED 1116 1117 1118 1119 1120 1121 DCL 1112 XR VAR REF 1171 1180 1184 1202 1204 1216 DCL 1154 XS VAR REF 1171 1185 1187 1217 DCL 1155 ZM VAR REF 1171 1174 1190 1208 DCL 1149 ZR VAR REF 1171 1178 1192 DCL 1150 ZS VAR REF 1171 1182 1194 DCL 1151 SETS CE COMMODITIES FOR EXPORTS CF FINAL PRODUCTS CFV IMPORTED FINAL PRODUCTS CM COMMODITIES AT MINES CMPOSN COMMODITY CONSUMPTION POSSIBILITY: MINES CMPOSP COMMODITY PRODUCTION POSSIBILITY: MINES CMR COMMODITIES SHIPPED FROM MINES TO RAW MATERIAL PLANTS CMS COMMODITIES SHIPPED FROM MINES TO STEEL PLANTS CR COMMODITIES AT RAW MATERIAL PLANTS GAMS 1.0 M E X I C 0 S T E EL M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 34 REFERENCE MAP OF VARIABLES SETS CRAW DOMESTIC SAW MATERIALS CEFOEM COMMODITY CONSUMPTION FOSSIBILITY: RAW MATERIAL PLANTS CEFOOF COMMODITY FRODECTION POSSIBILITY: RAW MATERIAL PLANTS CRS COMMODITIES SNIPPED PROM RAW MATERIAL PLANTS TD STEEL MILLS CRV IMPORTED RAW MATERIALS ARE INTERMEDIATE PRODCTS CS COMMODITIES AT STEEL MILLS CSPOSN COMMODITY CONDUMPTION POSSIBILITY: STEEL MILLS CSpOSP COMMODETY PROEUCTION POSSIBILITY: STEEL MILLS cgs COMMODITIES FOR INTERPLANT SHIPMENT RETRESN STEEL MILLS OS DEMAND DATA COMPONENTS IN IRON ORE AND COAL MINES IMFREE FREE MINES IMSES RESTRICTED MINER IR RAW MATERIAL PLAS is STEEL MILLS ISEX PLANTS ECLUDES FROM ALZADA SEES ISP ALIAS FOR ID j DOMESTIC MARKET ARIAS L EXPORT POINTS 155 PRODUCTIVE SMITE AT MINED MMPOS FRODUCTIVE UNIT POSSIBILITY: MIRES ME PRODUCTIVE ENITD AT RAW MATERIAL PLANTS MR MEPOS FRODUCTIE OMIT POSSINILITY: RAW MATERIAL PLANTD s PRODUCTIVE EMITS AT STEEL MILLS MSPOS PRODUCTIVE EMIT PSSIBILITY: DTEEL MILLS 0OWSEN NUMBERD OWN OWNER GROUPS PM PRODCTION PROCESSES AT MINED PMOS PROCESS POSSIBILITY: MIMES PR PRODECTION PROCESSES AT RAW MATERIAL PLANTD PRESS PROCESS POSSIBILITY: RA MATERIAL PLANTS PS PRODCTION FROCESSES AT STEEL MILLS pFOS PROCESS FOSEIRILITY: STEEL MILLS RES RESERVE TYPES AT LOCATIS PO OMESTIC AND INTERNATIONAL PRICES EHFOS POSIBLE SHIFMENTS OF MINING FRODUCTS TO RAW MAT PLANTS PARAMETERS AAREM A MATRI FOR AHMEA AFUND A MATRIX FOR FUNDIDORA AHYL A MATRIX FOR NYLSA IS MONTERREY AHYLP A MATRIX FOR NYLSA IN PUERLA AM A MATRIX FOR MESSRS PRODUCTS AR A MATRIX FOR RAM MATERIAL PLANTS AS INPET OTPUT RELATIONS FOE STEEL MILLS ASIC A MATRIX FOE SICARTDA ADA A MATRIX FOR TAMEA Bm CAPACITY ISLIZATION PMATRI FOE MINES R CAFACITY TILIATION FOR RA MATERIALS PLANTS CAMS 1.0 M C X I C 0 S T E P L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 35 REFERENCE MAP OF VARIABLES PARAMETERS BS CAPACITY UTILIZATION MATRIX FOR STEEL MILLS D ADJUSTED DEMAND FOR SEMI-INTECR PLANTS (1000 TPY) DEMDAT DEMAND AND SEMI-INTGRATED OUTPUT (1000 TPY) EMAX EXPORT LIMIT BY PRODUCT (1000 TPY) ETOT TOTAL EXPORT LIMIT (1000 TPY) KM INITIAL CAPACITIES FOR MINES (1000 TPY) KR INITIAL CAPACITIES FOR RAW MATERIAL, PLANTS (1000 TPY) KS INITIAL CAPACITIES FOR STEEL MILLS (1000 TPY) LOSS CORRECTION FACTOR FOR COKE LOSSES DURING INTERMILL SHIPMENTS OF COKE MC MINING COST (PESOS PER TON) MROD MAP FOR DISACREGATINC DEMAND FOR REINFORCED BARS TO LARGE AND SMALL DIAMETERS MUMR TRANSPORT COST: MINES TO PLANTS (US$ PER TON) MuMs TRANSPORT COST: MINES TO MILLS (US$ PER TON) MUPJ TRANSPORT COST: PORTS TO MARKETS (US$ PER TON) MUPSR TRANSPORT COST: PORTS TO MILLS - RAW MATERIAL (US$ PER TON) MURS TRANSPORT COST: PLANTS TO MILLS (US$ PER TON) MUSJ TRANSPORT COST: MILLS TO MARKETS (US$ PER TON) MUSPF TRANSPORT COST: MILLS TO PORTS - FINAL PRODUCT ($ PER TON) muss TRANSPORT COST: BETWEEN MILLS (US$ PER TON) PET SHARE OF PELLET SHIPMENTS FROM PENA COLARADA BY OWNERSHIP PD PRICES OF DOMESTIC PRODUCTS (1979 PESOS PER UNIT) PH EXPORT PRICES (1979 US $ PER TON) PRICES DOMESTIC AND INTERNATIONAL PRICES OF COMMODITIES PV PRICES OF IMPORTS (1979 US $ PER TON) RDMR RAIL DISTANCES FROM MINES TO RAW MATERIAL PLANTS RES RAIL DISTANCES FROM MINES TO STEEL PLANTS RDPJ RAIL DISTANCES FROM NEAREST PORT TO MARKETS RDPS RAIL DISTANCES FROM NEAREST PORT TO STEEL MILL RDRS RAIL DISTANCES FROM RAW MATERIAL PLANTS TO STEEL RILLS RDSJ RAIL DISTANCES FROM STEEL MILLS TO MARKETS (KM) RDSS RAIL DISTANCES BETWEEN STEEL PLANTS REGDEM REGIONAL DEAND PER PRODUCT ( % OF TOTAL SH SHADOW EXCHANGE RATE (1979 PESOS PER US$) UT CAPACITY UTILIZATION VARIABLES COST TOTAL COST (MILL US$) E EXPORTS (1000 TPY) EXPORT COST (MIllL US$) IMPORT COST (MILL US$) RECURRENT COST (MILL USS) TRANSPORT COST (MILL US$) UR DOMESTIC PRODUCTS PURCHASE: RAW MAT. PLANTS (1000 UNITS TPY) US DOMESTIC PRODUCTS PURCHASE: STEEL MILLS (1000 UNITS rPY) VF ImPORT OF FINAL PRODUCTS (1000 TPY) VS IMPORTS TO STEEL MILLS (1000 TPY) XF SHIPMENTS: FINAL PRODUCES (1000 TPY) XM SHIPMENTS: MINE PRODUCTS (1000 TPY) XR SHIPMENTS: FROM RAW MATERIAL PLANTS (1000 TPY) CAMS 1.0 M E X I C 0 S T E L M 0 D E L FOR 1979 01/13/83 09.02.38. PAGE 36 REFERENCE MAP OF VARIABLES VARIABLES XS SHIPMENTS: INTERPLANT (1000 TPY) ZM PROCESS LEVEL: MINES (1000 TPY) ZR PROCESS LEVEL: RAW MATERIAL PLANTS (1000 TPY) zS PROCESS LEVEL: STEEL MILLS (1000 TPY) EQUATIONS ACOST ACCOUNTING: TOTAL COST (MILL USS) AEXP ACCOUNTING: EXPORT REVENUE (MILL US$) AIMP ACCOUNTING: IMPORT COST (MILL US$) AREC ACCOUNTING: RECURRENT COST (MILL US$) ATRANS ACCOUNTING: TRANSPORT COST (MILL US$) CCM CAPACITY CONSTRAINT: MINES (1000 TPY) CCR CAPACITY CONSTRAINT: RAW MATERIAL PLANTS (1000 TPY) CCS CAPACITY CONSTRAINT: STEEL MILLS (1000 TPY) MBM MATERIAL BALANCE: MINES (1000 TPY) MBR MATERIAL BALANCE: RAW MATERIAL PLANTS (1000 UNITS TPY) MBS MATERIAL BALANCE: STEEL MILLS (1000 UNITS TPY) ME EXPORT BOUNDS (1000 TPY) ME2 TOTAL EXPORTS (1000 TPY) MREQ MARKET REQUIREMENTS (1000 TPY) PELAL PELLET SHIPMENTS FROM ALZADA (1000 TPY) PELPC PELLET SHIPMENTS FROM PENA COLARADA (1000 TPY) MODELS ONE 7 Results of the Large Static Model AN ILLUSTRATIVE SOLUTION to the static model is presented in this chapter. The purpose is not to obtain the optimal operating pattern for the Mexican steel industry but rather to characterize the solution for this kind of problem and to discuss the strong and weak points of the analysis. This solution is a logical step along the way to the small dynamic model of the industry presented in chapter 8. Although some of the actual institutional constraints facing the industry in 1979 were imposed on the model, the solution was neither expected nor desired to be the same as the actual pattern of operation in the industry. It was hoped, however, that the solution might provide some ideas about gains in efficiency that could have been made in the industry. Several of the institutional constraints listed below are relaxed in alternative solutions to the model presented in the last part of this chapter. The constraints are: (1) no domestic scrap purchases, (2) strikes at AHMSA and Fundidora, (3) limited exports, (4) limited interplant shipments of intermediate products, and (5) no imports of coke. The first constraint arises from an assumption that the domestic rerollers would buy all of the domestic scrap and leave the major plants to import any scrap required above and beyond their own internally generated scrap. The second constraint comes from actual strikes in 1979 that reduced the effective capacity of AHMSA by 10 percent and that of Fundidora by 5 percent. Exports are limited by the third constraint to a total of no more than 250,000 tons of final products--roughly the magnitude of exports in 1979. The fourth constraint limits interplant shipments to coke, pellets, and sponge iron. In some of the experiments, 175 176 MEXICAN CASE STUDY this constraint is dropped and interplant shipments of a wide variety of intermediate products are permitted. This provides a useful means of mitigating the effects of bottlenecks at individual plants. The final constraint prohibits the importation of coke, though importation of coal is permitted. This corresponds to the national policy of using domestic raw material insofar as possible. With all these institutional constraints in place, the results of the model correspond roughly to the actual steel production (in millions of tons) in Mexico in 1979: Model solution Actual Open hearth 1.94 1.47 Basic oxygen 2.70 2.61 Electric arc 2.00 2.02 The model solution will differ in many particulars from the actual situation, but these results indicate that the model is fairly close to reality in the crucial dimension of total steel production by type of technology. First, the solution with all five constraints will be discussed in some detail to give an idea of the richness of results which can be obtained with this class of steel industry models. Then in the last part of the chapter the experiments are discussed to analyze the benefits which might have accrued to the industry from the removal of different combinations of these constraints. Each solution will be discussed briefly. The solution of the version of the model with all the constraints is presented here by following the flow of material through the steel industry from raw material to final products. Thus, the discussion will proceed from mines, to separate pellet and coke plants, to steel mills, and finally to markets. At each step the incoming material, the processing of that material, and the outgoing material will be discussed and illustrated. Raw Material Coal and Coke The flows of coal and coke between plants are shown in figure 7-1. The domestic coal mines are located in a small region near Sabinas in the state of Coahuila. In the solution of this model for 1979 the coal mines extract 6.3 million tons of raw unwashed coal. This yields 3.0 million tons of washed coal, of which 2.08 million tons are shipped from the mines to RESULTS OF LARGE STATIC MODEL 177 Figure 7-1. Flows of Coal and Coke (thousand metric tons a year) Coahuila 920 Las Esperanzas AHMSA 470 0 Fundidora Imports O SICARTSA 450 O Coal mines A Separate coke plants O Steel mills Coal -- Coke AHMSA.' The remaining 920 thousand tons are shipped to the nearby coking plant at Las Esperanzas where they are transformed into 620 thousand tons of coke, which are then shipped to AHMSA and Fundidora. SICARTSA imports 450 thousand tons of coal which it transforms to coke in its own ovens. Iron Ore and Pellets The flows of ore and pellets are shown in figure 7-2. Although there are other mines in Mexico, the six identified here are the largest and most 1. The apparent accuracy of a number such as 2.08 million tons is misleading. The actual quality of our data would justify rounding off such numbers to 2 million tons, but we have retained all the digits in this discussion to make it easier to retain the consistency of the detailed results that models of this kind typically yield. 178 MEXICAN CASE STUDY Figure 7-2. Flows of Ore and Pellets (thousand metric tons a year) La Perla Q - 140 534\ AHMSA La Perla 540 439 Fundidora OdHercules -r291 / HYLSA /265 634./,- 175 o 'Cerro de Mercado 1,242 270 619 Alzada 730 1, 3 .'El Encino 2,523 702 b Peita Colorado HYLSAP 335 TAMSA 0 Mines 915. Las Truchas A Separate pellet plants O Steel mills SICARTSA 108 - - - Lump ore -.-- Concentrated ore Pellets important. One other mine in the model (La Chula) does not enter the solution of this run. To begin with the southernmost mine in the solution, Las Truchas produces 1.36 million tons of ore (see table 7-1). About 108 thousand RESULTS OF LARGE STATIC MODEL 179 Table 7-1. Extraction at Mines (thousand metric tons) Mine Commodity Production Pefa Colorado Southern ore 3,230 Las Truchas Las Truchas ore 1,362 La Perla Northern ore 900 Cerro de Mercado Northern ore 2,041 Hercules Northern ore 900 La Chula Southern ore 0 El Encino Southern ore 1,710 Coahuila Raw unwashed coal 6,300 tons of the ore are shipped directly to SICARTSA and the remaining 1.254 million tons are passed through the magnetic separator to yield 915 thousand tons of concentrated ore which is shipped to SICARTSA in a slurry pipeline. The mine at Pefia Colorado produces 3.23 million tons of ore that is passed through a magnetic separator to yield (3.23/1.28) = 2.523 million tons of concentrated ore, which is shipped from the mine to the pellet plant at Pefia Colorado. The pellets produced at Pefia Colorado cannot be shipped freely to any steel mill since the shipment pattern is constrained by the ownership (see table 7-2). AHMSA owns 46 percent, TAMSA owns 18 percent, Fundidora owns 10 percent, and HYLSA and HYLSAP together own 26 percent. The model therefore includes con- straints that no more than 46 percent of the pellets produced at Pefia Colorado may be shipped to AHMSA. Shipments to the other plants are constrained in a similar manner. For example, the capacity of the pellet plant at Pefia Colorado is given in the model as 3 million tons of pellets a year, and it is assumed that all productive units can be operated at 90 percent of rated capacity. Thus, the usable capacity is 2.7 million tons of pellets. AHMSA's share of this is (0.46)(2.7) = 1.242 million tons. The upper Table 7-2. Ownership Quota for Pellet Plants (percent) Pellet plant Peia Colorado Alzada AHMSA 46 0 TAMSA 18 0 HYLSA and HYLSAP 26 100 Fundidora 10 0 180 MEXICAN CASE STUDY bound on shipments to TAMSA is (0.18)(2.7) = 486 thousand tons, and the bound on shipments to Fundidora is (0.10)(2.7) = 270 thousand tons. Finally, the sum of the shipments to HYLSA and HYLSAP is constrained to be less than 702 thousand tons; that is, less than 26 percent of the capacity may be used to provide shipments to HYLSA and HYLSAP [(0.26)(2.7) = 702 thousand tons]. Figure 7-2 shows that the shipments to AHMSA, Fundidora, and the HYLSA plants are bound by the ownership constraints. The shipment from Pefia Colorado to AHMSA is 1.242 million tons, to Fundidora is 270 thousand tons, and to HYLSAP is 702 thousand tons. The bound on shipments to TAMSA is not tight since the bound is 486 thousand tons and the shipment level is 335 thousand tons of pellets. In the model all of the HYLSA and HYLSAP quota is shipped to HYLSAP. HYLSA then gets its pellets from the pellet plant at Alzada and from Fundidora. In effect, Fundidora sells its quota to HYLSA. The shipments from Alzada (figure 7-2) go to HYLSA (619 thousand tons) and to HYLSAP (730 thousand tons). Table 7-2 shows that all of Alzada's product must go to these two plants. Proceeding from the southern to the northern mines, one encounters next in figure 7-2 the Cerro de Mercado mine. This mine ships 634 thousand tons of concentrated ore and 875 thousand tons of lump ore to Fundidora in Monterrey. This mine also ships 265 thousand tons of lump ore to AHMSA. The rest of AHMSA's requirements are satisfied in this solution by 140 thousand tons of lump ore and 540 thousand tons of pellets from La Perla. Shipments of pellets are also received from Fundidora (439 thousand tons) and from SICARTSA (175 thousand tons). It is unlikely that Fundidora actually sold its quota of Pefia Colorado pellets to HYLSA or that Fundidora and SICARTSA shipped pellets to AHMSA in 1979. The model solution suggests, however, that this alternative might be explored in the future as a means of increasing the output of the industry without additional investment. Of course, this assumes that the railroad system has the capacity to carry those quantities of raw material. This assumption has been of questionable validity in some years. Steel Mills Each steel mill in Mexico has a different capacity configuration. For example, some have rolling mills for flat products, others for nonflat RESULTS OF LARGE STATIC MODEL 181 products, and one has both types of capacity. As a result of this pattern, each mill has a comparative advantage in producing certain products. In this section, material flow charts for each plant illustrate the flow of commodities through the plants-from inputs of pellets, coke, and natural gas to the final product. No attempt is made to be comprehensive by showing all the inputs, outputs, processes, and productive units used in the model. Rather, the flow charts illustrate the key commodity flows and productive units in each plant. Each of the six plants will be discussed in turn. In the SICARTSA plant, shown in figure 7-3, coke and pellets are used in a blast furnace to Figure 7-3. Commodity Flows at SICARTSA (thousand metric tons a year) Coal 448 Coke Lump ore Pellets oven 108 175 Coke Pellets Pellet Concentrated ore 324 750 plant 915 324C7 91Scrap Light shapes 1457 large-diameter Billets SOO 154 mea func 6195O Reinorcig rds' ollng mllsContinuous small-diameter ocasting 115 Weifreigros 170-jamtrBllt 182 MEXICAN CASE STUDY Table 7-3. Capacity and Shadow Prices at SICARTSA (capacity in thousand metric tons) Shadow price Capacity (thousand pesos Productive unit Available Utilized per ton) Pellet plant 925 925 0.38 Coke oven 330 324 0 Blast furnace 550 541 0 BOFS 650 650 4.49 Continuous casting of billets 650 619 0 Bar mill 300 300 0.02 Wire mill 300 285 0 make hot metal (pig iron), which is reduced in basic oxygen furnaces and then rolled into shapes. In this solution for 1979 the plant produces roughly half a million tons of hot metal which is combined with 117 thousand tons of scrap to produce 584 thousand tons of final products. The final product mix includes light shapes, large- and small-diameter reinforcing rods, and wire in roughly equal amounts. The bottleneck for SICARTSA in this solution is the basic oxygen furnaces (BoFs). This is apparent from a glance at the capacity rentals (shadow prices on capacity constraints) shown in table 7-3. The other nonzero shadow prices are for the pellet plant and the bar mill. The pellet mill is used to full capacity by shipping the excess above the plant requirement to AHMSA (175 thousand tons). AHMSA, the largest plant in Mexico, has a blast furnace, both open hearths and BOFs, and rolling mills for both flat products and shapes. Figure 7-4 shows that in the solution for 1979 the plant transformed about 4 million tons of pellets, ore, and sinter into roughly 2 million tons of final products. About 1.7 million tons of the final products are flat products and 0.3 million tons are shapes. Before tracing through the commodity flows in figure 7-4, look at the available capacity, the capacity utilized, and the shadow price results from this solution of the model in table 7-4. The bottleneck is in the casting units -both the continuous casting units for slabs and the ingot casting facilities. The steelmaking facilities are also used at virtually full capacity. Recall, however, that a strike decreased the effective capacity of the plant by 10 percent in this solution, and that the full utilization of the RESULTS OF LARGE STATIC MODEL 183 Figure 7-4. Commodity Flows at AHMSA (thousand metric tons a year) Sinter Ore 1,305 745 1 ca Coke Pellets 1,532 /- 2,39640 BlastSca afurnaces Hot metal / _2 2,221 Plate 778 Plate1,7 Tinning ml line aBscoye 9 Tin Q 260 0frae 255 Q \ Cold Cold0 S sheet strip 0 ,9 Tempered /0929 millSasH0 she Temper Hot 55 0 csi 669 mill sheet 0 I 1,087 U ot rHot sheet Hot strip Slb2,04 0~~~~4 i137 no HeavOpe Steel il hearth 1,215 Heavfurnaces Reinforc575 Oa castingQ 0 mill rodPrimary castin Hev shape mill Biamr 3 Brml ilesBomn Reinforcing rods, small-diameter Billetml o0\ Wire 219 Wire mill 184 MEXICAN CASE STUDY Table 7-4. Capacity and Shadow Prices at AHMSA (capacity in thousand metric tons) Shadow price Capacity (thousand pesos Productive unit Available Utilized per ton) Sinter plant 1,215 745 0 Coke ovens 1,701 1,384 0 Blast furnaces 2,630 2,071 0 Open hearths 1,215 1,215 0.258 BOFS 1,676 1,573 0 Continuous casting of slabs 575 575 1.273 Ingot casting 2,106 2,106 0.578 Primary mill for flats 1,498 1,375 0 Primary mill for shapes 972 424 0 Plate mill 777 777 0.924 Hot mill 1,296 1,087 0 Pickling line 1,296 1,087 0 Cold mill 1,210 929 0 Annealing 1,091 929 0 Temper mill 992 929 0.966 Tinning mill 255 255 0 Billet mill 810 334 0 Heavy shapes mill 162 28 0 Bar mill 109 109 0.067 Wire mill 218 218 0.257 plant is abetted by the receipt of 175 thousand tons of pellets from SICARTSA and 439 thousand tons of pellets from Fundidora. Table 7-4 gives one result that seems to be incorrect: the open hearths at AHMSA are used to full capacity and the BOFs have excess capacity in this solution. This is akin to one of the results in the small static model. Perhaps this result is due to the fact that the BOFs require relatively higher charges of hot metal and lower charges of scrap than the open hearths. A higher scrap price might therefore reverse this utilization pattern. Since capital costs are treated as sunk costs in this static model, the fact that the BOFs require less capital per ton of steel than do the open hearths plays no role in the decision about which of the existing furnaces to use. The shadow prices in table 7-4 give the amount by which the objective function could be reduced if capacity were to be expanded by 1,000 tons. Of course, this is only true for small changes, in the sense that expanding RESULTS OF LARGE STATIC MODEL 185 the capacity by 1,000 tons might decrease the cost, but expanding it by 2,000 tons could shift the bottleneck to some other productive unit. The shadow prices on the new bottleneck unit would become larger. Even with these limitations there is useful information in the shadow prices. For example, table 7-4 shows that the open hearths, the continuous casting unit for slabs, the ingot casting plant, and the plate, temper, bar, and wire mills are the effective constraints on production at AHMSA in this solution. In figure 7-4 some of the hot metal flows go to the BOFs and some to the open hearths. Most steel goes to ingot casting, and 598 thousand tons is used in the continuous casting unit for slabs. The continuous caster is used at full capacity. The rest of the slabs are produced by the primary Figure 7-5. Receipt of Raw Material by Fundidora (thousand metric tons a year) Las Esperanzas 4, Imported co scrap Electricity 531 136 million kwh Pellets AHMSA 439 Fundidora oTe Pellets --- 291 1HYLSA \ Natural gas 75 million cubic meters Cerro de Mercado Pefia Colorado A Coke plant O Iron ore mine 0 Pellet plant 186 MEXICAN CASE STUDY mill for flats. The blooming mill (primary mill for shapes) plays a similar role for nonflat products. For the last of the three government-owned plants, Fundidora in Monterrey, figure 7-5 shows the receipt of raw material and the shipment of pellets from the plant. Since there is no coking plant at Figure 7-6. Commodity Flows at Fundidora (thousand metric tons a year) 291 Lump ore xHYLSA 875 A3 'HMSA Coke Pellets Pellet Concentrated ore 467 180 plant 634 Scrap Pil.letsOpen Steel 727 270 hearths Scrap Blast 130 Lfurnactes Hotmetal 623 Steel 483 Basic oxygen furnaces Steel Plate 1,209 213 Plate mill Hot sheet Slabs Ingots 323 1,020 ) 1,163 Primary mill Ingot Hot sheet casting 743 Hot sheet Tempered Cold Hot Mill sheet sheet s set 359 359 0- 420 Temper Cold sheet mill Mill RESULTS OF LARGE STATIC MODEL 187 Fundidora, 468 thousand tons of coke are brought in by train from Las Esperanzas. Fundidora has three sources of iron ore in this solution: 875 thousand tons of lump ore from Cerro de Mercado are charged directly to the blast furnace, and 634 thousand tons of concentrated ore from Cerro de Mercado are converted to pellets in the pellet plant. Fundidora also receives 270 thousand tons of pellets from Pefia Colorado. This gives Fundidora an excess of pellets, so 291 thousand tons are sold to HYLSA and 439 thousand tons are sold to AHMSA. Fundidora purchases 531 thousand tons of scrap, 136 million kilowatt-hours of electricity, and 75 million cubic meters of natural gas. This raw material is processed into final products as shown in figure 7-6. Fundidora has a blast furnace, BOFS, and flat product mills as well as some older open hearths. In this solution, the plant produced roughly 1.2 million tons of steel from 623 thousand tons of hot metal and 711 thousand tons of scrap. The steel was then cast into ingots and rolled into 895 thousand tons of flat products. Table 7-5 shows some unused capacity at Fundidora in this solution, mainly because HYLSA and HYLSAP are the least-cost producers with the natural gas and electricity prices used in this solution. As in the solution for AHMSA, the open hearths are more fully utilized at Fundidora than are the BOFs. This occurs in spite of the fact that the Table 7-5. Capacity and Shadow Prices at Fundidora (capacity in thousand metric tons) Shadow prices Capacity (thousand pesos Productive unit Available Utilized per ton) Pellet plant 641 641 0.402 Blast furnaces 1,197 623 0 Open hearths 726 726 0.114 BOFS 1,282 483 0 Ingot casting 1,710 1,163 0 Primary mill for flats 1,239 1,020 0 Plate mill 213 213 2.552 Hot mill 743 743 1.565 Pickling line 491 420 0 Cold mill 427 359 0 Annealing 359 359 0.143 Temper mill 444 359 0 Billet mill 171 0 0 188 MEXICAN CASE STUDY Table 7-6. Steel Production Technologies at AHMSA and Fundidora (tons per ton of steel) Input STL-OH-S STL-OH-S2 STL-BOF-P STL-BOF-S AHMSA Pig iron -0.77 - - 1.02 -0.74 Scrap -0.33 - -0.11 -0.42 Fundidora Pig iron -0.74 -0.32 -0.96 - 0.81 Scrap -0.42 -0.80 -0.15 -0.27 -Not applicable. Note: STL-OH-S = Steel production in open hearths with average scrap charge. STL-OH-S2 = Steel production in open hearths with high scrap charge. STL-BOF-P = Steel production in BoFs with high pig iron charge. STL-BOF-S = Steel production in BOFS with high scrap iron charge. model includes an alternative technology for steel production in the BOFS at Fundidora and AHMSA (see table 7-6). The available technologies include a high-scrap-charge open hearth process (ST-OH-S2), which is not in the model for AHMSA but is the process used at Fundidora. Given the relative price of scrap and cost of hot metal (pig iron), this high-scrap- charge open hearth process is apparently very efficient. The commodity flows in the HYLSA plant at Monterrey are shown in figure 7-7. The plant produces 660 thousand tons of sponge iron by direct reduction of 910 thousand tons of pellets using 356 million cubic meters of natural gas. It also receives about 300 thousand tons of sponge iron from the HYLSAP plant. The sponge iron is then complemented with 123 thousand tons of scrap iron to produce 1 million tons of steel in electric arc furnaces. The steel is then rolled into 800 thousand tons of flat products. Table 7-7 shows that the bottlenecks at the plant are the direct reduction units and the electric arc furnaces. The direct reduction units alone cannot be a bottleneck because there are two alternative processes in the model for producing steel (see the A matrix for HYLSA in the GAMS statement of the large static model in chapter 6, appendix B). One process uses sponge iron and the other uses scrap to produce steel. If there is a shortage of sponge iron, more scrap can be purchased to produce more steel. Thus, the capacity of the electric are furnaces is the most important constraint on total steel production at HYLSA. The result of these constraints on steel production is to leave RESULTS OF LARGE STATIC MODEL 189 Figure 7-7. Commodity Flows at HYL SA (thousand metric tons a year) Natural gas Pellets Scrap Electricity 356 million 910 123 724 million kwh cubic meters1 Direct Steel reduction units Sponge iron 1,000 WSP9660 Electric arc Sponge iron frae 299 Slabs Ingots 916 980 Hot sheet Primary Ingot 517 millcatn Tempered sheet Tempered sheet C)Hot sheet Temper Hot sheet Tin Mill mill 70 .)/23-85 Tinning line Cold sheet 304 U Cold sheet mill substantial unused capacity in the rolling mills at HYLSA aS shown in table 7-7. This raises the possibility that interplant shipments of hot strip could be used to increase the overall efficiency of the industry. This type of shipment is not permitted in this particular solution of the model but will be permitted in some other solutions discussed later in this chapter. 190 MEXICAN CASE STUDY Table 7-7. Capacity and Shadow Prices at HYLSA (capacity in thousand metric tons) Shadow price Capacity (thousand pesos Productive unit Available Utilized per ton) Direct reduction 660 660 0.056 Electric are furnaces 1,000 1,000 4.099 Ingot casting 1,000 980 0 Primary mill for flats 1,000 916 0 Hot strip mill 900 856 0 Pickling line 650 320 0 Cold strip mill 600 304 0 Annealing furnaces 450 304 0 Temper mill 450 293 0 Tinning line 70 70 0.979 A high shadow price of 979 pesos per ton is associated with the tinning line at HYLSA (see table 7-7). This high shadow price stems from the fact that the capacity of the two tinning lines in Mexico (at HYLSA and at AHMSA) have a total effective capacity which is less than total demand. Consequently, it is necessary to import tin at an international price of $393 a ton (see table 6-16), which is substantially above the domestic cost of production. The HYLSAP plant employs the same technology for steel production as does its sister plant, HYLSA. However, HYLSAP specializes in shapes while HYLSA specializes in flat products. Figure 7-8 shows the technology and the commodity flows of the HYLSAP plant in Puebla, which produces about 1 million tons of sponge iron and about 600 thousand tons of steel. Roughly 400 thousand tons of sponge iron are sent to the HYLSA and TAMSA plants. The 600 thousand tons of steel are transformed into 550 thousand tons of shapes. Table 7-8 shows that the shadow price on the electric arc furnaces at HYLSAP is high since this is the effective bottleneck on production in that plant, as it is at HYLSA in Monterrey. One of the shortcomings of the model is shown by the structure of the flow chart for the rolling mills in figure 7-8. In the figure billets can be processed either through the bar mill into light shapes, bars, and large- diameter reinforcing rods, or through the wire mill into small-diameter reinforcing rods or wire. In fact, the two rolling mills act in tandem rather than in parallel. That structure has not yet been fully captured in the RESULTS OF LARGE STATIC MODEL 191 Figure 7-8. Commodity Flows at HYLSAP (thousand metric tons a year) Natural gas Pellets 435 million 1,432 cubic meters Scrap Electricity 1,038 20 440 million kwh Steel 1,038616 Sponge iron 65 1 1 DirectElectric arc reduction furnaces units 299 HYLSA Sponge iron 88 TAMSA Billets O0 0 sLight shapes 581 Cotnuu Continuous .5 casting Bars 126 Reinforcing rod:s' Bar mill large- diameter 202 Reinforcing rods, small-diameter 186 Wire 30 Wire mill model, however, because it required adding additional types of rolling mills and substantially increasing the size of the model. The final plant to consider is TAMSA (figure 7-9), which produces 252 thousand tons of seamless pipe from steel which is in turn produced from sponge iron. Table 7-9 shows that the bottleneck at TAMSA is the seamless pipe mill. 192 MEXICAN CASE STUDY Table 7-8. Capacity and Shadow Prices at HYLSAP (capacity in thousand metric tons) Shadow price Capacity (thousand pesos Productive unit Available Utilized per ton) Direct reduction 1,100 1,038 0 Electric arc furnaces 616 616 5.458 Continuous casting of billets 616 581 0 Bar mill 473 333 0 Wire mill 220 216 0 Figure 7-9. Commodity Flows at TAMSA (thousand metric tons a year) Natural gas Pellets Scrap Electricity 11 million 3 88 cubic meters\kh Sov Sponge iron 0o Steel Direct 2438 reduction Electric arc units furnaces Sponge iron HYLSAP 88 Seamless pipe Ingots 252 365 Seamless Ingot pipe mill casting RESULTS OF LARGE STATIC MODEL 193 Table 7-9. Capacity and Shadow Prices at TAMSA (capacity in thousand metric tons) Shadow price Capacity (thousand pesos Productive unit Available Utilized per ton) Direct reduction 243 243 0.515 Electric arc furnaces 405 387 0 Ingot casting 378 365 0 Bar mill 72 0 0 Seamless pipe mill 252 252 7.649 Markets There are two aspects to the solution of the problem with regard to markets. The first is the flow of final products (1) from plants to domestic markets and to exports and (2) from imports to domestic markets. The second aspect relates to the shadow prices on final products at each market. Total Product Shipments The variable of interest here is x{-, the shipment of final product c from plant i to marketj. Since there are 12 final products, 6 plants, and 8 markets, more than 500 numbers are required to fully specify this part of the solution. Only a small percentage of these numbers will be presented-those representing the largest product flows. The aggregate product flows from plants to markets, the variables x{, are defined as ceCF that is, the total flow of all final products from plant i to marketj. The largest of these flows is shown in figure 7-10. Basically AHMSA and HYLSA serve both Monterrey and Mexico City, Fundidora serves Monterrey, HYLSAP serves Mexico City, and SICARTSA serves Guadalajara and Mexico City. This aggregated shipment pattern is similar to the solution to the small static model shown in table 5-8. AHMSA and HYLSAP serve Mexico City, and HYLSA and Fundidora serve Monterrey in both. The solutions differ, however, in that SICARTSA serves Mexico City in the large but not in 194 MEXICAN CASE STUDY Figure 7-10. Selected Product Flows (thousand metric tons a year) AHMSA Fundidora 262 790 Monterrey 2 00 Guadalajara 1,555 % HYLSA 343 TAMSA 143 Mexico City 281 382 Puebla HYLSAP SICARTSA the small static model solution. Since figure 7-10 shows only aggregate product flows greater than 140 thousand tons, the smaller markets are excluded. A slightly different picture of total product flows is given by figure 7-11, which shows the shipments from the five largest steel mills to each of the three largest market areas. Most of the mills have at least small shipments of some type of final product to each of the three largest market areas. For example, SICARTSA sends products to Mexico City, Monterrey, and Guadalajara. This of course differs from the small static model solution since that model does not have any final product disaggregation. RESULTS OF LARGE STATIC MODEL 195 Figure 7-11. Product Flows between Major Mills and Markets (thousand metric tons a year) Fundidora AHMSA 062 0 790 HMS 26 Monterrey0 Guadalajara W Guadalajara Monterrey 1,555 0 0 143 51Guadalajara Monterrey S343 281 SICARTSAMexico City Mexico City Guadalajara Monterrey 0 0 HYLSA 382 Mexico City 196 MEXICAN CASE STUDY Table 7-10. Shipments of Final Products (thousand metric tons) Fundi- Market SICARTSA AHMSA dora HYLSA HYLSAP TAMSA Imports Total Mexico City 281 1,555 0 343 382 84 177 2,823 Puebla 0 31 0 17 111 165 71 394 Quer&taro 33 93 0 10 32 3 5 177 San Luis Potosi 13 53 0 17 0 0 13 95 Monterrey 51 262 790 200 0 0 169 1,472 Guadalajara 143 54 0 76 0 0 178 450 Lzaro Cardenas 56 5 0 3 0 0 24 88 Coatzacoalcos 0 5 10 10 24 0 341 380 Exports 9 0 97 144 0 0 0 250 Total 586 2,059 896 809 550 252 978 6,129 Note: Row and column totals may be off slightly because of rounding errors. The details of the total product flows for 1979, including domestic shipments, exports, and imports, are shown in table 7-10. A breakdown of products that are imported is shown in table 7-11. There is greater demand for each of those products than there is domestic capacity to meet that demand. Just as in the small model solutions, the imports are used to satisfy demand at markets in or near ports, such as Lazaro Cardenas and Coatzacoalcos. Guadalajara is the receiving market for many imported products because it is relatively near the ocean. Table 7-11. Imports of Final Products (thousand metric tons) Heavy Seamless Market Plate Tin shapes pipe Rebars' Rails Bars Total Mexico City 7 64 62 0 0 44 0 177 Puebla 2 0 4 59 0 6 0 71 Queritaro 0 0 0 0 0 6 0 6 San Luis Potosi 0 0 0 2 0 11 0 13 Monterrey 0 0 0 147 0 22 0 169 Guadalajara 47 11 72 14 0 11 22 177 Lizaro Cardenas 1 0 2 14 0 6 1 24 Coatzacoalcos 1 0 1 312 22 6 0 342 Total 58 75 141 548 22 112 23 979 a. Large-diameter reinforcing rods. RESULTS OF LARGE STATIC MODEL 197 Figure 7-12. Shipments of Hot Sheet (thousand metric tons a year) AHMSA Monterrey 04ii I O 217 76 HYLSA Guadalajara 251 Fundidora Mexico City Figure 7-13. Shipments of Tempered (Cold) Sheet (thousand metric tons a year) AHMSA Monterrey 55 6 162 t] HYLSA 00 Guadalajara 0 Queretaro 359 Fundidora Mexico City 198 MEXICAN CASE STUDY Figure 7-14. Shipments of Large-diameter Reinforcing Rods (thousand metric tons a year) AHMSA Guadalajara Monterrey Puebla 53 . 3/ 46 HYLSAP 155 g\J / / 56 \ SICARTSA //lff Mexico City Figure 7-15. Shipments of Small-diameter Reinforcing Rods (thousand metric tons a year) Monterrey Guadalajara HYLSAP 36 o* 000*"14~ ~31 0" Puebla SICARTSA Mexico City RESULTS OF LARGE STATIC MODEL 199 Specific Product Shipments Next, the shipment of specific final products, such as hot strip, reinforcing rods, and seamless pipe is discussed. Since the plants have different structures of rolling mill capacity and the markets require different types of final product, these shipment breakdowns should show the comparative advantage of the various plants. Our results indicate that the optimal pattern of final product shipments can vary con- siderably without changes in the total cost of the solution. This is not true for production but is true for shipment patterns. Figure 7-12 shows the shipments of hot sheet, and figure 7-13 shows the flows of tempered (cold) sheet. Only shipments greater than 35 thousand tons are shown in order to simplify the figures. Of the six plants, only AHMSA, Fundidora, and HYLSA have capacity to produce both hot and cold sheet. Even though AHMSA has the capacity to sell hot sheet, it uses that capacity instead to provide intermediate products which are Figure 7-16. Shipments of Seamless Pipe (thousand metric tons a year) Monterrey 84 TAMSA M\\\8 exico City 04lilmllnnnnn"H" ""N Coatzacoalcos Puebla 312 200 MEXICAN CASE STUDY further processed into tempered sheets. Thus, in these figures, AHMSA ships no hot sheet but more than 600 thousand tons of tempered sheets. One undesirable characteristic of linear programming solutions appears in figures 7-12 and 7-13, which show most cities served by only one plant. In fact, several plants probably serve each city. The product breakdown used in this model is not disaggregated enough to show this, however, nor does the model capture important institutional arrange- ments between buyers and sellers of steel products. Figures 7-14 and 7-15 show shipments of large-diameter reinforcing rods of more than 25 thousand tons, and shipments of small-diameter reinforcing rods of more than 20 thousand tons. Once again, only three of the plants -SICARTSA, AHMSA, and HYLSAP-can produce these shapes. HYLSAP takes the largest share in both markets. The product shipment pattern for all four products discussed above was determined in large part by the capacity structure in the plants. In contrast, the shipment pattern for seamless pipe is determined largely by the geographic distribution of demand. Figure 7-16 shows the pattern of shipments of more than 80 thousand tons. TAMSA is the only plant that produces seamless pipe. The market for this product is concentrated not in Mexico City but rather in Puebla, Coatzacoalcos, and Monterrey, which receive imported pipe in this solution. Shadow Prices of Products Table 7-12 gives the shadow prices of the final products in three of the market areas. These prices differ from the actual prices in Mexico Table 7-12. Shadow Prices on Final Products (thousand pesos per ton) Product Mexico City Monterrey Guadalajara Plate 8.81 8.63 8.79 Hot sheet 7.80 7.55 7.80 Tempered sheet 8.83 8.58 8.81 Tin 9.96 9.71 9.94 Heavy shapes 8.59 8.40 8.56 Light shapes 8.81 8.90 8.79 Bars 8.82 8.73 8.67 Reinforcing rods Large-diameter 8.82 8.73 8.79 Small-diameter 8.75 8.89 8.78 Wire 8.75 8.56 8.72 Seamless pipe 11.52 11.53 11.49 Rails 8.76 8.78 8.74 RESULTS OF LARGE STATIC MODEL 201 because the cost of labor, capital, and marketing is not included in this version of the model. The differences in the shadow prices in the table reflect primarily differences in raw material processing and transport cost. For example, tempered sheet is more expensive than hot sheet because it requires relatively more raw material and processing. The differences in shadow prices also reflect the fact that some products must be at least partially imported. For example, the price of tin in Mexico City of 9,960 pesos per ton reflects the fact that some tin has to be imported. The prices for products also differ across markets because of the availability of nearby capacity. For example, hot sheet is cheaper in Monterrey (7,550 pesos per ton) than in Mexico City (7,800) or Guadalajara (7,800). In contrast, light shapes are less expensive in Mexico City (8,810) than in Monterrey (8,900). Experimental Runs So far this chapter has provided a discussion of the main results from one solution to the large static model. As such these results provide a rich fabric that interweaves the cost and availability of raw material, production capacity and cost in steel mills, transport cost, and market requirements. The results are best used in comparisons of several solutions rather than in discussion of a single solution. Five experimental runs of the model were made. The runs involved the progressive release of the five institutional constraints mentioned at the Table 7-13. Experimental Runs and Cost Differences Run Constraint 1 2 3 4 5 1. No coke imports 2. Limited exports 3. Limited interplant shipments 4. Strikes 5. No domestic scrap Objective function value (billion pesos) 27.2 26.6 26.5 25.4 24.0 Difference between runs Billion pesos 0.6 0.1 1.1 1.4 Million dollars 25 4 44 56 * Indicates that the constraint was used in the run. 202 MEXICAN CASE STUDY beginning of this chapter. The constraints and the run numbers are given in table 7-13. The asterisks in that table indicate that the constraint was active. Thus, the first run was constrained as follows: 1. There were no imports of coke. 2. Exports were limited to a total of 250 thousand tons of final products. 3. Interplant shipments were limited to coke, pellets, and sponge iron. 4. A strike reduced effective capacity of AHMSA by 10 percent and of Fundidora by 5 percent. 5. Domestic scrap was all purchased by rerollers so the integrated mills had to import their scrap. The objective function value in table 7-13 is the total cost of production and shipping to meet the market requirements in 1979. Since this figure excludes the cost of capital and labor it is considerably lower than the actual cost of operating the industry. The objective value is a net cost term since export revenues are subtracted from the total cost. Table 7-13 shows that the objective value declines as one progresses from Run 1 to Run 5. That is, as fewer institutional constraints are imposed, the cost of operating the industry declines. Thus, the difference in cost between Run I and Run 5 is (27.2 - 24.0) = 3.2 billion pesos or 8 139 million. Even though labor and capital costs are excluded from the objective function value, this may be a fairly good estimate of the cost difference because both capital and labor costs are fixed and do not change much with variations in output levels. In contrast, the raw material cost included in the objective function value is extremely responsive to changes in output levels. The differences in cost between the various runs are shown at the bottom of table 7-13 in both billions of pesos and millions of dollars. The only difference between Runs 1 and 2 is that coke imports are allowed in Run 2 but not in Run 1. This makes a difference in cost of 0.6 billion pesos, or $25 million, that arises entirely because in Run 2 Fundidora imports roughly 500 thousand tons of coke. This permits the whole industry to readjust in such a fashion that substantial cost savings are realized. Compare the steel output levels (in millions of metric tons) by process for Runs I and 2: Run I Run 2 Open hearth 1.9 1.1 Basic oxygen 2.7 3.5 Electric arc 2.0 2.0 RESULTS OF LARGE STATIC MODEL 203 The coke imports permit greater use of the basic oxygen furnaces and less use of the open hearths. This occurs because the coke constraint limits hot metal production. Therefore, it is necessary to import scrap to provide enough iron to meet market requirements. In Run I roughly 1 million tons of scrap are imported but no coke. In Run 2, 265 thousand tons of scrap and 559 thousand tons of coke are imported, so substantial savings are achieved. The comparison of these two runs illustrates how import restrictions interact with operating decisions in steel mills to affect the economics of the industry. Next, compare Runs 2 and 3 in table 7-13. Total exports of final products are constrained to be less than 250 thousand tons in Run 2 but are effectively unconstrained in Run 3. (There is a constraint that the exports of each final product should be less than 500 thousand tons, but this constraint is not binding.) The result is only a small change in exports from a total of 250 thousand tons to 335 thousand tons. This occurs because the industry is operating at close to full capacity in Run 2. The next comparison is of Runs 3 and 4, where the change is to permit more interplant shipments of intermediate products. In Run 3 only coke, pellets, and sponge iron are permitted to be shipped between plants. In Run 4 steel ingots, slabs, hot sheet, blooms, and billets may also be Table 7-14. Capacity Utilization with and without Interplant Shipments of Ingots and Slabs (percent) Interplant shipments Productive unit Constrained Permitted and plant (Run 3) (Run 4) Ingot casting unit AHMSA 100 100 Fundidora 68 100 HYLSA 98 98 Primary mill for flats AHMSA 97 89 Fundidora 82 100 HYLSA 91 100 Hot strip mill AHMSA 89 100 Fundidora 100 100 HYLSA 95 100 204 MEXICAN CASE STUDY shipped between plants. Table 7-13 shows that these additional in- terplant shipments permit a decrease in total cost of 1.1 billion pesos ($44 million). The reason for this can be partially seen in table 7-14, which shows capacity utilization percentages in selected productive units when interplant shipments of rolled products are included and when they are excluded from the model. In Run 3, when interplant shipments of ingots and slabs are excluded, Fundidora has capacity utilization in its ingot casting shop of 68 percent and in its primary mill for flats of 82 percent. HYLSA has capacity utilization in its primary mill for flats of 91 percent, and both AHMSA and HYLSA have less than full capacity utilization in their hot strip mills. Thus, production efficiency in the system can be improved with the interplant shipments shown in figure 7-17. In Run 4, 90 thousand tons of ingots are shipped from Fundidora to HYLSA. This permits full utilization of HYLSA's primary mill for flats by an increased Figure 7-17. Selected Interplant Shipments of Ingots and Slabs in Run 4 (thousand metric tons a year) AHMSA Slabs 37 ", HYLSA Slabs 219 Ingots 90 Fundidora RESULTS OF LARGE STATIC MODEL 205 Table 7-15. Capacity Utilization with and without Interplant Shipments of Ingots, Blooms, and Billets (percent) Interplant shipments Productive unit Constrained Permitted and plant (Run 3) (Run 4) Ingot casting unit AHMSA 100 100 Fundidora 68 100 Primary mill for nonflats AHMSA 36 65 Billet mill AHMSA 34 29 Fundidora 0 100 Bar mill AHMSA 51 100 HYLSAP 69 83 production of slabs. Part of these slabs are then sent to AHMSA to permit fuller utilization of the hot strip mill there. In addition, 219 thousand tons of slabs are shipped from Fundidora to AHMSA. This increases capacity utilization in Fundidora's primary mill from 82 to 100 percent and in AHMSA's hot strip mill from 89 to 100 percent. A similar situation occurs for interplant shipments of ingots, blooms, and billets for shapes. As shown in table 7-15, in Run 3 without interplant shipments AHMSA operates its ingot casting facility at full capacity but Fundidora uses its facility at only 68 percent of capacity. Furthermore, AHMSA has excess capacity for making blooms in its primary mill for nonflats, both plants have excess capacity in their billet mills, and AHMSA and HYLSAP have excess capacity in their bar mills. Under Run 4 in table 7-15 it is shown that interplant shipments permit much more complete utilization of these facilities. This is accomplished as shown in figure 7-18. Fundidora ships ingots to AHMSA, which transforms them to blooms and ships them back to Fundidora. Then Fundidora rolls the blooms into billets and sends them back to AHMSA and also to HYLSAP. All of these cross shipments are complicated, but they permit a more efficient use of the capacity in the industry that saves 1.1 billion pesos ($44 million) per year. 206 MEXICAN CASE STUDY Figure 7-18. Selected Interplant Shipments of Ingots, Blooms, and Billets in Run 4 (thousand metric tons a year) AHMSA Ingots 207 Blooms 176 Billets Fundidora 100 Billets 69 0 HYLSAP In the last set of comparisons in table 7-13, Runs 4 and 5, two changes are made. The first asks the question of the effective cost of the strike against AHMSA and Fundidora. The second change lowered the domestic price of scrap in the model so that the integrated mills could purchase it instead of having to import it. Although it would have been better to make these changes separately, so that the two effects could be untangled, the result does at least indicate that the strike cost no more than the 1.4 billion pesos ($56 million) indicated in table 7-13. This chapter has shown what a rich level of detail can be developed and studied in a static model that is still small enough to be solved at RESULTS OF LARGE STATIC MODEL 207 reasonable cost. It has also shown how the model can be used in searching for more efficient operational procedures such as interplant shipments. These kinds of result might be even more interesting in dynamic models that include investment. Therefore, the next chapter discusses a small dynamic model. 8 A Small Dynamic Model MODEL BUILDING IS BEST done in stages. On a typical project one does not simply build a single large model and solve it, but rather builds up from simpler to more complex models. Thus, one can gain experience with the problem while working with smaller, less complicated models that can be solved in less time and at less expense. It is also possible to learn about the problem a little bit at a time. In fact, this procedure is basic to our modeling work. The purpose of modeling is not to find an optimal solution, but rather to enhance understanding of the problem at hand. Another reason for building multiple models is that each model has a comparative advantage. Since small models are easier to understand and less costly to solve, one can solve the model repeatedly while attempting to gain a better understanding of the industry. In contrast, large models provide more detailed specification that allows one to analyze certain problems of interest and to check the validity of the solutions to the small models. Also, static models have a comparative advantage in studying problems of operation, and dynamic models have a comparative advantage in analyzing investment problems. This chapter returns to the small static model of chapter 5 and enriches it by making it dynamic and by adding exhaustible resources. Only the new elements are explained; then the entire model is stated in summary form. Sets The small static model had five plants (AHMSA, Fundidora, SICARTSA, HYLSA, and HYLSAP), the largest existing steel millS. TAMSA is not included 208 A SMALL DYNAMIC MODEL 209 in this model because it specializes in a single product, seamless pipe. It is possible that all expansion in the period covered by the dynamic model will be accomplished by constructing additional productive units at these five plants. It is useful, however, to consider the possibility that one or more entirely new plants will be constructed on "green field" sites. Two green field sites, Tampico and Coatzacoalcos, are considered in this small dynamic model (see map 1, p. 41). Coatzacoalcos was chosen because it is near the large natural gas fields discovered recently. If direct reduction methods are used in the future and if domestic ores are depleted to the point that importation of pellets is necessary, then Coatzacoalcos might be an attractive site for a new steel mill. Tampico was chosen as a potential site for similar reasons. First, it is a port. Second, it is in the vicinity of gas fields and near the existing natural gas pipeline that goes from Coatzacoalcos to the Texas border. Third, it is closer to the existing coal and northern ores than is Coatzacoalcos. Thus, a plant established there could use existing northern ores and coal until they are depleted and then could switch to imported pellets and coke. This model also has a set of mines that is not considered in the small static model. The mines are included so that the model can be used to analyze the effect of declining ore grades and coal quality. Although there are many different ore mines in Mexico, in this small dynamic model they are represented by only two sites, one in the northern part of the country and one in the southern part. All of the reserves of iron ore are assumed to be concentrated at one or the other of these two sites. In contrast, there is really only one large coal mining area, and this can be satisfactorily represented in the model as a single coal mine in Coahuila. A subset of the plants is used in the model to identify locations that are permitted to purchase natural gas and electricity at subsidized prices. This set is: IE = plants that qualify for subsidized energy prices = {Coatzacoalcos, SICARTSA, Tampico}. In summary, then, the sets of plants and mines in the model are: IM Mines = {Coahuila coal mines, northern iron ore mines, southern iron ore mines} I Plants = {AHMSA, Fundidora, SICARTSA, HYLSA, HYLSAP, Tampico, Coatzacoalcos}. 210 MEXICAN CASE STUDY The set of markets remains the same as in the small static model: J= {Mexico City, Monterrey, Guadalajara). The set of productive units is also the same as in the small static model: M = {Blast furnace, open hearth furnace, basic oxygen fur- nace, direct reduction furnace, electric arc furnace}. The set of processes is the same as in the small static model with one exception: a process for production in BOFS with a high scrap charge was added to the original small static model to correct an inaccuracy in that model. The change was reflected in the second linear programming solution, which was discussed in chapter 5. Thus, the set of processes is: P = {pig iron production, sponge iron production, steel pro- duction in open hearths, steel production in electric arc furnaces, steel production in BOF s, steel production in BOF s with high scrap). The set of commodities is the same for this model as for the small static model, but the subsets are treated in a slightly different manner. The set of commodities is: C = {pellets, coke, natural gas, electricity, scrap, pig iron, sponge iron, steel}. The subsets of C are: CR = raw material = {natural gas, electricity, scrap} CV = imported raw material = {coke, pellets} CM = mining products = {coke, pellets} CI = interplant shipment commodities = {sponge iron CF = final products = (steel} CE = exported commodities = {steel} CENR = subsidized energy commodities = (natural gas, electricity}. The set CM is used differently here than in the small static model. There, it defines the set of intermediate products. In the small dynamic model, however, the input-output matrix defines implicitly the set of A SMALL DYNAMIC MODEL 211 intermediate products, and the set CM is used for the commodities (coke and pellets) that are shipped from mines to plants. In fact, most of the productive units that convert coal to coke and some of the units that convert iron ore to pellets are located at plants rather than at mines, but this abstraction serves a useful purpose in this small model Three sets not used in the small static model are necessary in the dynamic model: the sets of expansion units, of time periods, and of expansion periods. The expansion units are the productive units considered in the expansion plans. As discussed in chapter 3, in some cases this set will be identical to the set of productive units. Some productive units may be unlikely candidates for investment, however, and are therefore excluded from the set of expansion units. Open hearth furnaces, for example, are in the set of productive units but not in the set of expansion units since they are dominated as investment choices by basic oxygen furnaces. Some new technologies that are not in the existing plants may also be considered in the set of expansion units. In summary, the set of expansion units is: ME = {blast furnace, basic oxygen furnace, direct reduction furnace, electric are furnace}. The set of time periods covers the time horizon from 1981 to 1995 in three-year intervals. Thus, there are five time periods of three years each: T= time periods = {1981-83, 1984-86, 1987-89, 1990-92, 1993-95}. There is also a subset of time periods during which capacity can be expanded. This is used to represent the long lags in construction times. Thus, new capacity which comes on-line in the first time period (1981-83) must already be under construction and should be exogenously added to the model. Therefore, the following set is used: TE = time periods during which capacity can be expanded = {1984-86, 1987-89,1990-92, 1993-95). This model uses a set of quality levels (Q) for coal and iron ore, but since those commodities are not in this small model, Q actually refers to coke and pellets. The quality levels are used to model the declining quality (and rising cost of mining) of both coal and iron ore as the present reserves in Mexico are exploited. With level I as the best quality and level 5 as the worst, this set is: Q = quality levels for coal and iron ore = {1, 2,3,4, 5}. 212 MEXICAN CASE STUDY Another new set, G, is used for the grid points of the investment cost function. The set is simply the integers from I to 4 to represent the four grid points used in approximating the investment cost functions: G grid points for the investment cost function approximation = (1, 2, 3, 4}. In summary, the sets are: IM = mines I = plants J = markets M = productive units ME = productive units for expansion P = processes C = commodities CR = raw material CV = imported raw material CM = mining products CI = interplant shipment commodities CF = final products CE = exported commodities CENR = subsidized energy commodities T = time periods TE = expansion time periods TS = set of time period pairs for the investment equations Q = quality levels for coal and iron ore G = grid points for investment function approximation Variables Table 8-1 lists the variables in the small dynamic model. The process levels z, shipments x, domestic purchases u, imports v, and exports e are familiar from the small static model. And the specification of the shipment variables xf for final products, x" for intermediate product shipment between plants, and x- for raw material shipments from mines to plants are familiar from the large static model. The notation for the process-level variables w at the mines is new. The cost category variables are all familiar except for the capital cost variables K. Thus, the new variables in the small dynamic model which were not in the small static A SMALL DYNAMIC MODEL 213 Table 8-1. Variables in the Small Dynamic Model wc1u Production of commodity c of quality level q at mine i in time period t z,, Process level of process p at plant i in time period t xfii, Shipment of final product c from plant i to market j in time period t xd,,, Shipment of intermediate product c from plant i' to plant i in time period t xl,, Shipment of commodities from mine i' to plant i in time period t u, Purchases of raw material c at plant i in time period t vi, Imports of raw material c to plant i in time period t vcj Imports of final product c to market j in time period t ecu Exports of commodity c from plant i in time period t h, Expansion of productive unit m at plant i in time period t s,i Auxiliary variable for investment in productive unit m at plant i in time period t ymi Zero-one variable for investment in productive unit m at plant I in time period t Total discounted cost less discounted export revenues K Capital cost in time period t Recurrent raw material and labor cost in time period t (0, Transport cost in time period t Import cost in time period t Export revenues in time period t model are: the investment variables h, s, and y and the associated investment cost variables 0; the shipment variables x'; and the mine process-level variables w. The only change to the familiar variables is that they now have a subscript for time period t. Thus, the variable zi, for Zpig iron production, Altos Hornos, 1981-83 1.25 means that average annual production of pig iron at Altos Hornos in the three-year interval 1981-83 would be 1.25 million metric tons. The variable does not represent the total production in the three-year interval but rather the average annual production level. It is assumed that the process level will be different in the three years in the 1981-83 interval, and the model solution will be the average annual production level in the interval. The same treatment of time holds for the other variables w, x, u, v, and e. That is, they all represent average annual activity levels within the time interval. In contrast, the investment variables do not represent the average amount of capacity added in each year of the time interval, but rather the total amount of new capacity that comes on-line at the beginning of the time interval. To see this, consider the investment variables introduced in this chapter: h, y, and s. Of these, the h variables are the simplest to 214 MEXICAN CASE STUDY interpret. They are the expansion of productive unit m at plant i in time period t. For example, hmi, for "blast furnace, Altos Hornos, 1984-6 = 1.5 means that a new blast furnace with a capacity of 1.5 million metric tons per year would be put into production at Altos Hornos at the beginning of 1984. The ymt variables are the zero-one variables associated with the expansion of productive unit m at plant i in time period t. In the continuous solutions to the problem the y variables take on a value in the interval from zero to one, and in the mixed integer programming (MIP) solutions they take on either the value zero or the value one. In the mip solutions the y variables indicate whether there is any expansion of the productive unit in the particular plant and time period. Thus, the y's indicate yes or no and the h's indicate the amount of capacity expansion when the y's are one. The s variables are used in the approximation of the investment cost function as shown in figure 8-1. That figure shows four grid points on the horizontal axis for the size of the additions to capacity: n,, h2, li, and l4. The first of these points is set to zero: (8.1) hl = 0. The second is chosen as the size at which economies of scale are exhausted, h: (8.2) h2 For example, if economies of scale for basic oxygen furnaces (BoFs) are exhausted at a furnace size of 1.5 million tons, then h2 = 1.5 million tons. That is, E2 is the size at which capacity is expanded by replicating units rather than by increasing the size of individual units. In a BOF shop there may thus be several furnaces, each with a capacity no larger than 1.5 million tons per year. (Theoretically, economies of scale may not be exhausted at the point of the largest size of productive unit observed, but this notion is accurate enough for purposes of the approximation used here.) Next, the grid point variable h3 is chosen to be a multiple of the size h: (8.3) h3 = nconsth. It is the multiple at which diseconomies of scale are expected. In this study nco.,s is chosen to be 3; that is, it is assumed that after the unit is replicated three times diseconomies of scale begin to occur. In the case of A SMALL DYNAMIC MODEL 215 Figure 8-1. Points for the Investment Cost Function Approximation 6J)3 (0, I - I I WIII I I I /11 3 hi Addition to capacity a BOF shop, for example, three furnaces might be mounted side by side, each with a capacity of 1.5 million tons, without diseconomies of scale occurring. It is assumed that the addition of a fourth furnace would result in diseconomies of scale in investment cost. Finally, the grid point h4 is chosen to be a multiple of li that is an upper bound on the capacity of a set of productive units which would be installed at a single point in time: (8.4) h4 maxh* 216 MEXICAN CASE STUDY For this study, nmax is set at 6; that is, it is assumed that no more than six identical units of a size at which economies of scale are exhausted would be installed at a single plant in a particular time period. Thus, for the BOF example, the restriction in the model is that no more than six BOFS of 1.5 million tons would be installed at one time. This is the first use of this particular type of investment function approximation in this series of books, so there is relatively little experience with it and caution in its use is appropriate. However, it embodies the old idea from economic theory that there are economies of scale in investment cost for small plant sizes, constant unit cost for intermediate sizes, and diseconomies of scale for large sizes. It therefore seems a useful approximation with which to experiment. Figure 8-1 also shows the parameter values og. It is sufficient here to say that Co is the investment cost for a plant of size h. where g is the running index for the grid points (1, 2, 3, 4) of the investment function approximation. A full discussion of how these parameters are de- termined is deferred to the next section on parameters. The investment function approximation used in this study is obtained graphically by connecting the points shown in figure 8-1. This is displayed with the dark line in figure 8-2. This approximation is represented mathematically by the function (8.5) = 69sg geG (8.6) YSg= geG where og = investment cost at grid point g Sg = a set of variables used to obtain a convex combination of the approximation points (Cog, h.) for the investment cost function. Thus, to represent points on the line in figure 8-2 between the points (61, j) and (62, E2), the variables s, and s, will vary in a complementary way between zero and one. That is, a point relatively near (62, h2) would be obtained by setting s, = 0.2, s2 = 0.8, s1 = 0, and s4 = 0. Finally, the amount of capacity added is also a convex combination, but a combination of the h's instead of the 67's: (8.7) h= ' hsg. The discussion above has been simplified by ignoring most of the subscripts on the investment variables h and s. When those subscripts are A SMALL DYNAMIC MODEL 217 Figure 8-2. Three-Segment Investment Cost Approximation 04 0I CI I Addition to capacity added back into the variables they become hmit= expansion of productive unit m at plant i in time period t smit = level of convex combination variable at grid point g for productive unit m at plant i in time period t. Two other new variables, the shipment variables xm and the mine process variables w, need to be discussed. The shipment variables xm,, are added to the model to represent the shipment from mines to steel mills of raw material. The production of this raw material at the mines is represented with the mine process variables wcqit. It is assumed that the raw material is available in deposits of varying quality. The quality index q = 1 represents the highest quality ores and larger values of q represent ores of lower quality. 218 MEXICAN CASE STUDY Parameters Table 8-2 lists the parameters in this model. Only the parameters which differ from those of the small static model will be discussed in detail. The first three parameters in the table-the input-output coefficients a, the capacity utilization coefficients b, and the initial capacity parameters k-are identical to those in the small static model. In contrast, the demand parameters d have been changed from de; to dcjt; that is, a time subscript has been added. This represents the demand projections in the model. Recall that demand in the small static model is treated in the following fashion: (8.8) d; = dP (1.4) (5.2) Table 8-2. Parameters in the Small Dynamic Model ac, Input (-) or output (+) of commodity c per unit level of operation of process p b I if productive unit m is used by process p 0 if productive unit m is not used by process p kmi Initial capacity of productive unit m at plant i 0 Years per time period y, Midyear for time period t d Demand for commodity c at market j in time period t e, Upper bound on exports of all commodities from all plants in time period t C., Capital cost at grid point g for productive unit m at plant i k.0 Plant size for productive unit m at grid point g 6, Discount term for time period t U Capital recovery factor pl Price of commodity c produced from coal or ores of quality q at mine i p d Domestic price of commodity c delivered to plant i in time period t pC Import price of commodity c at the port pf Export price commodity c at the port Unit cost of transporting final products from plant i to marketj Unit cost of transporting final products from the port to market j pf Unit cost of transporting final products from plant i to nearest port PH, Unit cost of transporting intermediate products from plant i to plant i' p Unit cost of transporting commodities from mine i to plant i , Reserves of each quality level q of commodity c at mine i A SMALL DYNAMIC MODEL 219 where de; = demand for final product c in market j in 1979 dP = the percentage of the total national demand which is located in market area j 1.4 = tons of ingot steel required per ton of final products 5.2 = million metric tons of final products consumed in 1979. In this small dynamic model the demand projections are made with the expression: (8.9) dajt= (d,j,199)(1. 10op, - 1979) d,= demand for final product c in market area j in time period t d,Ji, 79= dcj = demand for final product c in market area j in 1979 1.10 = 1 plus the annual growth rate of the demand for final products, in this case 10 percent 7, = the midyear of time period t. The parameter 7, is the only unusual part of the expression (8.9). Since each time period consist of three years and the time periods are 1981-83, 1984-86, and so on, the parameter y, can be defined as (8.10) Yt = 1979 + Ot where 0 = years per time period = 3 t = the time period number (1, 2, 3,...) As an example, consider the demand for steel in Mexico City in the time period 1981-83. From (8.9), (8.11) steel, Mexico City, 1981-83 = (dsteel, Mexico City, 1979) (1.10)1981-93-979), then from (8.8) (8.12) dsteel, Mexico City, 1979 = (dMexico City)(1.4)(5.2) = (0.55)(1.4)(5.2) = 4.004, and from (8.10) (8.13) ?1981-83 = 1979 + 3(1) since 1981-83 is the first time period = 1982. Then substitution of (8.12) and (8.13) into (8.11) yields (8.14) dsteeL, Mexico City, 1981-83 = (4.004) (1.10) (1982-1979) = (4.004) (1.1)3 = (4.004) (1.331) = 5.329. 220 MEXICAN CASE STUDY Table 8-3. Demand Projections for the Small Dynamic Model (million metric tons of steel per year) Time period Mexico City Monterrey Guadalajara Total 1981-83 5.329 2.907 1.453 9.689 1984-86 7.093 3.869 1.935 12.897 1987-89 9.441 5.150 2.575 17.166 1990-92 12.566 6.854 3.427 22.847 1993-95 16.726 9.123 4.562 30.411 This number and the remaining demand projections are shown in table 8-3. The numbers in this table are the demand for (ingot) steel in each year of the three-year period covered by each time interval. The next parameter in table 8-2 is e', the upper bound on exports of all products from all markets in period t. Though it would be interesting to experiment with the effects of an upper bound which changes across time periods, it has been assumed here that this bound is constant across time periods: (8.15) e, = 0.2. te T Thus, the bound is set at 200 thousand tons of steel products. The next new parameters in table 8-2 are the capital cost parameters 6m,.i These parameters were discussed above along with the description of the capital cost variables h, s, and y. They were shown graphically in figures 8-1 and 8-2. In that discussion, four grid points for investment cost were selected: Grid point g Investment size h I Zero 2 Size at which economies of scale are exhausted 3 Size at which diseconomies of scale begin 4 Maximum size The capital costs which correspond to each of these grid points are: (8.16) (m1 =m(0.5'-1- 1) (8.17) (m2 m (8.18) wm = nconst6m (8.19) (m4 = nmax(1.25) <. where c = capital cost for an investment of size h h = size at which economies of scale are exhausted A SMALL DYNAMIC MODEL 221 Table 8-4. Investment Cost Parameters Size (h) (million Cost (c6) metric tons (million Productive unit a year) dollars) Scale (fi) Blast furnace 1.5 250 0.6 BOF 1.5 120 0.6 Direct reduction 0.8 100 0.6 Electric arc 0.5 42 0.6 Note :The cost parameters in this table were provided by HYLSA officials, who indicated that the data were taken from an article by R. T. Kuhl in the June 1979 issue of Steel Times International. neonst = 3 = multiple of size h at which diseconomies of scale begin nmax = 6 = multiple of h representing the maximum amount of equipment which can be installed in a single time period. Since c6, nco,s,, and nmax are given data, only the cost a is difficult to obtain. The derivation of the expression (8.16) is relatively long and is therefore relegated to appendix C to this chapter. The parameters hm, 6m' and Pm are given in table 8-4. The expressions (8.16)-(8.19) embody the assumption that capital costs are the same at all plant locations. That is frequently not the case in investment planning problems and is not the case for the problem at hand. Rather the investment costs at each plant location are adjusted by a site factor, 7c,. Thus, the expressions (8.16)-(8.19) become (8.20) mmu 7i m(0.5# ) (8.21) wm4n2= 7ti6m (8.22) wm,3 = i9nconst6m (8.23) wm4i 7 Timax(l.25)6m The values for the parameters 7r, are given in table 8-5. The site factors for Fundidora and HYLSA are set slightly higher because both are in the midst of the city of Monterrey and land costs are relatively high. The factors for Tampico and Coatzacoalcos are set relatively high because both are green field sites, and all the required infrastructure would have to be installed. The next two parameters in table 8-2 are the discount term bt and the capital recovery factor a. The expression for the discount term is (8.24) 6, = ( + p)1979 -y, 222 MEXICAN CASE STUDY Table 8-5. Site Construction Cost Factors Site (i) Factor (7ir) AHMSA 1.0 Fundidora 1.1 SICARTSA 1.0 HYLSA 1.1 HYLSAP 1.0 Tampico 1.2 Coatzacoalcos 1.2 where p = discount rate = 10 percent 7t = midyear of period t. For example, (8.25) 198 s-86 =(1 9-0) ""-19*= (1.10)6 0.564. The capital recovery factor is defined by the expression p (1 + p) (8.26) (1 +p) (I + P)c -I where (= equipment life in years. This expression is derived in Kendrick and Stoutjesdijk (1978, pp. 47- 49). For example, in the case at hand p = 0.1 and (= 20 years, so (0.1)(1.1)20 (8.27) o - 20 - =0.117. The price parameters p are the next set in table 8-2. There are four sets of prices in the model: prices of mining products pw, domestic prices of other raw material pd, import prices pv, and export prices pe. Consider first the prices of mining products. One of the most important economic realities for the Mexican steel industry is the likely increase in mining cost per ton for coal and iron ore as the known reserves are exhausted. Of course, it is possible that new and richer coal and iron ore deposits will be discovered. More likely, however, is a slow but sure increase in the cost of mining coal and iron ore with the depletion of existing reserves. Therefore, the model includes prices for coke (as a proxy for coal) and for pellets (as a proxy for iron ore) that are equated with production costs and rise as the existing reserves are used up in the coming years. This is done by assuming there are five qualities A SMALL DYNAMIC MODEL 223 of reserves for both coal and iron ore, from q = 1 for the best quality to q = 5 for the worst quality. Coke produced from the highest quality coal is assumed to sell at the 1979 domestic price of S52 per metric ton, and coke produced from the lowest quality coal is assumed to cost $100 per metric ton. Similarly, it is assumed that pellets produced from the highest quality ores sell at the 1979 domestic price level of $18.70 per metric ton and that pellets produced from the lowest quality ores will cost $38 per metric ton. Then the price, or production cost, for coke and pellets produced from the intermediate quality levels of coal and iron ore respectively are assumed to be determined by the following exponential function: ( ord(q) - 1 cE CM (8.28) p" W PQ + (ph?gh ) (card(Q) - q eQ i elM where P i= price of commodity c produced from coal or ores of quality q at mine i p"-= the domestic price in 1979 (a relatively low price) of commodity c at plant i pCgh = the projected domestic price (a relatively high price) of commodity c in the future when it is produced with the lowest quality of ores ord(q) = the ordinal number associated with the quality level q: ord(1) = 1, ord(2)= 2, and so on card (Q) = the cardinal number associated with the num- ber of elements in the set Q; that is, the number of different quality levels of coal and ore used in the model a = 1.3 = an exponential parameter representing the fact that the quality of coal and ores will decline slowly at first and then rapidly as the reserves are exhausted. For example, the price of pellets produced from ores of the third quality level at the northern mines is estimated to be Ppellets, 3, northern ore mines - 18.7 + (38 - 18.7) 5- 1 = 18.7 + 19.3 (0.5)1. = $26.5 per metric ton. 224 MEXICAN CASE STUDY Table 8-6. Prices of Commodities Produced at Mines (dollars per metric ton) Pellets Pellets from from Quality Coke at northern southern level (q) Coahuila mines mines 1 52.0 18.7 18.7 2 59.9 21.9 21.9 3 71.5 26.5 26.5 4 85.0 32.0 32.0 5 100.0 38.0 38.0 The prices of coke and pellets which result from these transformations are shown in table 8-6. Consider next the prices of other domestic raw material in the model: electricity, scrap, and natural gas. The price of natural gas is discussed first since it is the most complicated of the three. The domestic price of natural gas in Mexico in 1979 was $14 per thousand cubic meters (roughly 40 cents per thousand cubic feet-using 0.0283 cubic meters per cubic foot). In contrast, the international price of natural gas (as represented by the contract price between Mexico and the United States) was 5128 per thousand cubic meters ($3.62 per thousand cubic feet). It has been assumed in this model that the Mexican government will gradually let the domestic price of natural gas rise to the level of the international price. This has been represented in the model with the following relationship: (p -p c= natural gas (8.29) Pe = p + ps ord (t) - 1) where Pct= domestic price of commodity c in time period t p = lower (or initial) price pb = higher (or international) price steps = number of steps taken in changing the price from the lower to the higher level ord(t) = the ordinal number associated with t: ord (1981-83)= 1, and ord (1984-86)= 2. For example, with p'= $14 per thousand cubic meters (lower natural gas price) A SMALL DYNAMIC MODEL 225 Table 8-7. Domestic Price of Natural Gas Domestic price Dollars per Dollars per thousand thousand Time period cubic meters cubic feet 1981-83 14.0 0.40 1984-86 42.5 1.20 1987-89 71.0 2.00 1990-92 99.5 2.81 1993-95 128.0 3.62 pu = $128 per thousand cubic meters (international natural gas price) steps = 4; that is, the price would be changed from the low to the high level in 4 steps. Then the price of natural gas in the 1984-86 time period could be 128 - 14 Png,1984-86 = 14+ 4 (2-1) 4 = 14 + 28.5 = S42.50 per thousand cubic meters. The resulting time path for natural gas prices is shown in table 8-7. Natural gas and electricity prices in Mexico are further complicated because some plants are close to natural gas supplies and some are distant, and the government has introduced an energy pricing scheme to promote industrialization at some locations. In an attempt to capture both phenomena, this version of the model employs site factors for natural gas prices. With these factors the natural gas and electricity prices are computed with the relationship (8.30) P= (1 - ) ieI ceCENR teT The values for the location factor (nq) are given in table 8-8. The base run in this case represents government policy rather than the real cost of resources. Thus, the fact that some plants are closer to natural gas supplies than others is ignored, and natural gas is priced in such a way as to encourage decentralization of industry. The sites for the older plants 226 MEXICAN CASE STUDY Table 8-8. Location Factor and Price of Natural Gas (dollars per thousand cubic meters) Location Plant factor 1981-83 1984-86 1987-89 1990-92 1993-95 AHMSA 1.00 14.0 42.5 71.0 99.5 128.0 Fundidora 1.00 14.0 42.5 71.0 99.5 128,0 SICARTSA 0.70 9.8 29.7 49.7 69.5 89.6 HYLSA 1.00 14.0 42.5 71.0 99.5 128.0 HYLSAP 1.00 14.0 42.5 71.0 99.5 128.0 Tampico 0.70 9.8 29.7 49.7 69.5 89.6 Coatzacoalcos 0.70 9.8 29.7 49.7 69.5 89.6 (AHMSA, Fundidora, HYLSA, and HYLSAP) are assigned factors of 1.0, and those for the newer plant at SICARTSA and the potential sites at Tampico and Coatzacoalcos are assigned factors of 0.7. Thus, there is a 30 percent reduction in actual gas and electricity prices to the plants at sICARTSA, Tampico, and Coatzacoalcos. After all these transformations, the resulting prices of natural gas used in the model are shown in table 8-8. Since the electricity price calculations are less complicated they are not shown explicitly. Next consider the domestic prices of the other raw material, scrap steel. The model is developed in a manner that permits price projections over time, as was done with natural gas. Locational factors could also be used. However, neither of these modeling capabilities has yet been exploited, and it is assumed that this price remains constant over time and is the same at all plant locations. (8.31) pcit = p c = scrap steel ielI te T where pfi = the domestic price of raw material c at plant i in time period t pd = the 1979 domestic price of commodity c with Psdcrap steel = S 105 per metric ton. This leaves only two groups of prices to be discussed: import prices pu, and export prices pe. It is assumed that two raw materials and one final product can be imported and that one final product can be exported. The prices used for those imports and exports (in dollars per metric ton) are: A SMALL DYNAMIC MODEL 227 Table 8-9. Interplant Rail Distances (kilometers) AHMSA Fundidora SICARTSA HYLSA HYLSAP Tampico Fundidora 218 SICARTSA 1,416 1,322 HYLSA 218 10 1,327 HYLSAP 1,300 1,159 995 1,159 Tampico 739 521 1,319 521 1,111 Coatzacoalcos 1,850 1,756 1,638 1,756 671 1,702 Import Export price price Coke 60 - Pellets 40 - Steel 150 140 The next set of parameters in table 8-2 is the transport costs. These costs are the same as for the small static model with two exceptions: the new sets of terms for the costs of interplant shipments and of shipments from mines to plants. The interplant shipment costs are: (8.32) A,= 00, +j3'bM! where pg, = cost per metric ton for transporting intermediate products from plant i to plant i' al = loading and unloading cost per metric ton = $2.48 per ton fl= cost per ton mile = $0.0084 per ton mile 6R, = distance from plant i to plant i' The interplant distances are given in table 8-9. The mine-to-plant shipment costs are: (8.33) p = A + flp6m where p7 = cost per metric ton for transporting commodities from the mine i' to plant i a"= loading and unloading cost per metric ton = $2.48 per ton fU = cost per ton mile= $0.0084 per ton mile bm =distance from mine i' to plant i The distances from mines to plants are given in table 8-10. 228 MEXICAN CASE STUDY Table 8-10. Rail Distances from Mines to Plants (kilometers) Coahuila Northern Southern coal ore ore Plant mines mines mines AHMSA 120 219 1,490 Fundidora 400 563 1,396 SICARTSA 1,500 1,613 0 HYLSA 400 563 1,396 HYLSAP 1,420 1,411 1,116 Tampico 900 1,048 1,338 Coatzacoalcos 2,100 2,195 1,500 The last set of parameters in table 8-2 is the reserves of mining products: OVcqi = the reserves of quality level q of commodity c at mine i. The commodities are coke and pellets. Obviously, there are no reserves of coke and pellets at the mines but rather of coal and iron ore. Therefore, it is necessary to obtain the data on coal and iron ore reserves and to transform those figures into the equivalent figures for reserves of coke and pellets. This is a slightly roundabout procedure. It would have been more straightforward to have added the commodities coal and iron ore to the model and to have introduced production activities for transform- ing the coal into coke and the iron ore into pellets. To keep the model as small as possible, however, this was not done. It is therefore necessary to think of the reserve figures as the amount of coke which could be produced by the existing coal reserves and the amount of pellets which could be produced with the existing iron ore reserves. These reserves were computed by beginning with the measured, indicated, and inferred reserves of each mine as shown in table 8-11. There are 650 million tons of unwashed coal reserves at Coahuila. Since about 2 tons of unwashed coal are required to produce a ton of washed coal, the reserves may be thought of as 325 million tons of washed coal. And about 1.4 tons of washed coal are required to produce a ton of coke, so the positive coal reserves would be equivalent to 232 million tons of coke. As discussed earlier, to keep the model small, the existing iron ore mines are aggregated into two mines, one in the north and one in the south. The iron ore reserves at La Perla, Cerro de Mercado, and A SMALL DYNAMIC MODEL 229 Table 8-11. Coal and Iron Ore Reserves (million metric tons) Mine Measured Indicated Inferred Coal Coahuila 650 40 15 Iron ore Pefia Colorado 103.9 6.2 0.0 Las Truchas 105.6 11.6 0.0 La Perla 49.0 8.1 0.0 Cerro de Mercado 20.6 2.7 0.0 Hercules 61.0 5.4 25.0 La Chula 4.6 28.2 0.0 El Encino 14.7 0.0 0.0 El Violin 20.0 10.0 10.0 Total iron ore 379.4 72.2 35.0 Hercules were grouped together to provide a northern mine with 130.6 million tons of measured reserves. The reserves at Pefia Colorado, Las Truchas, La Chula, El Encino, and El Violin were grouped together to form a southern mine with 248.8 million tons of measured reserves. It was assumed that only 70 percent of the total measured reserves should be used during the time horizon covered by the model. Thus, 30 percent of the measured reserves would be set aside for use by the steel industry in the years after the period covered by the model. In the north (130.6) (0.7) = 91 million tons and in the south (248.8) (0.7) = 174 million tons of measured reserves would be available for use during the period covered by the model. Using a ratio of 1.5 tons of ore per ton of pellets provides roughly 60 million tons in the north and 115 million tons in the south of pellet-equivalent reserves for use during the time horizon covered by the model. One final step was necessary in preparing the data for the model. It is assumed that there are several grades of ore in each mine and that the grades are exhausted one by one, moving from superior to inferior quality. This is modeled by using the set Q of quality levels. These quality levels are the integers 1 to 5, and the size (cardinality) of the set gives the number of grades used in the model. It is then assumed that the available reserves are evenly distributed among the grades so that (8.34) w, = w'"/card(Q) where Oves = reserves of each quality level of commodity c at plant i 230 MEXICAN CASE STUDY w's = reserves of all quality levels at mine i card (Q) = cardinality of the set Q, that is, the number of quality levels. Constraints All of the constraints for the small dynamic model will be displayed in this section, but only those aspects that differ substantially from the small static model will be discussed in detail. The first set of constraints are material balance inequalities for the mines. They require that no more material be shipped from the mines than is produced. They are written as MATERIAL BALANCE CONSTRAINTS FOR MINES (8.35) Y_ Weju _ E x", cc CM qEQ iel i elM teT Production of all Shipment of product quality grades of e from mine i commoine at in prodin commodity c at ~ to all plants in mine i in pro rperiodi The material balance constraints for plants in this model differ substantially from those in the small static model-not because of the difference between static and dynamic models, but because of a different procedure for disaggregating commodities. In the small static model there are separate sets of contraints for final products, intermediate products, and raw material. This treatment was possible because the three sets are disjoint; that is, no commodity belonged to two different sets. If the sets had not been disjoint, a given commodity (say, sponge iron) might be both a final product and an intermediate product. Thus, it would be necessary to write constraints for final products, intermediate products, and products that are both final and intermediate. When other commodity sets, such as exported products or products shipped between plants, are added to the model the situation becomes even more complicated. It may be necessary to write six or eight types of material balance constraints. An alternative approach is used here. A single set of material balance constraints for plants is used. Then it is left to the pattern of entries in the A SMALL DYNAMIC MODEL 231 input-output matrix to determine which commodities are final products, intermediate products, raw material, and a combination of these. Restrictions are introduced on the summation signs as was done on the large static model in chapter 6. For example, the term in the material balance constraint which relates to interplant shipments is restricted to apply only to products that can be shipped between plants. MATERIAL BALANCE CONSTRAINTS FOR STEEL MILLS (8.36) appit + cit PEP ceCR inputs and outputs] [Domestic purchases of commodity c at 1 of raw material c plant i at plant i + - x'",, + v i'el1M ceC t ceCV [Shipments from all mines to] Imports of commodity c + steel mill i of mine + to steel mill i product i el CI i'EI CECI [Interplant shipments Interplant shipments from plant i' to Pt from plant ito plant i plant i' +~ xi|+ecit ICEc C jeJ IcetCF IcECE ieI teT Final product shipments Exportsfrom +1 from plant ito all Explat markets IL p The next set of constraints is the capacity constraints. First, it is necessary to include a constraint on the total supply of each quality of mining commodities. It is assumed that there is a fixed supply of each quality of mining product. As discussed above, the mining products actually used in the model are coke and pellets, while the reserves used in the production of these commodities are coal and iron ore respectively. Therefore, the reserves of coal and iron ore are transformed into the equivalent reserves of coke and pellets and the constraints are written for coke and pellets. 232 MEXICAN CASE STUDY CAPACITY CONSTRAINTS FOR MINING RESERVES (8.37) 0 wci qi) ki cc CM eeQ qEQ Number Production of commodity Reserves of ofyer c of quality level q quality q [ at mine i in one year of commodity per tie of each time period for c at period IL - all time periods _ mine i Since the units of the w variables are average annual production in each year of the years in the time period, it is necessary to multiply the annual production times the number of years per time period in order to obtain the total production. The next set of constraints is the capacity constraints for steel mills. They differ substantially from those in the small static model because they include additions to capacity. CAPACITY CONSTRAINTS FOR STEEL MILLS (8.38) YbZ, k+ Y hmM1 eEM PEP reT I.l teT Capacity Initial + Capacity added utilized capacity before or during [ time period t The distinction between c and t in this equation is noteworthy. As elsewhere in the model, t is the time period index. AlthoughT is also a time period index, it is used in (8.38) as the running index to sum over the periods prior to time period t. Thus, the summation on the right-hand side of (8.38) is over e T and T t; that is, for the time periods before and including time period t. Consistent with this, the subscript on h is T rather than t. The next three constraints are for the investment variables h, s, and y. The first of these is like equation (8.7) discussed earlier. DEFINITION OF h (8.39) h.it = mhmgSgit meME EicI teB TE A SMALL DYNAMIC MODEL 233 Addition to L apai Adi to 1 .n Convex combination capacity in of investment sizes expansion unit = h at grid points m at steel mill ha rdpit imastlil . mg for expansion period t inLt Since the s variables are nonnegative and must sum to one (as indicated in the next constraint), the right-hand side of this constraint is said to be a "convex combination" of the investment-size grid points I. The sum- mation requirement on the s variables is written in combination with the zero-one requirement on the y variables to provide the constraint. CONVEX COMBINATION CONSTRAINTS (8.40) Ymit = Ys,gi mEME geG iel teTE In the mixed integer programming solutions to this problem the y variables are required to be either zero or one. If y is equal to one the s variables when summed over the grid points g must equal to one. This produces the convex combination. When the y variable is zero then the corresponding s variables must be zero. When the problem was solved in the linear rather than the mixed integer form, the y variables were restricted to be less than or equal to one. The market requirement constraint for this model is the same as for the small static model with the exception that time subscripts are added. MARKET REQUIREMENT CONSTRAINTS (8.41) 1 x,ij + cjt dcj ceCF i6l je-J to T [ latsto 1+Imports to Markel Shipment from all1 rem:t plants to + market j >rqi n market j m I I [at market j The next set of constraints is a set of upper bounds on total exports. EXPORT UPPER BOUNDS (8.42) £ Ze:! e" toT ceCE iel 234 MEXICAN CASE STUDY L Total exports in Export upper period t bound This constraint requires that exports of all products from all plants in each time period be less than or equal to an upper bound. It might be preferable to have an upper bound on the total exports of each type of product, but that level of detail is not used here. Although the model includes increasing marginal cost for investment in each expansion unit of each steel mill in each time period, it does not represent the fact that since most steel mills are surrounded by oceans, mountains, and cities it is impossible to construct a steel mill of more than a certain size at each location. In this model that size was set at 30 million tons of iron (both pig iron and sponge iron). It would be desirable in future versions of the model to replace this constraint with a site- specific upper bound or an increasing investment cost when total capacity exceeds certain levels. The constraint used in this model is: LIMIT ON IRON PRODUCTION AT EACH SITE (8.43) zpi, < 30 ieI pelpig iron, sponge iron) tET NONNEGATIVITY CONSTRAINTS (8.44) wcqit, z,,,, x , x " x uc- v'. vc., e,, hmr, smo >0 BINARY VARIABLE (8.45) Ymit = 0 or 1 These constraints restrict the investment variables y to be zero or one. Objective Function The objective function of this model is identical to the function for the small static model with two exceptions: there is a summation for all time periods and an appropriate discounting procedure, and there is an additional term for investment cost. OBJECTIVE FUNCTION (8.46) = 6,0 teT [ Total] [Discount] Years per costI Lfactor J Ltime period A SMALL DYNAMIC MODEL 235 + 00 + , + 0,, - 0"') Investment [aterial +[Transport] + [Imports] - [Exports] The only unusual thing about this objective function is the 0 parameter. Since the costs in all the cost component terms are on an annual basis and there are several years in each time period, it is necessary to multiply the annual cost by the number of years per time period. Of course, this arrangement embodies the assumption that the level of activity is the average for the years in the time period. This assumption is necessary to reduce the size of the model. The investment cost term 40 is new and therefore worthy of special attention. INVESTMENT COST (8.47) m= o tsm9ir te T ,eT meME geG i Investment Capital Convex combination of capital cost cost recover] at grid points I= I factor J The summation for the running time index - is over all time periods previous to and including time period t. This is required because investment costs are treated here like rental payments, and it is necessary to pay rent on all the investment done in previous periods and in the current period. For the sake of completeness, all the other cost terms are listed here. The only changes in these terms from those in the small static model are the addition of a time subscript and the addition of one term to the raw material cost equality. RAW MATERIAL COST (8.48) = Pd,U,i, u Y Y Y PciWcqit teT ceCR iel ceCM qeQ ieIM Raw . DomesticI [Production] material purchases of mining cost products TRANSPORT COST (8.49) e l + ceCF jJV ceCF ieI jeJ ceCF jcJ 236 MEXICAN CASE STUDY Transport Final products to Imports cost = L markets I+[to markets] ceCM 'elM iel ceCE iel + [Mines to steel mills] + [Exports] + .X + _ X Zi4 tt cCIC We VI'e ceCV iel + [Interplant shipments+ Imorts to IMPORT COST (8.50) 0. = ± pvVcj + _ L pvi, te T ceCF jeJ ceCV iE FImport [ Imports I Fmports Imprt+toto cost [markets La EXPORT REVENUES (8.51) Y peect teT ceCE iel Export Price revenues of Exports exports Appendix A. Notational Equivalence Sets Mathematical GAMS Mines IM IM Plants I I Markets J J Productive units M M Productive units for expansion ME ME Processes P P Commodities C C Raw material CR CR Imported raw material CV CV Mining products CM CM A SMALL DYNAMIC MODEL 237 Sets Mathematical GAMS Interplant shipments CI CI Final products CF CF Exportable commodities CE CE Energy commodities CENR ENERGY Time period T T Expansion time periods TE TE Quality levels Q Q Grid points G G Inequalities Mathematical GA cS Material balance constraints for mines (8.35) MBM Material balance constraints for steel mills (8.36) MB Capacity constraints for mining reserves (8.37) CCM Capacity constraints for steel mills (8.38) cc Definition of h (8.39) IH Convex combination constraints (8.40) IC Market requirement constraints (8.41) MR Export upper bounds (8.42) EB Limit on iron production at each site (8.43) ZB Objective function (8.46) OBJ Investment cost (8.47) AKAP Raw material cost (8.48) APSI Transport cost (8.49) ALAM Import cost (8.50) API Export revenues (8.51) AEPS Variables Mathematical GAMS z Z w W f XN XM XM U U h H 5 S y Y v V (continued) 238 MEXICAN CASE STUDY Variables (continued) Mathematical GAMS vr VR e E PHI PHIKAP PHIPSI PHILAM PHIPI PHIEPS Appendix B. GAMS Statement of the Small Dynamic Model A GAMs statement of the small dynamic model begins on the following page. GANS 1.0 M E X I C S - SMALL DYNAMIC BASIC DEFINITIONS 08/11/83 13.43.33. PAGE SET DEFINITIONS NEW MARGIN - 002-120 4 SET I STEEL PLANTS / ARMSA ALTOS HORNOS - MONCLOVA 5 FUNDIDORA MONTERREY 6 SICARTSA LAZARD CARDENAS 7 HYLSA MONTERREY 8 HYLSAP PUEBLA 9 TAMPICO TAMPICO 10 COATZA COATZACOALCOS / 11 12 IM MINES / COAHUILA COAL MINING REGION 13 ORE-NORTH NORTHERN IRON-ORE MINES 14 ORE-SOUTH SOUTHERN IRON-ORE MINES / 15 16 J MARKETS / MEXICO-DF MEXICO CITY 17 MONTERREY MONTERREY 18 GUADALAJA GUADALAJABA / 19 20 C COMMODITIES / PELLETS IRON ORE PELLETS - TONS 21 COKE TONS 22 NAT-GAS NATURAL GAS - 1000 N CUBIC METERS 23 ELECTRIC ELECTRICITY - MWH 24 SCRAP TONS 25 PIG-IRON MOLTEN PIG IRON - TONS 26 SPONGE SPONGE IRON - TONS 27 STEEL TONS / 28 29 CF(C) FINAL PRODUCTS / STEEL / 30 31 CE(C) EXPORT PRODUCT / STEEL / 32 33 CI(C) INTERMEDIATE PRODUCTS / SPONGE / 34 35 CR(C) RAW MATERIALS / NAT-GAS, ELECTRIC, SCRAP / 36 37 CM(C) MINING PRODUCTS / COKE, PELLETS / 38 39 CV(C) RAW MATERIALS IMPORTED / COKE, PELLETS / 40 41 P PROCESSES / PIG-IRON PIG IRON PRODUCTION FROM PELLETS 42 SPONCE SPONGE IRON PRODUCTION 43 STEEL-OH STEEL PRODUCTION IN OPEN HEARTH 44 STEEL-EL STEEL PRODUCTION IN ELECTRIC FURNACE 45 STEEL-BOF STEEL PRODUCTION IN SOF 46 STEEL-BOFS STEEL PRODUCTION IN BOF WITH HIGH SCRAP / 47 48 M PRODUCTIVE UNITS / BLAST-FURN BLAST FURNACES 49 OPENHEARTH OPEN HEARTH FURNACES 50 ROE BASIC OYCEN FURNACES 51 DIRECT-RED DIRECT REDUCTION UNITS 52 ELEC-ARC ELECTRIC ARC FURNACES / 53 54 ME(M) EXPANSION UNITS / BLAST-FURN, BOF, DIRECT-RED, ELEC-ARC / SAMS 1.0 ME X I C 0 - SMALL DYNAMIC BASIC DEFINITIONS 08/11/83 13.43.33. PAGE 2 SET DEFINITIONS 55 56 T TIME PERIODS / 1981-83, 1984-86, 1987-89, 1990-92, 1993-95 / 57 58 TE(T) EXPANSION PERIODS / 1984-86, 1987-89, 1990-92, 1993-95 / 59 60 ENERGY(CR) / NAT-GAS, ELECTRIC / 61 62 Q COST LEVELS / 1*5 / 63 64 G INVESTMENT FUNCTION SEGMENTS / 1*4 / 65 66 ALIAS (T,TAU),(I,IP),(TE,TAUE); 67 68 SCALAR BASEYEAR BASE YEAR / 1979 / 69 THETA YEARS PER TIME PERIOD / 3 / 70 PARAMETER MIDYEAR(T) PERIOD MID-YEARS 71 TS(T,TAU) TIME SUMMATION MATRIX; 72 73 MIDYEAR(T) - BASEYEAR + THETA*0RD(T) 74 TS(TE,TAUE)$(ORD(TAUE) LE ORD(TE)) = 1 75 76 DISPLAY MIDYEAR,TS; GAMS 1.0 M E X I C S - SMALL DYNAMIC BASIC DEFINITIONS 08/11/83 13.43.33. PAGE 3 TECHNOLOGY DATA 78 TABLE A(C,F) INPUT-OUTFUT COEFFICIENTS 79 80 FIG-IEON SFONGE STEEL-SM STEEL-EL STEEL-BSF STEEL-MEFS 81 82 PELLETS -1.58 -1.38 83 COKE -.63 84 NAT-S -.38 85 ELECTRIC -.68 86 SCRAP -.33 -.12 -.25 87 FIG-IN 1.0 -.77 -.95 -.82 88 SFONGE 1.0 -1.09 89 STEEL 1.0 1.0 1.0 1.0 90 91 *TWO 10 COEFFSCIENTS WERE CHNMEDS ACCORDING TO SUGGESTIOS MY ETLS 92 93 NAT-GAM,SPOE FROM -.57 TO -.38 94 ELECTEIC,STEEL-EL FNOW -.5M TO -.68 95 96 TMESE FIGUEES CORRESPOND TO SUMEE 1980 MYLSAF FEEFOEMANCE 97 98 99 TABLE B(M,F) CAPACITY UTILIZATION 100 101 PIG-lEON SPOMGE STEEL-ON STEEL-EL STEEL-BOF STEEL-ROS 102 103 LAST-FURM E.O 104 OPENMEARTH 1.0 105 DOF 1.0 1.D 106 DIEECT-RED 1.0 107 ELEC-AEC 1.0 108 109 1 10 TARLE K(M,I) CAPACITIES SF PRODUCTIVE 0NIT0 (MILL TONS FEE YEAR) 111 112 AHMSA FUNDEDORA SICAETSA HYLSA HYLDAP 113 114 BLAST-FUEN 3.25 1.40 1.10 115 OPENMEARTH 1.00 .85 116 BSF 2.07 1.00 1.30 117 DIRECT-ED .98 1.01 118 ELEC-AEC 1.13 .56 119 NEW MARG1IN 002-072 121 TADLE KM(CM,IM,-) MINING CAPACITY DATA 122 1 23 F-LOW F-HSGS %MAS EXPO F-LOW LOW FEECS (00$ FEE TON) 1 24 S-MIEN: HIGE PRICE (US$ FEE TON) 1 25 COKE.COAHVILA 52 100 230 1.3 WNlAX : MAXIMUM MINE CAPACITY (MILLION TOSS) 126 ELLETS.OE-NOETH 10.7 38 60 1.3 127 FELLETSORE-SOUTH 18.7 38 115 1.3 NEW MARGIN 002-120 129 CAMS 1.0 M E XI C 0 - SMALL DYNAMIC BASIC DEFINITIONS 08/11/83 13.43.33. PAGE 4 TECHNOLOGY DATA 130 PARAMETEE WBAE(CS,IM) STOCK OF NINE PRDUICTS (MlLLION TOSS) 131 PS(CM,Q,IM) PURCHASE PRICE OF SINS PRODUICTS (US $ PED TON); 132 133 WBAE(CM,IM) = KM(CM,IM,'WMAX')/CARD(Q); 134 PW(CM,Q,IM)$KM(CM,IM,"WMAXY) -KM(CM,IM,*P-LOW") + (KM(CMl,IM,"P-ISD")--KM(CMIM*"P-LOW))- 135 ((ORD(Q)-I)/(CARD(Q)I))*KM(CMIM,EXPO); 136 137 DISPLAY WBAR,PW; 138 139 SCALAR DT TOTAL DEMAND POE FINAL. COODS IN 1979 (MILLION TONS) /5.2 140 DIE DAW STEEL EQUIVALENCE (PEDCENT) 40 141 GD ANNEAL GROWTH DATE OF DEMAND (PERCENT) 10 143 PARAMETER DD(J) DISTEEBUTION OF DEMAND MEXICODF .55, MONTEREE .3, GUADALAJA .15 143 D(CF,J,T) DEMAN POD STEEL (HILL TPE) 144 EU(T) EXMOET SOlND: UPPER 145 1 46 D(IYTEEL',J,T) =DY N (1 + ESF/100) * DD(J) * (I + OD/100)**(MIDYEAR(T)-BASEYEAE); 147 E(T) - .2; 14$ 148 49DISPLAY DBR,; OAMS 1.0 M XI C 0 - SMALL DYNAMIC BASIC DEFINITIONS 08/11/83 13.43.33. PAGE 5 TRANSPORTATION DATA 11TARLE RD(-) * RAIL DISTANCES FR0M PLANTS TOD 04SEXPS (EM) 152 153 MEXICO-SF M0NTER6EY 5WAD4LAJA 00204T 154 155 AHMS 1204 218 1125 139 156 FUNDIDORA 1017 1050 521 157 S1C45TS4 819 1305 704 158 SOLS 101.7 1030 521 159 H 4 lB1 1085 760 315 160 TAMPICO 941 521 995 161 COATZA 900 1756 1100 162 1H90RT 428 521 300 162 163 164 165 TABLE RI(1,1P) DNTERPLANT SAIL DISTANCES (KM) 166 167 AHMSA FONDIDOBA SICASA HYLSA BYLSAP TAMPICO CR6004 168 169 FUNDIDORA 218 170 SICARTSA 1416 1322 171 00504 18 SI 1327 172 05504A 300 159 995 19 17 3 TAMIPICO 239 5)1 1319 521 1111 N17 4 104004 1850 1756 1638 1756 671 1702 175 176 1717 TAILS RM(IM,N) SAIL DISTANCES FR5O1 MINES TO PLAITS (KMo) 177 178 179 AHMSA PUNDIDORA SICARTSA HYLSA BYLSAP TAMPICO COATZA 180 181 C0AHU1LA 120 400 I5IS 400 1420 900 2100 lBS2 ODE-SORTS 219 563 1 6 13 563 1411 1 048 2 195 183 ORC-SOUTH 1490 396 1396 1116 1338 1500 184 1 85 * HECULES 0100 A S THE CENTER OP TIE NORHERN OR E DSTRICT 186 * PENA COLOSORAO 00ED AlS TIE C ERISE P oER TIE SNOOTHERN ORE NISTRICT 1B87 * 00X8E 4104500RT4 AW IIC 0000E LAO TRUOCHAS D ISTANC ES 1 88 1 89 PARAMETER MUF( I J) TRANSPORT COST: PINAL PRODUCTS (00 $ PER TON) 190 0UN5(0I1I) TRANSPORT COOT: INTER PLAST SlilPENTS (US $ PER TON ) 1 91 MUMN(TI,) TRANSPORT COST: MINE To PLANT (NS S PER TON) 1 92 M100(J) TRASPORT COST: DM0010 (00 U $ PER TON ) 1 93 800P'(N) TRANSPORT COOT: EXPORTS (0s PER TON); 194 195 RI(DIDP) MAX(RI(D,IP),RD(IP,1) 196 MUF(i,) ( 2.48 + .00B4*RD(, $RS(I,J); 197 MIS(IP) ( 2.48 + 8S4 Ri(SIP)) ORI(I,IP); 198 (IM 1) 48 + :0084oRX(Is,s)) $RM(SM,I) 19 102 .B*.00004*S('NM PSIT',J))NRS("IMPORT,) 199 vj 200 MUE(I) 2 . 48 + .0084*R(I.EXPORT))$RD(I,'XPOT 201 207 NISPLA MLR,MD(,M*),MV,MRAR; CAMS 1.0 ME X I C 0 - SMALL DYNAMIC BASIC DEFINITIONS 08/11/83 13.43.33. PACE 6 INVESTMENT AND PRICE DATA NEW MIARGIN = 002-072 205 TABLE INV(ME,*) INVESTMENT EDIT TABLE 206 202 111AT PIHBAT BETA HHAT :ICOBOMIES SM SCALE SIZE (MILL TOSS/TM) 208 PHIHAT: COOT OP PLANT OP OIZS BRAT (BILL US$) 209 BLAST-FURN 1.5 230 .6 BETA ;SCALE MACTIE: PBIHAT =IX*HHAT**BETA 210 BOF 1.5 120 .6 211 DIRECT-RED .8 100 .6 ACCORDING TI R.J. EMIL, STIEL TIMES ENTIRE 212 ELEC-ARC .5 AT .6 JUNE 1979 213 NEW BASIS- 002-120 215 216 PARAMETER SITFI(() SITS MACTOER (FUNDIDORA,HYLSA) 1.1, (SSCARTSA,BYLSAP,ABMSA) 1, (TAMPICO,COATZA) 1.2/ 217 OMECA(ME,G,I) PLANT COST AT SEMENMT (MILLIOM 00$) 218 SB(ME,G) SEMMENT SIZE (MILLION TONS PES TEAM) 219 ZETA LIME OF PRODUCTIME UMIT (YRB) 220 RBO DISCOUNT SATE 221 MOMMA CAPITAL RECOPERT MACTOM 222 DELTA(T) SCOUNT MACTOE 223 224 INV(ME,'MIEB") - INV(ME,PHIHAT)(.5*(TNVME,BTA")-)-l); 225 226 OMEGA(ME,"1",I) =INV(ME, "FIXEDSIEI) SB(ME,"1") - 0 227 OMIEGA(MIE,"2',I) - INVME,"PHIHAT")*STTE(T) 1SB(ME, "2") - INV(ME,"HHAT") 228 ONEIA(ME,"3",I) = OMEGA(ME,"2",I)*3 SB(ME,*'3") -IS(ME,"2-)*3 229 OMECA(ME,'A4 .i) =OMEGA(ME,"2" ,I)*6*1.25 SBME,"4") - SB(ME,"2")*6 230 231 ZETA - 20; EDO =.1; SEIGMA -DRfM/(1=(1+RHO)**(-=ZETA)); 232 DELTA(T) =(1+RSB0)**(BASEYEAR-MIDYEAR(T)); 233 230 231 SCALAR BLED ESOURCE LEVEL 236 IEON IRSS PEODUCTIOE BOUD (MILLION TOMB PER YEAR) /30 237 PARAMETEE PD(CR,I,T) DOMESTBC PRICES 238 REGION(l) LOCATIONS WITH ENERGY SUBSIDY /(COATZA,SICARTSA,TAMPICO) .3/ 239 PDB(CR) BABE PRIZE OP BOMENTIC MATERIALS (PESOB PEE TOM) / NAT-MAO 14, ELECTRIC 26, BCRAP 105 / 240 PV(C) IMIPORT PRIES (U0$ PER TOE) / COKE 60, PELLETS A0, STEEL 150 / 241 PE(CE) EXPORT PRICEB (US$ PEE TON) / STEEL 140 242 2A3 PD(CR,S,T) - PDB(CR); 244 PD("NAT-ZAS",I,T) - MIN(12W, PDB("NAT-GAS") + (128-PDB("NAT-GAS"))/4E(OR(T)-E)); 215 PD(ENERGY,S,T) - PD(tNERGY,I,T)*(l=REGION(I)); 246 207 DSPLAY SSIEOA.0112A,BELTA,ISM,SB,PDIIONRLE. CAMS 1.0 M EX I C 0 - SMALL DYNAMIC BASIC DEFINITIONS 08/11/83 13.43.33. PAGE 7 MODEL DEFINITION 249 VARIABLES Z(P,I,T) PROCESS LEVEL (MILL TPY) 250 W(CM,Q,IM,T) PRODUCTION OF MINING PRODUCTS (MILL TPY) 251 X(C,I,J,T) SHIPMENT OF FINAL PRODUCTS (MILL TPY) 252 XN(C,I,IP,T) INTERPLANT SHIPMENTS (MILL TPY) 253 XM(C,IM,I,T) SHIPMENT OF MINING PRODUCTS (MILL TPY) 254 U(C,I,T) PURCHASE OF DOMESTIC MATERIALS (MILL UNITS PER YEAR) 255 H(M,I,T) CAPACITY EXPANSION (MILL TPY) 256 S(ME,G,I,T) INVESTMENT FUNCTION SEGMENT 257 Y(ME,I,TE) BINARY VARIABLE 258 V(CF,J,T) IMPORTS (MILL TPY) 259 VR(C,I,T) IMPORTS OF RAW MATERIALS (MILL TPY) 260 E(C,I,T) EXPORTS (MILL TPY) 261 262 PHI TOTAL COST (DISCOUNTED) (MILL US$) 263 PHIKAP(T) CAPITAL COST (MILL US$) 264 PHIPSI(T) RAW MATERIAL COST (MILL US$) 265 PHILAM(T) TRANSPORT COST (MILL US$) 266 PHIPI(T) IMPORT COST (MILL US$) 267 PHIEPS(T) EXPORT REVENUE (MILL US$) 268 269 POSITIVE VARIABLES Z,W,X,XN,XM,U,H,S,V,VR,E; BINARY VARIABLE Y; 270 271 EQUATIONS MB(C,I,T) MATERIAL BALANCE: STEEL PLANTS (MILL TPY) 272 MBM(CM,IM,T) MATERIAL BALANCE: MINES (MILL TPY) 273 CC(M,I,T) CAPACITY CONSTRAINT: STEEL PLANTS (MILL TPY) 274 CCM(CM,Q,IM) CAPACITY CONSTRAINT: MINES (MILL TPY) 275 IH(ME,I,TE) DEFINITION OF H 276 IC(ME,I,TE) CONVEX COMBINATION AND 0-1 CONSTR 277 MR(CF,J,T) MARKET REQUIREMENTS (MILL TPY) 278 EB(T) EXPORT BOUNDS (MILL TPY) 279 ZB(I,T) LIMIT ON STEEL PRODUCTION (MILL TPY) 280 281 OBJ ACCOUNTING: TOTAL DISCOUNTED COST (HILL US$) 282 AKAP(T) ACCOUNTING: INVESTMENT COST CHARGES (MILL US$) 283 APSI(T) ACCOUNTING: RAW MATERIALS (MILL US$) 284 ALAM(T) ACCOUNTING: TRANSPORT (MILL US$) 285 API(T) ACCOUNTING: IMPORT COST (MILL US$) 286 AEPS(T) ACCOUNTING: EXPORT REVENUE (MILL US$); 2 z- 22 2 CO C 0~ O C CO O C CO O C 0 0 0 0 0 0 0 2Q 24 飾 匕 《 ＇→卜 t嗎卜－ 尸＇、．》 尸→卜必Q 。U、j ‘凶＞& 么綱綱＇•｀ 飄、＇卜州卜州曰 、｀》、＇、＇- ｀、喪訌實》 切騙U O〉一卜→ 二＇&＇禹、匕 叩HH》 h UU》 斗之竅》 的p二么 + +＋→ 卜＇&＇、》 一卜曰Q Hh闕訌 自芝。勻 O。魚 →叩州＋卜 →之化＇，、卜 勿狀XP禺 斗文．斗、＇ rH一、＇望州 Z~r才‘U必 O一U〝＇必 HH‘。→他鰓 細→一→》么 Z訌。H。 H口文f，為訌 必魚魚一。J江 么UU么必C啊 心U→、州U→配配 的之芝r→7公 司斗p二東為斗7 引＋+,l曰。 留紹11望的 方―IU上 《＇一＇、H么 之卜＇、卜實 〉→卜→＜O O芝→的7才 記H么》H 嗣必么U二k 《奮江二必置 化之飢么斗斗H 頃O&Z H訌H ．卜的蠶 O究00 U么二k父 卹，“萬U HQ→．→究熙 曰＇｀曰 k必一仲→J圓 國0&H斗Qp OJ么國00 劉訌《＜《乞的 上 《 O 鉀7 CAMS 1-0 M E X I C 0 - SMALL DYNAMIC BASIC DEFINITIONS 08/11/83 13.43.33. PAGE 10 REFERENCE MAP OF VARIABLES VARIABLES TYPE REFERENCES A PARAM REP 289 DEFINED 78 DCL 78 AEPS EQU DEFINED 321 DCL 286 AKAP EQU DEFINED 311 DCL 282 ALAM EQU DEFINED 315 DCL 284 API EQU DEFINED 319 DCL 285 APSI EQU DEFINED 313 DCL 283 B PARAM REP 294 DEFINED 99 DCL 99 BASEYEAR PARAM REP 73 146 232 DEFINED 68 DCL 68 C SET REP 29 31 33 35 37 39 78 240 251 252 253 254 259 260 271 7-289 8*290 DEFINED 20 CONTROL 289 DCL 20 cc EQU DEFINED 294 DCL 273 CCM YOU DEFINED 296 DCL 274 CE SET REP 241 290 304 316 2*321 DEFINED 31 CONTROL 304 316 321 DCL 31 CF SET REP 143 258 277 290 3*302 2-315 2*319 DEFINED 29 CONTROL 302 315 319 DCL 29 Cl SET REY 2*290 317 DEFINED 33 CONTROL 317 DCL 33 cm SET REP 121 130 131 133 4*134 135 250 272 274 289 2*292 2*296 2*313 316 DEFINED 37 CONTROL 133 134 292 296 313 316 DCL 37 CR SET REP 60 237 239 243 289 2*313 DEFINED 35 CONTROL 243 313 DCL 35 cV SET REP 289 317 2*319 DEFINED 39 CONTROL 317 319 DCL 39 D PARAM. REY 149 W2 DEFINED 146 DCL 143 DO PARAM REP 146 DEFINED 142 DCL 142 DELTA PARAM REP 247 309 DEFINED 232 DCL 222 DT PARAM REP 146 DEFINED 139 DCL 139 E VAR REP 269 290 304 316 321 DCL 260 BE EQU DEFINED 3o4 DCL 278 ENERGY SET REP 245 DEFINED 60 CONTROL 245 DCL 60 ED PARAM REY 3o4 DEFINED 147 DCL 144 G SET REP 217 219 256 2*299 300 2-311 DEFINED 64 CONTROL 298 300 311 DCL 64 CD PARAM REP 146 DEFINED 141 DCL 141 H VAR REP 269 294 298 DCL 255 I SET REP 66 110 165 177 189 190 191 193 2*195 2*196 2*197 2*198 2*200 216 217 226 227 228 229 237 238 2*245 249 251 252 253 254 255 256 257 259 260 271 273 275 276 279 4*289 4*290 292 3*294 2-Z98 2*300 302 304 2*307 2-311 2*313 2*315 4*316 4*317 319 321 DEFINED 4 CONTROL 195 196 197 198 200 226 227 228 229 243 244 245 289 292 294 298 300 302 304 307 311 313 315 2*316 2-317 319 321 DCL 4 Ic EQU DEFINED 300 DCL 276 IH EQU DEFINED 298 DCL 275 IM SET REP 121 130 131 133 4*134 135 177 191 2*198 250 253 272 274 289 2*292 2*296 2*313 2-316 DEFINED CAMS 1.0 I E X I C S - SMALL DYNAMIC BASIC DEFINITIONS 08/11/83 13.43.33. PAGE 11 REFERENCE MAP OF VARIABLES VARIABLES TYPE REFERENCES 12 CONTROL 133 134 193 289 292 296 313 316 DCL 12 INV PARAM REP 2*224 226 2*227 247 DEFINED 205 224 DCL 205 IF SET REF 165 190 2*195 2*197 252 2*290 2*317 CONTROL 195 197 2*290 317 DCL 66 IRON PARAM REP 247 307 DEFINED 236 DCL 236 J SET REF 142 143 146 189 192 2*196 2*199 251 258 277 290 3*302 4*315 319 DEFINED 16 CONROL 146 196 199 290 302 2*315 319 DCL 16 K PARAM REP 294 DEFINED 110 DCL 110 KM PARAM REP 133 4*134 135 DEFINED 121 DCL 121 M SET REF 54 99 110 255 273 4R294 DEFINED 48 CONTROL 294 DCL 48 MAX FUNCT REF 195 MB EQU DEFINED 289 DCL 271 MBm EQU DEFINED 292 DCL 272 ME SET REP 205 217 218 2*224 226 2*227 2*228 2*229 256 257 275 276 294 3*298 2*300 2*311 DEFINED 54 CONTROL 224 2*226 2*227 2*228 2*229 298 300 311 DCL 54 MENSD MODEL REF 325 DEPINED 323 DCL 323 MIDYEAR FARAD REF 76 146 232 DEFINED 73 DCL 70 MIN FUNCT REF 244 MR EQU DEFINED 302 DCL 277 MUE PARAM REF 202 316 317 DEFINED 200 DCL 193 MUF PARAM REF 202 315 DEFINED 196 DCL 189 MUM PARAM REP 202 316 DEFINED 198 DEL 191 MUN PARAM REF 202 317 DEFINED 197 DCL 190 MUV PARAM REP 202 315 DEFINED 199 DCL 192 OBJ EQU DEFINED 309 DCL 281 OMEGA PARAM REF 228 229 247 311 DEFINED 226 227 228 229 DCL 217 P SET REF 78 99 249 2*289 2*294 DEFINED 41 CONTROL 289 294 DCL 41 PD PARAM REF 245 747 313 DEFINED 243 244 245 DCL 237 PDB PARAM REF 243 2*244 DEFINED 239 DCL 239 PE PARAM REF 321 DEFINED 241 DCL 241 PHI VAR REF 309 325 DCL 262 PHIEPS VAR REF 309 321 DCL 267 PHIKAP VAR REF 309 311 DCL 263 PRILAM VAR REF 309 315 DCL 265 PHIPI VAR REF 309 319 DCL 266 PRIPSI VAR REF 309 313 DCL 264 Pv PARAM REF 2*319 DEFINED 240 DCL 240 PW PARAM REF 137 313 DEFINED 134 DCL 131 Q SET REF 131 133 2*135 250 274 292 296 2*313 DEFINED 62 CONTROL 134 292 296 313 DCL 62 RD PARAM REF 2*196 2*199 2*200 DEFINED 151 DCL 151 REGION PARAM REF 245 DEFINED 238 DCL 238 RHO PARAM REF 2*231 232 DEFINED 231 DCL 220 RI PARAM REF 2*195 2*197 DEFINED 165 195 DCL 165 RAMS 1.0 It E X I C 0 - SMALL DYNAMIC BASIC DEFINITIONS 08/11/83 13.43.33. PAGE 12 REFERENCE MAP OF VARIABLES VARIABLES TYPE REFERENCES RLEV PARAM REP 247 296 DEFINED 235 DCL 235 RM PARAM REF 2*198 DEFINED 177 DCL 177 RSE PARAM REF 146 DEFINED 140 DCL 140 S VAR REF 269 298 300 311 DCL 256 sa PARAM REF 228 229 247 298 DEFINED 226 227 228 229 DtL 218 SIGMA PARAM REF 247 311 DEFINED 231 DCL 221 SITE PARAM REF 226 227 DEFINED 216 DCL 216 SET REF 58 66 70 71 73 143 144 146 222 232 237 244 245 249 250 251 252 253 254 255 256 258 259 260 263 264 265 266 267 271 272 273 277 278 279 282 283 284 285 286 4*289 4*290 2*292 2*294 296 3*302 2*304 2*307 6*309 2*311 4*313 3*315 2*316 2*317 3*319 2*321 DEFINED 56 CONTROL 73 146 147 232 243 244 245 289 292 294 296 302 304 307 309 311 313 315 319 321 DCL 56 TAU SET REF 71 2*294 2*311 CONTROL 294 311 DCL 66 TAE SET REP 74 CONTROL 74 DCL 66 TE SET REF 66 74 257 275 276 2*298 2*300 DEFINED 58 CONTROL 74 298 300 DCL 58 TIETA PARAM REF 73 296 309 DEFINED 69 DCL 69 TS PARAM REF 76 294 311 DEFINED 74 DCL 71 u VAR REF 269 289 313 DCL 254 V VAR REP 269 302 315 319 DCL 258 VR VAR REF 269 289 317 319 DCL 259 B VAR REF 269 292 296 313 DCL 250 WBAR PARAM REF 137 296 DEFINED 133 DCL 130 X VAR REF 269 290 302 315 DCL 251 KA VAR REF 269 289 292 316 DCL 253 XN VAR REP 269 2*290 317 DCL 252 y VAR REF 269 300 DCL 257 C VAR REF 269 289 294 2*307 DCL 249 ZB EQU DEFINED 307 DCL 279 ZETA PARAM REF 231 DEFINED 231 DCL 219 SETS C COMMODITIES CE EXPORT PRODUCT CF FINAL PRODUCTS Cl INTERMEDIATE PRODUCTS CM MINING PRODUCTS CR RAE MATERIALS CV RAW MATERIALS IMPORTED ENERGY G INVESTMENT FUNCTION SEGMENTS I STEEL PLANTS IM MINES IP ALIAS FOR I GAMS 1.0 M E X I C 0 - SMALL DYNAMIC BASIC DEFINITIONS 08/11/83 13.43.33. PAGE 13 REFERENCE MAP OF VARIABLES SETS J MARKETS M PRODUCTIVE UNITS ME EXPANSION UNITS P PROCESSES Q COST LEVELS T TIME PERIODS TAU ALIAS FOR T TAUE ALIAS FOR TE TE EXPANSION PERIODS PARAMETERS A INPT-OUTFIT COEFFICIENTS B CAPACITY UTELELATION BASEYEAR SE TEAR D DEMAND FOR STEEL (MILL TPY) D RISTRIRUTION OP DEMAND DELTA DISCOUNT PACTOR DT TOTAL DEMAND IDE FINAL COOEDS IN 1979 (MILLION TORNS) EU EXPERT BOEND: UPPER GO ANNUAL GROWTH NATE OF DEMAND (PERCENT) IRN INSTMENT COST TASIS IRON IRON PRODUCTION ROUND (MILLION TONS PEE YEAR) K CAPACITIES OF PRODECTIVE UEITS (MILL TONS PER TEAE) KM MINING CAPACITY EATA MIDYEAR PERIOD MID-YEARN MUE TRANSFORT COOT: EPORTS (US $ PER TON) MUF TRANSPORT COST: FINAL PRODUCTS (US $ FOR TON) mum TRANSPORT COST: MINE TO PLANT (OS $ PER TON) MEN TRANSPORT COST: UNTERPLANT SMLPMENTS (US $ PEE TON) MUV TRANSPORT COOT: IMPORTS (U0 $ FEE TON) OMEGA PLANT COST AT SEGMENT (MILLION 00$) PD ROMESTIC FRICES PDB RARE PRICE OF ROMESTIC MATERIALS (PEOS PER TON) PE EXPORT FEINE (00$ FOR TON) PV IMPORT PRICER (03$ PER TON) FW PURCHASE PRICE OF MORE PRODECTS (US $ PER TON) RD RAIL DISTANCES PROM PLANTS TO MARKETS (KM) REGION LOCATIONS NETS ENERGY SUSIDY RHO DISCOUNT RATE RI INTEFLANT RAIL DISTANCES (KM) RLEV REROERCE LEVEL ERR RAIL DISTANCES PROM MINER TO PLANTS (KM) ERR RAN STEEL EQUIVALENCE (PERCENT) SB DEGMENT NILE (MILLION TONS FIR TEAR) SIGMA CAPITAL RECOVERY FACTOR SITE RITE FACTOR THETA YEARS PER TIME PERIOD TS TIME DMMATION MATRIX WEAR STOCK OP MINE PRODUCTS (MLLOON TONS) GAMS 1.0 M E X I C 0 - SMALL DYNAMIC BASIC DEFINITIONS 08/11/83 13.43.33. PAGE 14 REFERENCE MAP OF VARIABLES PARAMETERS ZETA LIFE Of PRODUCTIVE UNIT (YEARS) VARIABLES E EXPORTS (MILL TPY) H CAPACITY EXPANSION (MILL TPY) PHI TOTAL COST (DISCOUNTED) (MILL 0S$) PHIEPS EXPORT REVENUE (MILL US$) PHIKAP CAPITAL COST (MILL US$) PHILAM TRANSPORT COST (MILL US$) PHIPI IMPORT COST (MILL US$) PHIPSI RAW MATERIAL COST (MILL US$) S INVESTMENT FUNCTION SEGMENT U PURCHASE OF DOMESTIC MATERIALS (MILL UNITS PER YEAR) V IMPORTS (MILL TPY) VR IMPORTS OF RAW MATERIALS (MILL TPY) w PRODUCTION OF MINING PRODUCTS (MILL TPY) x SHIPMENT OF FINAL PRODUCTS (MILL TPY) XM SHIPMENT OF MINING PRODUCTS (MILL TPY) XN INTERPLANT SHIPMENTS (MILL TPY) Y BINARY VARIABLE Z PROCESS LEVEL (MILL TPY) EQUATIONS AEPS ACCOUNTING: EXPORT REVENUE (MILL US$) AKAP ACCOUNTING: INVESTMENT COST CHARGES (MILL US$) ALAM ACCOUNTING: TRANSPORT (MILL US$) API ACCOUNTING: IMPORT COST (MILL US$) APSI ACCOUNTING: RAW MATERIALS (MILL US$) CC CAPACITY CONSTRAINT: STEEL PLANTS (MILL TPY) CCM CAPACITY CONSTRAINT: MINES (MILL TPY) EN EXPORT BOUNDS (MILL TPY) IC CONVEX COMBINATION AND 0-1 CONSTR EN DEFINITION OF H MB MATERIAL BALANCE: STEEL PLANTS (MILL TPY) MBM MATERIAL BALANCE: MINES (MILL TPY) MR MARKET REQUIREMENTS (MILL TPY) OBJ ACCOUNTING: TOTAL DISCOUNTED COST (MILL US$) ZB LIMIT ON STEEL PRODUCTION (MILL TPY) MODELS MERSD SMALL DYNAMIC STEEL PROBLEM A SMALL DYNAMIC MODEL 253 Appendix C. Derivation of Part of the Investment Cost This appendix derives the expression co, = 6(0.5#-' - 1), which is the fixed charge portion of the capital cost approximation. Consider first the general problem of specifying the investment cost function in industrial planning models. Frequently, the only data available from the engineers provide the analyst with a single point; for example, "the last blast furnace we built cost $250 million and had a capacity of 1.5 million tons of pig iron per year." This kind of information is used to provide the point (6, ) in figure 8-3. That is, h is the size of unit at which economies of scale are exhausted, and to is the investment cost for a productive unit of that size. It is then assumed that the investment cost between 0 and h is a smooth Figure 8-3. Investment Cost Approximation A 0 Adiintocpct 254 MEXICAN CASE STUDY Figure 8-4. Nonlinear Investment Cost Approximation 0 h* h Capacity Figure 8-5. Linearized Investment Cost Approximation E D A B 0 U C 0 h* Addition to capacity A SMALL DYNAMIC MODEL 255 exponential function of the form (8.52) w = phf where u = cost parameter # = scale parameter. This is shown in figure 8-4. It is fit through the origin 0 and the point A. For the case at hand, the parameter # is chosen to be 0.6, indicating the presence of substantial economies of scale in investment cost. Next the investment cost function (8.52) is evaluated at a capacity level equal to half the size at which the economies of scale are exhausted, that is, at h* = 0.5h. This yields the cost (8.53) * =(h*) = t(0.5 h)fl. The point (w*, h*) is plotted as point B in figure 8-4. Then two straight lines are constructed. The first one is through the points B and A. The point at which this line crosses the vertical axis is labeled point C, as shown in figure 8-5. Second, the horizontal line EDA is constructed. Using the proportionality of the triangle ACE we can write (8.54) - h h -h* and recognizing the two definitions (8.55) (0* =,u(ah) = 6t h* = A, we can rearrange expression (8.54) into (8.56) (0-0 (1 - 06 and thus (8.57) 10-c The special case of a = 0.5 gives S0.51- 0.5 (8.58) (o,= = c - (0.51'--1) 0.5 the expression sought in this appendix. 9 Results of the Small Dynamic Model IN DYNAMIC MODELS the results of greatest interest are the investment activities. Thus in this chapter investment results will be examined first and will be followed by an analysis of mining, steel production, and markets. As is customary, the results of a base solution will be discussed first in some detail. Then a variety of experimental results will be analyzed in less detail. The specification of and the parameters for the base solution have been described in considerable detail in the previous chapter. However, a few particularly important assumptions made in the base solution need to be reviewed since they will be varied during the experimental runs. In brief, these assumptions are: 1. Natural gas price rises from $14 to $128 per thousand cubic meters over the time horizon covered by the model 2. The electricity price is constant at $26 per megawatt-hour. 3. The price of energy inputs is 30 percent lower at SICARTSA, Tampico, and Coatzacoalcos than at the other plant sites. 4. No upper bounds are placed on steel production at each site. 5. Reserves of ore and coal are maintained at existing levels. 6. The price of imported coke is held constant at $60 per ton. The first assumption is one of the most important in this study. The domestic price of natural gas in Mexico in 1979 was $14 per thousand cubic meters (about 40 cents per thousand cubic feet) while the international price was $128 per thousand cubic meters (about $3.60 per thousand cubic feet). Thus it is assumed in the base run that the Mexican 256 RESULTS OF SMALL DYNAMIC MODEL 257 government will slowly allow the domestic price to rise from $14 to $128 over the period from 1981 to 1995. Of course, by that time the international price may be higher yet, but this possibility was not considered in the present study. It can be argued that, since the opportunity cost for the use of the gas is the international price, the base solution should include a price of $128 for natural gas in all time periods. However, the purpose of this study is not to recommend how capacity should be expanded in the Mexican steel industry but rather to analyze the logical consequences of various policy decisions affecting the capacity expansion of that industry. Second, for the base run the electricity price is held constant across all time periods at the base period price of $26 per megawatt-hour. This corresponds to the domestic price in 1979. The effective coal price in the model does rise somewhat as the higher quality coal is exhausted over the period covered by the model, but the imported price for coke remains constant. One of the experiments discussed below allows the electricity price to rise. Third, Mexico has a decentralization policy to encourage industry to locate in less congested areas. One part of that policy makes natural gas and electricity prices 30 percent lower at three sites in this model: SICARTSA, Tampico, and Coatzacoalcos. This policy, combined with the policy of keeping domestic natural gas prices below international prices, provides a strong incentive to use direct reduction methods rather than blast furnaces and to install these direct reduction units at one of these three sites. Fourth, though the model contains an upper bound on the amount of iron which can be produced at any particular site, this bound is so large (30 million tons) as to not limit the solutions very much. If one wished to examine solutions in which there is more decentralization, one could either tighten the iron production bound or add a bound on steel production at each site. The alternative of adding a bound on steel production is used in one of the experiments. Fifth, it is assumed that the existing reserves of coal and iron ore are not increased during the time horizon covered by the model. Although this is unlikely, it is useful to plan what to do in the event that no new reserves are discovered. An experiment in which the reserves are doubled is also included to see how much impact this has on the investment strategy for the industry. Moreover, the assumption of no new reserves allows one to study the effects of the exhaustion of domestic iron ores on the cost of steel and on the best locational investment strategy for the industry. 258 MEXICAN CASE STUDY Sixth, the price of imported coke is held constant at 560 per ton under the assumption that there are sufficient world reserves of coking coal to hold this price constant. This assumption is modified in one of the experiments discussed below. The base solution includes the six major characteristics described above and sets the stage for the following experiments: 1. Natural gas price constant at the domestic price level 2. Natural gas price constant at the international price level 3. Rising electricity price 4. Rising imported coke price 5. Removal of energy location subsidies 6. Iron ore and coal reserves doubled 7. Restriction of steel production at each site. A summary of these experiments is given in table 9-1. It seems likely that, if Mexico should hold domestic prices of natural gas constant at the 1979 level (roughly a factor of ten less than international prices), the best plan for the steel industry is to invest heavily in direct reduction facilities. Similarly, if natural gas prices are allowed to rise immediately to international levels, it seems likely the steel industry should invest in blast furnaces. The first two experiments provide an analysis which shows that both of these conjectures are correct. Since natural gas prices rise in the base solution, it seems logical that other energy sources such as electricity will also rise in price. If this Table 9-1. Summary of Experiments Natural Electric- gas ity price price Imported (dollars (dollars coke Energy Iron per 1,000 per price location Iron ore output Experiment cubic megawatt- (dollars subsidy and coal at each number meters) hour) per ton) (percent) reserves site Base 14 128 26 60 30 1 +INF 1 14 26 60 30 1 + INF 2 128 26 60 30 1 + INF 3 14 128 26-78 60 30 1 +INF 4 14-128 26-78 60-*90 30 1 +INF 5 14- 128 26 60 0 1 + INF 6 14 -128 26 60 30 2 + INF 7 14 128 26 60 30 1 10 RESULTS OF SMALL DYNAMIC MODEL 259 should occur, it would further reduce the attractiveness of investment in direct reduction facilities, since sponge iron is normally converted to steel in electric are furnaces. So the third experiment provides an analysis of the effects of increasing both natural gas and electricity prices. If imported coke prices rise along with electricity prices the shift to blast furnaces should be less pronounced. Thus the fourth experiment is used to analyze the effects of the world price of coke rising from $60 to $90 per metric ton. Some would argue that energy price subsidies at some locations but not at others will produce market disruptions which will be harmful rather than helpful to a country. The fifth experiment shows that the actual subsidies are large enough to have an effect on the desirable investment pattern. The sixth experiment tests the robustness of the investment strategy for the industry to changes in domestic reserves of iron ore and coal. It shows that increases in the availability of reserves cause only marginal shifts in capacity expansion from ports to interior sites. In the base solution a large share of the increase in capacity is at SICARTSA. The last experiment imposes a 10 million ton upper bound on steel production at any given site in order to force greater de- centralization and to permit an analysis of the cost of this decentralization. The next section provides a detailed discussion of the base solution. It is followed by discussion of each of the experiments. These solutions are mixed integer programming solutions; that is, all of the y variables are forced to be either one or zero. Even though the problems had 112 zero- one variables, it was possible to solve them for the global mixed integer programming solution because of the particular way the investment cost is modeled and because of the rapid growth of demand for steel products. The investment cost is modeled with economies of scale for small expansions, constant returns for medium expansions, and diseconomies of scale for large expansions. The rate of growth of demand was high enough that most of the expansions were in the range of the medium and large size, so the mixed integer programming solutions were relatively easy to obtain. Base Solution This section begins with an analysis of investment variables. In subsequent subsections the solution follows the flow of material from 260 MEXICAN CASE STUDY raw material at mines to intermediate and final products at steel mills and then to final products at markets. Investment Because this small model does not include investment in mines or in rolling mills, all the investment activities are for either iron or steel production in four types of productive unit: blast furnaces and direct reduction units for iron production, and basic oxygen furnaces (BoFs) and electric arc furnaces for steel production. Because of the simplified technological structure used in the model, the hot metal (pig iron) produced in the blast furnaces must be used entirely in BoFs, and the sponge iron produced in the direct reduction units must be used entirely in the electric arc furnaces: Iron production Steel production Blast furnaces Hot metal lBOFS Direct reduction units Sponge iron Electric arc furnaces Therefore, one can analyze the investment decisions by looking at capacity expansion in either iron or steel and be confident that expansion in the other will match fairly closely. Table 9-2 gives the capacity expansion in iron production by plant site. Mathematically, the results in table 9-2 are (9.1) hronh me{blast furnace, direct reduction} The key result in table 9-2 is that almost all of the investment goes to Table 9-2. Base Solution: Expansion of Blast Furnace and Direct Reduction Capacity (million metric tons of iron per year) Plant 1984-86 1987-89 1990-92 1993-95 Total AHMSA 0 0 0 0 0 Fundidora 0 0 0 1.5 1.5 SICARTSA 2.4 2.4 4.6 5.0 14.4 HYLSA 0 0 0 0 0 HYLSAP 0 0 0 0 0 Tampico 1.9 0 0 0 1.9 Coatzacoalcos 1.6 1.4 0 0 3.0 Total 5.9 3.8 4.6 6.5 20.8 RESULTS OF SMALL DYNAMIC MODEL 261 Table 9-3. Base Solution: Imports of Pellets (million metric tons) Plant 1981-83 1984-86 1987-89 1990-92 1993-95 AHMSA 0 0 0 1.6 5.1 Fundidora 0 2.2 2.2 2.2 4.6 SICARTSA 0 0 0 0 18.2 HYLSA 0 1.4 1.4 1.4 1.4 HYLSAP 0 2.6 1.4 1.4 1.4 Tampico 0 2.3 2.6 2.6 2.6 Coatzacoalcos 0 0 4.2 4.2 4.2 Total 0 8.5 11.8 13.4 37.5 plant sites at ports: SICARTSA on the Pacific Ocean and Tampico and Coatzacoalcos on the Gulf of Mexico. The reason for this is that the domestic ores are substantially exhausted during the period covered by the model, and pellets are imported to provide an iron source. As shown in table 9-3, there are no pellet imports in 1981-83, but then the imports rise sharply to 37.5 millions tons per year in the 1993-95 period as the domestic ores are used up and it becomes more and more expensive to mine them. Table 9-3 also shows that the plants nearest the domestic ores (Altos Hornos in the north and SICARTSA in the south) continue to use these ores, while the plants more distant from the ores and/or nearer to ports begin to import. Thus, Altos Hornos does not begin to import pellets until 1990-92 and SICARTSA not until 1993-95. The complementary pattern of domestic iron ore production is given in table 9-4. Recall that the existing reserves are divided into five groups by quality level, with 1 the highest quality ores and 5 the lowest quality. It is assumed that the ores are equally divided among those five quality groups. For example, the northern mines are assumed to have 130.6 million tons of iron ore reserves. In addition, it is assumed that only 70 percent of these reserves should be used during the time period covered by the model, that is, (130.6)(0.7) = 91 million tons. Thus, the reserves in pellet equivalents in the northern mines would be (91/1.5) = 60 million tons of pellet equivalents. Dividing this by the five quality groups leaves 12 million tons of pellet-equivalent reserves in each of the five quality groups. Compare this with the production shown in table 9-4 of 4 million tons of first-quality pellet-equivalent ore per year in 1981-83 at the northern mines. Since there are three years per time period this translates into a 262 MEXICAN CASE STUDY Table 9-4. Base Solution: Iron Ore Mining (million metric tons of pellet equivalents per year) Quality level 1981-83 1984-86 1987-89 1990-92 1993-95 Northern mines 1 4.0 0 0 0 0 2 4.0 0 0 0 0 3 0 4.0 0 0 0 4 0 0 4.0 0 0 5 0 0 0.5 3.5 0 Southern mines 1 3.4 4.2 0 0 0 2 0 2.2 5.5 0 0 3 0 0 2.9 4.8 0 4 0 0 0 7.7 0 5 0 0 0 3.0 4.8 Total 11.4 10.4 12.9 19.0 4.8 production of 12 million tons of pellet-equivalent ore in 1981-83. Thus, the first-quality level at the northern mines is exhausted in the 1981-83 time period. The second-quality level is also exhausted in this time period at the northern mines, but only part of the first-quality reserves at the southern mines are used up in 1981-83. From table 9-4 it can be seen that the northern ores are used up in the 1990-92 period while the southern reserves are not all used until the 1993-95 period. This accounts for the fact that in table 9-3 SICARTSA does not import any ores until the 1993-95 period, when it suddenly imports 18.2 million tons of pellets per year. In summary, most of the capacity additions in table 9-2 are at SICARTSA because of a combination of several factors. First, SICARTSA is located near the largest ore reserves available in the model. Second, it is located at a port so that pellets can be imported cheaply once the domestic ores are exhausted. Third, the energy location factor provides for cheaper natural gas here than at the other established plants. Most of the remaining capacity additions shown in table 9-2 are at Coatzacoalcos and Tampico. These two sites offer low natural gas prices because of the decentralization policy, and they offer port locations for relatively inexpensive importation of pellets. The second major result of the small dynamic model is the division of investment in ironmaking facilities between blast furnaces and direct reduction units. This result is shown in table 9-5 which gives the RESULTS OF SMALL DYNAMIC MODEL 263 Table 9-5. Base Solution: Investment in Blast Furnaces as Percentage of Total Investment in Iron Production Capacity Plant 1984-86 1987-89 1990-92 1993-95 AHMSA - - - - Fundidora - - - 100 SICARTSA 0 0 63 74 HYLSA - - - - HYLSAP - - Tampico 0 - - Coatzacoalcos 0 0 - -No new capacity installed. O Capacity expansion only in direct reduction facilities. percentage of total investment in iron production capacity that is directed to blast furnaces. Mathematically, this is (9.2) P = (hblast furnace, i, t/hon where pitf -percentage of new capacity for ironmaking in blast furnaces h'o = total new capacity in ironmaking facilities at plant i in time period t In table 9-5, a dash indicates that there was no new capacity installed in that plant and time period. In contrast, a zero indicates that there was capacity expansion in ironmaking, but it was all in direct reduction facilities. Thus in time periods 1984-86 and 1987-89 all of the investment in ironmaking is in direct reduction facilities. Because of the rising price of natural gas, however, 63 percent of the new investment at SICARTSA in 1990-92 is in blast furnaces and only 37 percent is in direct reduction units. By 1993-95 almost all the new capacity is in blast furnaces, with the exception of some units at SICARTSA. This is probably due to the 30 percent lower price of natural gas provided at SICARTSA under the decentralization policy. Of course, if the natural gas price in Mexico were not a factor of five below the international price in the first time period, this pattern of investment would be altered. This is discussed later in this chapter. Before continuing with the other results from the base solution, it is worth discussing the advantages and disadvantages of small models. The small models used in this book have the great advantage over the large models of being much easier to understand. It is also easier to do sensitivity analysis with them because it costs less to solve them. Thus, 264 MEXICAN CASE STUDY the small dynamic model offers an extremely useful tool for analyzing questions of the best technology and when and where to add to capacity in a system of plants. At the same time, one must treat the results with caution because many factors not included in the model may be of great importance. For example, the investment costs at Tampico and Coatzacoalcos are equal in the model, but the terrain may make it much more difficult to build and maintain a steel mill at one location than at the other. This problem could be corrected by simply assigning a higher investment cost to the site with the more difficult terrain. The point is not that the model could not provide a good solution, but that it will not in the absence of the correct data and specification. For this reason it is advisable for analysts to continually question the results from the model and to test the robustness of the solution to altered data and specifications. Furthermore, the results of the model should be exposed to the most searching analysis by experts in the industry. For example, failure to consider the quality of the subsoil for the foundation for a large plant or the depth of the water at a port could result in an optimal model solution which is in actual fact extremely uneconomical. Raw Material The most important result about raw material is the exhaustion of the domestic iron ores. This has been discussed fully above. Coal reserves are treated in a manner similar to iron ore, but the reported resources are sufficiently large that in the time horizon covered by the model only the highest quality reserves are used. This will, of course, differ in some of the experimental runs in which more of the added capacity is in the form of blast furnaces than direct reduction units. Table 9-6. Base Solution: Steel Production (million metric tons per year) Plant 1981-83 1984-86 1987-89 1990-92 1993-95 AHMSA 3.6 2.8 3.6 4.1 4.1 Fundidora 1.7 1.7 1.7 1.7 3.6 SICARTSA 1.3 3.5 5.7 10.9 16.6 HYLSA 1.1 1.1 1.1 1.1 1.1 HYLSAP 0.6 0.9 0.9 0.9 0.9 Tampico 0 1.5 1.5 1.5 1.5 Coatzacoalcos 0 1.5 2.8 2.8 2.8 Total 8.3 13.0 17.3 23.0 30.6 RESULTS OF SMALL DYNAMIC MODEL 265 Steel Mills The production levels for the base solution are given in table 9-6, which reflects the investment results. There is a large increase in production at SICARTSA to exploit the combined advantages of access to domestic ores, location at a port, and subsidized natural gas prices. The buildup to almost 17 million tons of production at SICARTSA by 1993-95 is so large that one of the experimental runs in the next section analyzes a case in which an upper bound of 10 million tons of steel at any one site is placed on the modeL Figure 9-1. Base Solution: Steel Shipments in 1981-83 (million metric tons a year) AHMSA Fundidora 0.1 1.7 Monterrey 1.1 Guadalajara 3.5 1.4 HYLSA Imports 0 Mexico City 1.3 HYLSAP SICARTSA 266 MEXICAN CASE STUDY In addition to the buildup at SICARTSA, sizable new steel mills are developed at both Tampico and Coatzacoalcos, the first being 1.5 million tons per year and the second constructed in two stages to reach 2.8 million tons per year. Markets Figure 9-1 shows the pattern of final product shipments in the 1981- 83 time period. This does not differ very much from the solution to the Figure 9-2. Base Solution: Steel Shipments in 1993-95 (million metric tons a year) AHMSA Fundidora 4.1 Monterrey 1.1 HYLSA o Guadalajara 0.4 9.5 Tampico 4.6 Mexico City 0.9 12.0 HYISAP SICARTSA 2.8 Coatzacoalcos RESULTS OF SMALL DYNAMIC MODEL 267 small static model. In contrast, figure 9-2 shows the shipment pattern for 1993-95. The country is divided into two parts with the northern steel mills (including Tampico) serving Monterrey and the southern steel mills (including Coatzacoalcos) serving Mexico City and Guadalajara. Experiments Of the seven experiments done with the small dynamic model, four were concerned with energy prices, one with reserves, and one with the limits on the size of plant at any single site. Each solution will be discussed in turn and compared with the base solution. Natural Gas at Domestic Price Level In the base solution, natural gas prices, which are controlled by the government, rise from $14 to $128 per thousand cubic meters over the time horizon covered by the model. In contrast, in experiment 1 natural gas prices are fixed at the low level of $14 and held at that level over the time horizon covered by the model. One would expect this to cause investment in ironmaking facilities to be directed more to direct reduction units and less to blast furnaces. Figure 9-3 shows that this does indeed occur. In the base solution most of the capacity built after 1990 is in blast furnaces. In contrast, in the solution to experiment 1 all the capacity additions are in direct reduction units. Lower natural gas prices also cause smaller productive units to be built and to be more decentralized than in the base solution. For example, in the base solution in the 1990-92 period 4.6 million tons of ironmaking capacity is brought on-line at SICARTSA. Of this, 1.6 million tons is in direct reduction units and 3.0 million tons is in a blast furnace or furnaces. In contrast, in experiment 1, 5.6 million tons of capacity in direct reduction units is started up, but it is divided among three locations: 2.4 million tons at SICARTSA, 1.6 million tons at Tampico, and 1.6 million tons at Coatzacoalcos. Thus, it seems that differences in economies of scale affect the solution. The economies of scale in direct reduction units are exhausted at an investment level of 0.8 million tons per year, while in blast furnaces they are exhausted at an investment level of 1.5 million tons per year. Thus, one would expect large blast furnaces to be constructed at fewer locations than direct reduction units. This expectation is fulfilled in this solution. One other aspect of experiment 1 is of particular interest. Recall that the energy location factors in the model are set such that the natural gas Figure 9-3. Investment in the Base Solution Compared with Seven Experimental Solutions (million metric tons of iron capacity a year) Coatzacoalcos Tampico HYLSAP HYLSA SICARTSA Fundidora AHMSA Base solution 1984-86 f 1.6 1.9 2.4 1987-89 1.4 2.4 1990-92 114.6 1.6 3.0 1993-95 5.0. O 5 1.3 3.7 1. Natural gas at domestic price 1984-86 1.6 1.9 1.2 3.3 1987-89 1.6 1.6 2.4 1990-92 1.6 1.6 2.4 1993-95 1.6 1.6 1.6 2.4 2. Natural gas at international price 1984-86 5.9 2.2 3.7 1987-89 = 3.5 1990-92 *0.8 = 2.9 1993-95 4.6 O18 0.9 3.7 3. Rising electricity price 1984-86 4.5 1.6 2.9 1987-89 3.7 1990-92 3.7 1.5 1993-95 01.7 4.5 268 Coatzacoalcos Tampico HYLSAP HYLSA SICARTSA Fundidora AHMSA 4. Rising prices of electricity and imported coke 1984-86 4.5 2.4 2.1 1987-89 4.1 16 25 1990-92 3.7 15 1993-95 1.5 =Z 3.1 5. Energy location factors equal 1984-86 4.2 1.6 2.6 1987-89 3.5 1990-92 4.3 1993-95 1 14.2 1112.0 6. Double reserves 1984-86 1.9 3.5 1987-89 3.3 1990-92 5.7 2.0 3.7 1993-95 5.3 1.5 1.6 3.7 7. Upper bound on production at each site 1984-86 f1.6 * 1.9 2.4 1987-89 1.4 2.4 1990-92 0.8 4.0 1.6 2.4 1993-95 0.8 3.7 1.8 E] Blast furnaces Direct reduction units 269 270 MEXICAN CASE STUDY price at SICARTSA, Tampico, and Coatzacoalcos is 30 percent lower than at the other plant sites. This apparently plays a substantial role in determining the location of the new capacity. If natural gas prices are held at the current low domestic level, this policy may therefore have its intended affect. Natural Gas at International Price Level Figure 9-3 provides a comparison of the investment results for ironmaking facilities for the base solution and experiment 2, in which the natural gas price is held constant over the time horizon at $128 per thousand cubic meters ($3.62 per thousand cubic feet), the contract price between Mexico and the United States in 1979. This price level is used to represent the opportunity cost for the natural gas. At this price, as figure 9-3 shows, almost all of the investment is in blast furnaces. The exceptions are 2.2 million tons in 1984-86 and 0.9 million tons in 1993-95 atSICARTSA, and 0.8 million tons in 1990-92 at Tampico. The shift from direct reduction units to blast furnaces also brings with it large unit sizes and a centralization of almost all of the investment at SICARTSA. The energy location factors are no longer sufficient to bring about a decentralization of investment, although they may account for the installation of direct reduction units at SICARTSA in 1984-86 and 1993-95. Rising Electricity Price In the base solution the electricity price remains constant at $26 per megawatt-hour. If natural gas prices rise as envisaged in the base solution, however, it is likely that electricity prices will also rise. Thus, in experiment 3 it is assumed that electricity prices rise in the same smooth way as natural gas prices, beginning at $26 per megawatt-hour in 1981- 83 and rising to $78 per megawatt-hour in 1993-95. One would expect that this would decrease the amount of investment in direct reduction units since the sponge iron produced by them is used entirely in electric arc furnaces in this model. (Although sponge iron can be charged to blast furnaces and to some extent to BOFS, those possibilities are not included in this small model.) Figure 9-3 shows that, indeed, all investment in iron production that comes on-line in or after 1987-89 is in blast furnaces. Thus, even if natural gas prices are allowed to rise slowly to the international price level, there is very little investment in direct reduction units if electricity prices are also allowed RESULTS OF SMALL DYNAMIC MODEL 271 to rise. The exception to this is 1.6 million metric tons of direct reduction units installed at SICARTSA in 1984-86. Rising Electricity and Imported Coke Prices Since rising electricity prices may be viewed as part of a worldwide increase in all kinds of energy prices, it is useful to do an experimental run in which both electricity prices and imported coke prices rise together. Recall that the cost of domestic coke will increase in the model to the extent that the domestic coal reserves are drawn down so that mining costs increase. In experiment 4, electricity prices rise just as in the previous experiment, and imported coke prices also increase-from $60 per metric ton to $90 per metric ton over the horizon covered by the model. The results, shown in figure 9-3, are best understood by contrasting them with the results for experiment 3. The first difference is that with rising prices for both electricity and imported coke, the expansion at SICARTSA in the first two time periods is in direct reduction units. Thus, 2.4 million tons of direct reduction capacity is added at SICARTSA in 1984-86 in experiment 4, while only 1.6 million tons of direction reduction capacity is added in experiment 3. Similarly, in 1987-89, 1.6 million tons of capacity is added in direction reduction units when the imported coke prices rise, but the expansion is only in blast furnaces when the imported coke prices do not rise. The other difference in the solutions is not in changes in technology but rather in changes in location and timing. For example, in experiment 3 a 1.7 million ton blast furnace is added at Tampico and in experiment 4 a 1.5 million ton unit is added at HYLSA instead. Caution is advised in interpreting this kind of a result from mixed integer programming (mw) solutions. The difference in total cost may be very small between two MIP solutions in which the location of capacity increase was the only difference. In summary, the increase in international coke prices changes only marginally the results of the experiment on rising electricity prices. Blast furnace investments still dominate the capacity expansion. Energy Location Factors Equal In the base solution natural gas and electricity prices are 30 percent lower at SICARTSA, Tampico, and Coatzacoalcos than at the other sites. In experiment 5 this subsidy is removed, and natural gas and electricity 272 MEXICAN CASE STUDY prices are equal at all sites. One would expect this to result in less investment at the three previously favored sites and more investment elsewhere. Experiment 5 shows that this occurs, but to a lesser extent than expected. There is a minor shift in investment away from Tampico and Coatzacoalcos, and the largest part of the investment remains at SICARTSA. There is also some shift from direct reduction methods to blast furnaces because the low energy prices at the favored locations work as a subsidy for direct reduction technology. Thus the location subsidies are sufficiently large to result in almost 5 million tons of capacity being built near energy sources. Without them roughly 2 million tons of additional capacity would be built in Monterrey at Fundidora, and more capacity would be built at SICARTSA. Double Reserves One of the greatest uncertainties facing any investment strategy in the steel industry is the availability of reserves. Consequently, in experiment 6 the iron ore reserves were doubled, although the distribution of reserves between the north and south was maintained. Since SICARTSA is both a port and near large iron ore reserves, the most pronounced part of the shift was from Tampico and Coatzacoalcos to SICARTSA. Experiment 6 helps make clear that the location and quantity of reserves is a very important factor in investment planning for the Mexican steel industry. If the reserves located near SICARTSA in this small model were less than assumed, it would no doubt affect the outcome substantially. Upper Bound on Production at Each Site There are many reasons for a country not to concentrate as much of its iron and steel capacity at one site as in the base solution to this model. Of a total capacity expansion of about 21 million tons of iron per year roughly 15 million would go to SICARTSA. Thus, it was decided to obtain an experimental solution in which steel production at any one site was limited to less than 10 million tons per year. In experiment 7 investment in the first three time periods is almost the same as in the base solution. The constraint becomes tight in 1993-95, however, and blast furnaces with capacities of 1.8 and 3.7 million tons per year are installed at Fundidora and HYLSAP. This occurs because the natural gas prices are sufficiently high by 1993-95 that the energy location factors no longer RESULTS OF SMALL DYNAMIC MODEL 273 have any effect. Then it is better to build blast furnaces close to markets and (to a lesser extent) to iron ore and coal resources. Conclusions One point cannot be emphasized too much. The base solution should not be looked upon as the best or most likely solution. Rather it should be viewed as a basis from which to do experimental runs in order to learn about the model and about the industry. The general results that emerge from these experiments are: 1. Policies affecting natural gas prices are important in determining investment strategy in the steel industry. At present domestic prices, considerable investment would be made in direct reduction units; at present international prices, almost all investment would be made in blast furnaces instead. 2. The limited availability of iron ore reserves means that almost all expansion of the steel industry will be at ports. ]In the case of SICARTSA, which is close to a port and existing iron ore reserves, there are very large investments. 3. Rising electricity prices would further shift the investment pattern toward blast furnaces and away from direct reduction units. This basic pattern holds even if imported coke prices are also increased. 4 The lower energy prices at some locations are important. The only solutions in which there was any significant level of investment at Tampico and Coatzacoalcos was when these subsidies were in place. 5. A doubling of iron ore reserves causes only a marginal shift of investment. 6. Placing a 10 million ton limit on SICARTsA results in sizable investment in Monterrey at Fundidora and in Puebla at HYLSAP. Finally, this small dynamic model is large enough to capture the tradeoffs between dwindling reserves at interior mines, shifts in relative prices of energy inputs, and decentralization policies. Appendix. Summary Tables of the Results In this appendix, tables 9-7 to 9-14 present the summary results of the base case and each of the seven experiments. Tables 9-15 to 9-17 compare selected results of the experiments with the base case. Table 9-7. Summary of Results for Base Case Category 1981-83 1984-86 1987-89 1990-92 1993-95 Cost (million U.S. dollars a year) Capital 0 162.0 263.5 403.3 594.7 Raw material 569.8 693.4 1,048.8 1,604.1 1,558.5 Transport 145.6 160.9 186.5 237.1 324.6 Import 252.9 378.6 513.4 692.4 1,795.2 Export revenues - 28.0 - 28.0 - 28.0 -28.0 Total cost 968.3 1,366.8 1,984.2 2,908.9 4,245.0 Total demand (million tons) 9.7 12.9 17.2 22.8 30.4 Production (million tons) Pig iron 5.6 5.0 5.4 8.7 13.9 Sponge iron 1.8 7.9 11.7 13.4 14.7 Open hearth 1.7 1.0 1.7 1.7 2.4 Electric furnace 1.7 7.2 10.8 12.3 13.5 DOF 2.3 2.2 0.3 0 0 BOF (max scrap) 2.5 2.7 4.6 9.1 14.8 Pig iron/Sponge iron 3.1 0.6 0.5 0.7 0.9 Imports (million tons) Pellets 0 8.4 11.8 13.4 37.5 Coke 0.7 0.7 0.7 2.6 4.9 Steel 1.4 0 0 0 0 Exports of steel (million tons) 0 0.2 0.2 0.2 0.2 Total capacity expansion (million tons) Blast furnace 0 0 3.0 5.2 1.0 BOF 0 0 4.2 5.7 1.0 Direct reduction 5.9 3.8 1.6 1.3 1.0 Electric arc 5.6 3.5 1.5 1.2 1.0 Domestic shipments of steel (million tons) AHMSA 3.6 2.8 3.6 4.1 4.1 Fundidora 1.7 1.7 1.7 1.7 3.6 SICARTSA 1.3 3.5 5.7 10.9 16.6 HYLSA 1.1 1.1 1.1 1.1 1.1 HYLSAP 0.6 0.9 0.9 0.9 0.9 Tampico 0 1.3 1.3 1.3 1.3 Coatzacoalcos 0 1.5 2.8 2.8 2.8 Total shipments 8.3 12.9 17.2 22.8 30.4 Detailed capacity expansion (million tons) AHMSA BOF 0 0 0 0.5 0 Fundidora Blast furnace 0 0 0 0 1.5 BOF 0 0 0 0 1.2 SICARTSA Blast furnace 0 0 0 3.0 3.7 BOF 0 0 0 3.7 4.5 Direct reduction 0 2.4 2.4 1.6 1.3 Electric arc 0 2.2 2.2 1.5 1.2 HYLSAP Electric arc 0 0.4 0 0 0 Tampico Direct reduction 0 1.9 0 0 0 Electric arc 0 1.5 0 0 0 Coatzacoalcos Direct reduction 0 1.6 1.4 0 0 Electric arc 0 1.5 1.3 0 0 Table 9-8. Summary of Results for Experiment 1: Natural Gas at Domestic Price Level Category 1981-83 1984-86 1987-89 1990-92 1993-95 Cost (million U.S. dollars a year) Capital 0 220.3 373.9 527.4 719.8 Raw material 573.7 659.4 687.3 953.7 875.2 Transport 142.1 156.3 167.4 217.2 290.0 Import 252.9 236.0 590.5 848.8 1,618.2 Export revenues 0 -28.0 -28.0 -28.0 - 28.0 Total cost 968.7 1,244.0 1,791.1 2,519.1 3,475.3 Total demand (million tons) 9.7 12.9 17.7 22.8 30.4 Production (million tons) Pig iron 5.6 3.6 2.9 3.0 3.7 Sponge iron 1.8 9.9 15.6 21.3 28.6 Open hearth 1.7 0 0 0 0 Electric furnace 1.7 9.1 14.3 19.5 26.2 BOF 2.3 2.7 3.0 1.2 1.2 BOF (max scrap) 2.5 1.2 0 2.4 3.2 Pig iron/Sponge iron 3.1 0.4 0.2 0.1 0.1 Imports (million tons) Pellets 0 4.9 13.7 20.2 39.4 Coke 0.7 0.7 0.7 0.7 0.7 Steel 1.4 0 0 0 0 Exports of steel (million tons) 0 0.2 0.2 0.2 0.2 Total capacity expansion (million tons) Blast furnace 0 0 0 0 0 BOF 0 0 0 0 0 Direct reduction 0 8.0 5.7 5.7 7.3 Electric arc 0 7.4 5.2 5.2 6.7 Domestic shipments of steel AHMSA 3.6 2.1 1.9 0.9 1.7 Fundidora 1.7 0.7 0 1.5 1.5 SICARTSA 1.3 4.2 6.4 8.6 10.8 HYLSA 1.1 1.1 1.1 1.1 1.1 HYLSAP 0.6 2.0 2.0 2.0 3.5 Tampico 0 1.3 2.8 4.3 5.8 Coatzacoalcos 0 1.5 3.0 4.5 6.0 Total shipments 8.3 12.9 17.2 22.8 30.4 Detailed capacity expansion (million tons) SICARTSA Direct reduction 0 3.3 2.4 2.4 2.4 Electric arc 0 3.0 2.2 2.2 2.2 HYLSAP Direct reduction 0 1.2 0 0 1.6 Electric arc 0 1.4 0 0 1.5 Tampico Direct reduction 0 1.9 1.6 1.6 1.6 Electric arc 0 1.5 1.5 1.5 1.5 Coatzacoalcos Direct reduction 0 1.6 1.6 1.6 1.6 Electric arc 0 1.5 1.5 1.5 1.5 Table 9-9. Summary of Results for Experiment 2: Natural Gas at International Price Level Category 1981-83 1984-86 1987-89 1990-92 1993-95 Cost (million U.S. dollars a year) Capital 0 160.8 274.4 386.7 576.6 Raw material 653.5 887.3 1,262.5 1,302.1 1,162.6 Transport 142.1 145.8 171.3 235.4 321.2 Import 252.9 268.3 400.6 1,189.8 2,178.3 Export revenues 0 -28.0 -28.0 - 28,0 -28.0 Total cost 1,048.5 1,434.2 2,080.7 3,086.0 4,210.7 Total demand (million tons) 9.7 12.9 17.1 22.8 30.4 Production (million tons) Pig iron 5.6 9.0 12.5 15.8 21.3 Sponge iron 1.8 2.2 2.2 4.0 4.9 Open hearth 1.7 1.7 1.7 1.7 2.4 Electric furnace 1.7 2.0 2.0 3.6 4.5 BOF 2.3 0 0 0 0 BOF (max scrap) 2.5 9.4 13.6 17.7 23.8 Pig iron/Sponge iron 3.1 4.1 5.7 4.0 4.4 Imports (million tons) Pellets 0 2.2 2.2 19.2 40.4 Coke 0.7 3.0 5.2 7.0 9.4 Steel 1.4 0 0 0 0 Exports of steel (million tons) 0 0.2 0.2 0.2 0.2 Total capacity expansion (million tons) Blast furnace 0 3.7 3.5 2.9 5.5 BOF 0 4.5 4.3 4.0 6.1 Direct reduction 0 2.2 0 0.8 0.9 Electric arc 0 1.5 0.5 0 0.8 Domestic shipments of steel AHMSA 3.6 3.6 3.6 4.1 4.1 Fundidora 1.7 1.7 1.7 1.7 3.9 SICARTSA 1.3 7.1 11.9 15.4 20.7 HYLSA 1.1 0 0 1.1 1.1 HYLSAP 0.6 0.5 0 0.6 0.6 Tampico 0 0 0 0 0 Coatzacoalcos 0 0 0 0 0 Total shipments 8.3 12.9 17.2 22.8 30.4 Detailed capacity expansion (million tons) AHMSA BOF 0 0 0 0.5 0 Fundidora Blast furnace 0 0 0 0 1.8 BOF 0 0 0 0 1.6 SICARTSA Blast furnace 0 3.7 3.5 2.9 3.7 BOF 0 4.5 4.3 3.6 4.5 Direct reduction 0 2.2 0 0 0.9 Electric arc 0 1.5 0.5 0 0.8 Tampico Direct reduction 0 0 0 0.8 0 Table 9-10. Summary of Results for Experiment 3: Rising Electricity Price Category 1981-83 1984-86 1987-89 1990-92 1993-95 Cost (million U.S. dollars a year) Capital 0 129.9 244.4 412.5 620.2 Raw material 573.7 824.8 1,217.9 1,415.0 1,101.4 Transport 142.1 151.6 178.2 245.7 316.7 Import 252.9 328.3 450.4 1,033.9 2,256.8 Export revenues 0 - 28.0 -28.0 - 28.0 - 28.0 Total cost 968.7 1,406.6 2,063.0 3,079.1 4,267.1 Total demand (million tons) 9.7 12.9 17.2 228 30.4 Production (million tons) Pig iron 5.6 8.2 12.0 17.6 23.8 Sponge iron 1.8 3.2 2.9 1.6 1.6 Open hearth 1.7 1.7 1.7 2.4 2.4 Electric furnace 1.7 3.0 2.7 1.5 1.5 BOF 2.3 0 0 0 0 BOF (max scrap) 2.5 8.5 13.0 19.2 26.8 Pig iron/Sponge iron 3.1 2.6 4.1 10.7 14.5 Imports (million tons) Pellets 0 4.4 4.4 15.1 39.8 Coke 0.7 2.5 4.9 7.2 11.1 Steel 1.4 0 0 0 0 Exports of steel (million tons) 0 0.2 0.2 0.2 0.2 Total capacity expansion (million tons) Blast furnace 0 2.9 3.7 5.2 6.2 BOF 0 3.6 4.5 6.2 7.6 Direct reduction 0 1.6 0 0 0 Electric arc 0 1.5 0 0 0 Domestic shipments of steel AHMSA 3.6 3.5 3.6 4.1 4.1 Fundidora 1.7 1.7 1.7 3.6 3.6 SICARTSA 1.3 6.2 10.7 15.2 20.9 HYLSA 1.1 0.9 0.6 0 0 HYLSAP 0.6 0.6 0.6 Q 0 Tampico 0 0 0 0 1.9 Coatzacoalcos 0 0 0 0 0 Total shipments 8.3 12.9 17.2 22.8 30.4 c Detailed capacity expansion (million tons) AHMSA BOF 0 0 0 0.5 0 Fundidora Blast furnace 0 0 0 1.5 0 BOF 0 0 0 1.2 0 SICARTSA Blast furnace 0 2.9 3.7 3.7 4.5 BOF 0 3.6 4.5 4.5 5.4 Direct reduction 0 1.6 0 0 0 Electric arc 0 1.5 0 0 0 Tampico Blast furnace 0 0 0 0 1.7 BOF 0 0 0 0 2.1 Table 9-11. Summary of Results for Experiment 4: Rising Electricity and Imported Coke Prices Category 1981-83 1984-86 1987-89 1990-92 1993-95 Cost (million U.S. dollars a year) Capital 0 126.3 241.4 409.5 557.9 Raw material 573.7 831.4 1,271.9 1,810.7 1,703.4 Transport 142.1 156.8 180.9 334.6 439.4 Import 252.9 326.7 444.2 616.8 1,796.1 Export revenues 0 - 28.0 - 28.0 0 0 Total cost 968.7 1,413.1 2,110.4 3,171.6 4,496.8 Total demand (million tons) 9.7 12.9 17.2 22.8 30.4 Production (million tons) Pig iron 5.6 7.5 9.9 15.5 20.1 Sponge iron 1.8 4.2 5.6 4.0 4.0 Open hearth 1.7 1.7 1.7 2.4 2.4 Electric furnace 1.7 3.9 5.2 3.7 3.7 BOF 2.3 0 0 0 0 BoF (max scrap) 2.5 7.5 10.5 16.7 22.4 Pig iron/Sponge iron 3.1 1.8 1.8 3.8 5.0 Imports (million tons) Pellets 0 4.8 4.4 15.1 37.4 Coke 0.7 2.0 3.6 0 0 Steel 1.4 0 0 0.1 2.0 Exports of steel (million tons) 0 0.2 0.2 0 0 Total capacity expansion (million tons) Blast furnace 0 2.1 2.5 5.2 4.6 BOF 0 2.6 3.0 6.2 5.6 Direct reduction 0 2.4 1.6 0 0 Electric arc 0 2.2 1.5 0 0 Domestic shipments of steel AHMSA 3.6 3.6 3.6 4.1 4.1 Fundidora 1.7 1.7 1.7 3.6 3.6 SICARTSA 1.3 5.9 10.4 15.1 18.9 HYLSA 1.1 1.1 0.9 0 1.8 HYLSAP 0.6 0.6 0.6 0 0 Tampico 0 0 0 0 0 Coatzacoalcos 0 0 0 0 0 Total shipments 8.3 12.9 17.2 22.8 28.4 Detailed capacity expansion (million tons) AHMSA BOF 0 0 0 0.5 0 Fundidora Blast furnace 0 0 0 1.5 0 BOF 0 0 0 1.2 0 SICARTSA Blast furnace 0 2.1 2.5 3.7 3.1 BOF 0 2.6 3.0 4.5 3.8 Direct reduction 0 2.4 1.6 0 0 Electric arc 0 2.2 1.5 0 0 HYLSA Blast-Furnace 0 0 0 0 1.5 BOF 0 0 0 0 1.8 Table 9-12. Summary of Results for Experiment 5: Energy Location Factors Equal Category 1981-83 1984-86 1987-89 1990 92 1993-95 Cost (million U.S. dollars a year) Capital 0 123.3 231.9 375.1 569.5 Raw material 573.7 814.2 1,181.5 1,459.9 1,187.7 Transport 142.1 153.0 181.8 238.9 324.5 Import 252.9 336.9 469.3 1,000.5 2,197.7 Export revenues 0 - 28.0 - 28.0 - 28.0 - 28,0 Total cost 968.7 1,399.4 2,036.5 3,046.3 4,251.4 Total demand (million tons) 9.7 12.9 17.2 22.8 30.4 Production (million tons) Pig iron 5.6 7.9 11.4 16.1 22.3 Sponge iron 1.8 3.6 3.6 3.6 3.6 Open hearth 1.7 1.7 1.7 1.7 2.4 Electric furnace 1.7 3.3 3.3 3.3 3.3 BOF 2.3 0 0 0 0 BOF (max scrap) 2.5 8.1 12.3 18.0 24.9 Pig iron/Sponge iron 3.1 2.2 3.2 4.5 6.2 Imports (million tons) Pellets 0 4.9 4.9 14.2 40.2 Coke 0.7 2.3 4.5 7.2 9.9 Steel 1.4 0 0 0 0 Exports of steel (million tons) 0 0.2 0.2 0.2 0.2 Total capacity expansion (million tons) Blast furnace 0 2.6 3.5 4.3 6.2 BOF 0 3.2 4.3 5.7 6.9 Direct reduction 0 1.6 0 0 0 Electric arc 0 1.9 0 0 0 Domestic shipments of steel AHMSA 3.6 3.6 3.6 4.1 4.1 Fundidora 1.7 1.7 1.7 1.7 4.2 SICARTSA 1.3 5.8 10.1 15.3 20.4 HYLSA 1.1 0.9 0.9 0.9 0.9 HYLSAP 0.6 0.9 0.9 0.9 0.9 Tampico 0 0 0 0 0 Coatzacoalcos 0 0 0 0 0 Total shipments 8.3 12.9 17.2 22.8 30.4 00 Detailed capacity expansion (million tons) AHMSA BOF 0 0 0 0.5 0 Fundidora Blast furnace 0 0 0 0 2.0 BOF 0 0 0 0 1.8 SICARTSA Blast furnace 0 2.6 3.5 4.3 4.2 BOF 0 3.1 4.3 5.2 5.1 Direct reduction 0 1.6 0 0 0 Electric arc 0 1.5 0 0 0 HYLSAP Electric arc 0 0.4 0 0 0 Table 9-13. Summary of Results br Experiment 6: Double Reserves Category 1981-83 1984-86 1987-89 1990-92 1993-95 Cost (million U.S. dollars a year) Capital 0 152.0 251.0 412.8 612.7 Raw material 558.7 804.1 1,194.8 1,680.7 2,553.1 Transport 142.1 170.2 200.4 229.2 299.9 Import 252.9 145.7 200.2 411.9 602.0 Export revenues 0 -28.0 0 - 28.0 - 28,0 Total cost 953.7 1,244.1 1,846.4 2,706.7 4,039.7 Total demand (million tons) 9.7 12.9 17.2 22.8 30.4 Production (million tons) Pig iron 5.6 5.6 5.8 9.4 14.6 Sponge iron 1.8 7.3 10.6 12.5 13.8 Open hearth 1.7 1.5 1.7 1.7 1.7 Electric furnace 1.7 6.7 9.7 11.5 12.7 BOF 2.3 3.6 0.3 0 0 BOF (max scrap) 2.5 1.2 5.1 9.9 16.2 Pig iron/Sponge iron 3.1 0.8 0.5 0.8 1.1 Imports (million tons) Pellets 0 2.6 2.6 5.8 7.1 Coke 0.7 0.7 0.7 3.0 5.3 Steel 1.4 0 0.4 0 0 Exports of steel (million tons) 0 0.2 0 0.2 0.2 Total capacity expansion (million tons) Blast furnace 0 0 0 3.7 5.2 BOF 0 0 0.5 4.5 6.3 Direct reduction 0 5.4 3.3 2.0 1.6 Electric arc 0 5.0 3.0 1.8 1.5 Domestic shipments of steel AHMSA 3.6 3.6 4.1 4.1 5.9 Fundidora 1.7 1.5 1.7 1.7 1.7 SICARTSA 1.3 4.3 7.3 13.6 19.6 HYLSA 1.1 1.1 1.1 1.1 0.8 HYLSAP 0.6 1.1 1.1 1.1 1.1 Tampico 0 1.3 1.5 1.3 1.3 Coatzacoalcos 0 0 0 0 0 Total shipments 8.3 12.9 16.8 22.8 30.4 Detailed capacity expansion (million tons) AHMSA Blast furnace 0 0 0 0 1.5 BOF 0 0 0.5 0 1.8 SICARTSA Blast furnace 0 0 0 3.7 3.7 BOF 0 0 0 4.5 4.5 Direct reduction 0 3.5 3.3 2.0 1.6 Electric arc 0 3.0 3.0 1.8 1.5 HYLSAP Electric arc 0 0.5 0 0 0 Tampico Direct reduction 0 1.9 0 0 0 Electric arc 0 1.5 0 0 0 Table 9-14. Summary of Results for Experiment 7: Upper Bound on Production at Each Site Category 1981-83 1984-86 1987-89 1990-92 1993-95 Cost (million U.S. dollars a year) Capital 0 162.0 263.5 407.4 599.6 Raw material 569.8 693.4 1,048.8 1,579.0 1,607.5 Transport 145.6 160.9 186.5 237.6 345.7 Import 252.9 378.6 513.4 713.8 1,730.9 Export revenues 0 -28.0 -28.0 -28.0 - 12.4 Total cost 968.3 1,366.8 1,984.2 2,909.8 4,271.3 Total demand (million tons) 9.7 12.9 17.2 22.8 30.4 Production (million tons) Pig iron 5.6 5.0 5.4 8.1 13.6 Sponge iron 1.8 7.9 11.7 14.2 15.0 Open hearth 1.7 1.0 1.7 1.7 2.4 Electric furnace 1.7 7.2 10.8 13.0 13.7 BOF 2.3 2.2 0.3 0 0 BOF (max scrap) 2.5 2.7 4.6 8.3 14.4 Pig iron/Sponge iron 3.1 0.6 0.5 0.6 0.9 Imports (million tons) Pellets 0 8.4 11.8 14.5 36.5 Coke 0.7 0.7 0.7 2.2 4.5 Steel 1.4 0 0 0 0 Exports of steel (million tons) Total capacity expansion (million tons) 0 0.2 0.2 0.2 0.1 Blast furnace 0 0 0 2.4 5.5 BOF 0 0 0 3.4 6.1 Direct reduction 0 5.9 3.8 2.4 0.8 Electric arc 0 5.6 3.5 2.2 0.7 Domestic shipments of steel AHMSA 3.6 2.8 3.6 4.1 4.1 Fundidora 1.7 1.7 1.7 1.7 3.9 SICARTSA 1.3 3.5 5.7 10.2 10.2 HYLSA 1.1 1.1 1.1 1.1 1.1 HYLSAP 0.6 0.9 0.9 0.9 5.4 Tampico 0 1.3 1.3 1.3 1.4 Coatzacoalos 0 1.5 2.8 3.6 4.3 Total shipments 8.3 12.9 17.2 22.8 30.4 Detailed capacity expansion (million tons) AHMSA BOF 0 0 0 0.5 0 Fundidora Blast furnace 0 0 0 0 1.8 BOF 0 0 0 0 1.6 SICARTSA Blast furnace 0 0 0 2.4 0 BOF 0 0 0 3.0 0 Direct reduction 0 2.4 2.4 1.6 0 Electric arc 0 2.2 2.2 1.5 0 HYLSAP Blast furnace 0 0 0 0 3.7 BOF 0 0 0 0 4.5 Electric arc 0 0.4 0 0 0 Tampico Direct reduction 0 1.9 0 0 0 Electric arc 0 1.5 0 0 0 Coatzacoalcos Direct reduction 0 1.6 1.4 0.8 0.8 Electric arc 0 1.5 1.3 0.7 0.7 Table 9-15. Comparison of Summary Results Experimenta Category Base case 1 2 3 4 5 6 7 Costh (million U.S. dollars) Capital 1,422.2 1,869.9 1,405.1 1,370.5 1,3132 1,271.4 1,411.4 1,429.6 Raw material 6,445.6 4,824.3 6,661.5 6,383.0 7,273.4 6,423.5 7,581.1 6,456.7 Transport 1,297.5 1,213.8 1,240.9 1,266.1 1,451.4 1,272.2 1,298.0 1,313.2 Import 3,815.4 3,694.4 4,235.6 4,308.2 3,567.8 4,272.3 1,897.7 3,789.7 Export revenues -129.9 - 129.9 -129.9 -129.9 -83.0 -129.9 -94.3 -118.7 Total cost 12,850.9 11,472.6 13,413.2 13,197.9 13,522.8 13,109.5 12,093.9 12,870.5 Experiment/base case x 100 100,0 89.3 104.4 102.7 105.2 102,0 94.1 100.2 Cost contributions (percent) Capital 11.1 16.3 10.5 10.4 9.7 9.7 11.7 11.1 Raw material 50.2 42.1 49.7 48.4 53.8 49.0 62.7 50.2 Transport 10.1 10.6 9.3 9.6 10.7 9.7 10.7 10.2 Import 29.7 32.2 31.6 32.6 26.4 32.6 15.7 29.5 Export revenues - 1.0 - 1.1 - 1.0 - 1.0 -0.6 -1.0 -0.8 -0.9 Total capacity expansion (million tons) Blast furnace 8.2 0 15.6 18.0 14.4 16.5 8.8 7.9 Open hearth 0 0 0 0 0 0 0 0 BOF 9.9 0 18.9 21.9 17.5 20.1 11.3 9.5 Direct reduction 12.7 26.6 3.9 1.6 4.0 1.6 12.2 13,0 Electric arc 11.8 24.5 2.8 1.5 3.7 1.9 11.3 12.1 a. Experiment 1, natural gas price constant at the domestic price level; 2, natural gas price constant at the international price level; 3, rising electricity price; 4, rising imported coke price; 5, removal of energy location subsidies; 6, iron ore and coal reserves doubled; 7, restriction of steel production at each site. b. Total discounted value from 1981 to 1995. RESULTS OF SMALL DYNAMIC MODEL 291 Table 9-16. Comparison of Capacity Expansion by Location and Unit (million tons) Experiment Base Location and unit case 1 2 3 4 5 6 7 AHMSA Blast furnace 0 0 0 0 0 0 1.5 0 Open hearth 0 0 0 0 0 0 0 0 BOF 0.5 0 0.5 0.5 0.5 0.5 2.3 0.5 Direct reduction 0 0 0 0 0 0 0 0 Electric arc 0 0 0 0 0 0 0 0 Fundidora Blast furnace 1.5 0 1.8 1.5 1.5 2.0 0 1.8 Open hearth 0 0 0 0 0 0 0 0 BOF 1.2 0 1.6 1.2 1.2 1.8 0 1.6 Direct reduction 0 0 0 0 0 0 0 0 Electric arc 0 0 0 0 0 0 0 0 SICARTSA Blast furnace 6.7 0 13.8 14.8 11.4 14.5 7.3 2.4 Open hearth 0 0 0 0 0 0 0 0 BOF 8.2 0 16.8 18.1 13.9 17.8 9.0 3.0 Direct reduction 7.7 10.5 3.1 1.6 4,0 1.6 10.3 6.4 Electric arc 7.1 9.6 2.8 1.5 3.7 1.5 9.3 5.9 HYLSA Blast furnace 0 0 0 0 1.5 0 0 0 Open hearth 0 0 0 0 0 0 0 0 BOF 0 0 0 0 1.8 0 0 0 Direct reduction 0 0 0 0 0 0 0 0 Electric arc 0 0 0 0 0 0 0 0 HYLSAP Blast furnace 0 0 0 0 0 0 0 3.7 Open hearth 0 0 0 0 0 0 0 0 BOF 0 0 0 0 0 0 0 4.5 Direct reduction 0 2.8 0 0 0 0 0 0 Electric arc 0.4 2.9 0 0 0 0.4 0.5 0.4 Tampico Blast furnace 0 0 0 1.7 0 0 0 0 Open hearth 0 0 0 0 0 0 0 0 BOF 0 0 0 2.1 0 0 0 0 Direct reduction 1.9 6.8 0.8 0 0 0 1.9 1.9 Electric arc 1.5 6.0 0 0 0 0 1.5 1.5 Coatzacoalcos Blast furnace 0 0 0 0 0 0 0 0 Open hearth 0 0 0 0 0 0 0 0 BOF 0 0 0 0 0 0 0 0 Direct reduction 3.1 6.5 0 0 0 0 0 4.7 Electric arc 2.8 6.0 0 0 0 0 0 4.3 292 MEXICAN CASE STUDY Table 9-17. Comparison of Capacity Expansion by Time Period and Technology (million tons) Experiment Base Technology case 1 2 3 4 5 6 7 and period Blast furnace 1981-83 0 0 0 0 0 0 0 0 1984-86 0 0 3.7 2.9 2.1 2.6 0 0 1987-89 0 0 3.5 3.7 2.5 3.5 0 0 1990-92 3.0 0 2.9 5.2 5.2 4.3 3.7 2.4 1993-95 5.2 0 5.5 6.2 4.6 6.2 5.2 5.5 Direct reduction 1981-83 0 0 0 0 0 0 0 0 1984-86 5.9 8.0 2.2 1.6 2.4 1.6 5.4 5.9 1987-89 3.8 5.7 0 0 1.6 0 3.3 3.8 1990-92 1.6 5.7 0.8 0 0 0 2.0 2.4 1993-95 1.3 7.3 0.9 0 0 0 1.6 0.8 10 Extensions, Summary, and Conclusions THIS CHAPTER INCLUDEs a discussion of possible extensions of the models outlined in the previous chapter, as well as a summary of the book and its conclusions. Extensions The previous chapters describe a small and a large static model and a small dynamic model. In a governmental or commercial application of this investment planning method, two further steps would normally be desirable. One would want to construct, first, a large comparative static capacity planning model, to be followed by a large dynamic model. For the purposes of this volume, neither extension appeared possible because of the effort and resources required. A static capacity expansion model is constructed for some future year-say, 2000-and contains investment activities for the productive units. It would be constructed before a large dynamic model because the static capacity expansion model would be smaller than a large dynamic model by a factor of four or five and yet would provide an opportunity to analyze investments in the disaggregated setting of a large model. The results from the static capacity expansion model provide an indication of where investments should be made and the technology to be used but do not indicate when the investments should be made. Therefore an extension to a large dynamic model should be made after the static capacity expansion model has been solved and analyzed. A large dynamic model may contain the level of disaggregation of 293 294 MEXICAN CASE STUDY commodities, processes, productive units, plants, markets, and so on used in the large static model. This is combined with the dynamic structure used in the small dynamic model. The resulting model would be large and expensive to solve but would permit the analysis of when and where to invest and what technology to use. Furthermore, it would do this at a level of disaggregation used by engineers in steel companies; that is, individual productive units such as BOF converters and hot strip mills. It would also permit investment analysis in a model that includes interplant shipments of intermediate products. Thus one can anticipate that the results would include, for example, the efficiency gains from postponing an investment and buying intermediate materials from another plant until demand has grown enough to justify investment in a large productive unit. The completion of a large dynamic model should not in our opinion be the occasion for discarding the other models. Rather, each of the models discussed in this book has a comparative advantage for use in analyzing certain kinds of operational or investment problems. Summary The purpose of this book has been to outline a methodology for the planning of investment programs in the steel industry and to illustrate the application of this methodology with a case study of the Mexican steel industry. This has been done with a series of models. Two static models were solved as linear programs and one dynamic model was solved as a mixed integer program. The small static model introduces the use of the methodology in the steel industry and is simple enough to be readily understood and easily solved. The large static model provides a basis for a study of operational procedures in the industry. For example, the results indicate that $26 million a year might have been saved in the Mexican steel industry by easing restrictions on coke imports, and that $48 million a year could have been saved by exploiting the possibility of additional interplant shipments of intermediate products. These two results illustrate the kinds of outcome which can be obtained from large static models of the steel industry. The results from such a modeling exercise should not be treated as definitive but rather should be used to point the direction to possible cost-saving actions. The special capability of this type of model is to do cost studies on a number EXTENSIONS, SUMMARY, AND CONCLUSIONS 295 of steel mills at the same time. By considering the interdependencies between the plants, one can find savings that are not obvious from the more customary studies of individual steel mills. The small dynamic model permits the focus to shift from operational problems to investment problems. Consider the problems faced by the investment analysts in the example of the Mexican steel industry. The ores from the interior mines are declining in quality, as is the coal. Part of the industry uses natural gas for direct reduction while part uses coke. The government is employing a policy of differential pricing of natural gas and electricity at different locations to encourage decentralization of industry. From this matrix of problems the model results indicate that policies for natural gas pricing are crucial to determining the most efficient investment pattern for the industry. If the low domestic price is allowed to rise slowly to the world price level, the choice of technology shifts from direct reduction to blast furnaces. In addition, the price differentials for natural gas and electricity are found to be sufficiently large to encourage decentralization, which is the government's objective. Moreover, almost all of the expansion of the industry is done at ports where imported pellets can be obtained at lower prices than domestic ores as the domestic ores are exhausted. These results indicate policies which can be used to plan an efficient investment strategy for the industry and also demonstrate the effects of various public policies on that strategy. Conclusions The methodology outlined and applied in this book provides a useful vehicle for analyzing both operational and investment problems in the steel industry. The multiplant focus of the large static linear pro- gramming model permits the analyst to find cost-saving opportunities which are not so readily perceived when each plant is studied inde- pendently. One example of this is in the study of interplant shipments of intermediate products. Similarly, the multiplant focus allows one to gain a global view for use in investment analysis with dynamic models. Many important factors are changing in the steel industry. Prices of energy inputs have been rising rapidly, the quality of ore has been declining in many locations, and market demand is growing rapidly, particularly in many developing nations. Governments offer energy subsidies for plants at some locations 296 MEXICAN CASE STUDY but not at others. All of these changes make investment analysis difficult. The methodology outlined in this book provides no crystal ball for making investment decisions, but it does provide a clear and logical process for considering the alternatives and for analyzing the major factors which affect investment decisions in the steel industry. 11 A Postscript: Observations on Industrial Modeling THERE HAS BEEN enough experience with industrial modeling that it is useful to begin work to establish some basic principles. As a step in that direction, this last chapter contains a set of "observations" on industrial modeling. Some of these observations may be confirmed by others until they eventually become "principles." Others will be dropped from the literature.' One observation which will surely become a principle is an article by A. M. Geoffrion (1976) entitled, "The Purpose of Mathematical Pro- gramming Is Insight, Not Numbers." This is one of the themes of this chapter. The development and use of industrial planning models should not be directed toward the determination of a single optimal solution but rather toward the enhancement of understanding of the problem at hand. It is hoped that these observations will contribute to high-quality economic modeling. The topics to be discussed are: multiple models, modeling languages, set specification, model size calculations, model debugging strategies, and industry experts. The unifying elements in this diverse list are that all the items are parts of the process of good model building and that several are all too frequently overlooked. Each will be discussed in turn. 1. We are grateful to J. Scott Rogers of the University of Toronto for suggesting this chapter. 297 298 MEXICAN CASE STUDY Multiple Models In most industrial modeling projects it is useful to construct not one but a group of models. Two different purposes are served by multiple models: slow increase in complexity and comparative advantage. The first refers to the fact that it is frequently useful at the beginning of a project to construct relatively small models and then slowly but surely increase their size and complexity. This approach is from the school of "keep the complexity under control."2 Since industrial planning models are difficult to develop and debug, the analyst who attempts to immediately develop a large and complex model may never complete the task. It is better to begin with a small and simple model which is easy to understand and debug and then gradually progress to larger and more complicated models while "keeping the complexity under control" at every step along the way. This approach also lends itself well to the second purpose served by multiple models: models of various sizes and complexities have compara- tive advantages that can be exploited. Thus, if a small static model is developed at the beginning of a modeling project, it should not be discarded once larger models are developed, but rather retained for certain kinds of analyses. For example, static models have a comparative advantage for doing operational studies as opposed to investment studies. Small models can be used much more readily than large models for sensitivity testing. Finally, small models are sometimes useful in doing presentations since they are easier to grasp in a short time. A new theme emerging in the literature of multiple models is the idea of aggregation. This approach to multiple models argues that at times it is advantageous to construct a large and disaggregated model first and then to apply formal aggregation procedures to it to produce a small and highly aggregated model. To do this while maintaining the advantage of a slow increase in complexity, it is advisable to build first a small model and then a large model. Then formal aggregation procedures can be applied to the large model to produce a revised small model in which the data are consistent with the data in the large model. In summary, multiple models permit slow but steady development from small and simple to large and complex models and provide a set in 2. Verbal communication from Fred Norman. INDUSTRIAL MODELING 299 which each model has its own comparative advantage for use in analyzing the industry. Modeling Languages One of the themes of this book is that a modeling language such as GAMS can greatly facilitate industrial modeling. Though this subject alone would merit a separate chapter or book, it is worthwhile here to point out a few of the advantages that accrue to the user who has access to a modeling language (see, for example, Bisschop and Meeraus 1982, and Meeraus 1983). One of the key advantages is increases in productivity. Models can be developed in much less time when it is not necessary to write Fortran programs or use a matrix generator to prepare the input for a linear program. Moreover, improvements in quality can also be obtained with the use of a modeling language. One improvement is much greater assurance that the model described in the report is actually the one that was solved in the computer. With modeling languages it is much easier to verify that the equations written out in a report match those in the software used to generate the computer model. The modeling language can also aid in debugging by providing lists of sets, variables, and equations and their locations in the input. Further- more, a list of unique elements such as set elements can be provided. This type of information is useful in catching spelling errors in the input. Finally, the use of a modeling language enables the investigator to make specification changes with much greater ease. This is particularly useful as a project nears completion and is presented to others for suggestions and criticisms. When specification changes are easy to make, useful suggestions can be accepted and the model can be improved- instead of defended to the hilt because changes are so difficult to make. Set Specification One key element in good model building is set specification. This contrasts with the usual notion that the most important element in model construction is the development of the objective function and the constraints. Set specification plays two distinct roles in designing models. The first role is to determine the basic degree of complexity of the model. This is 300 MEXICAN CASE STUDY done while choosing the number of key sets, that is, the number of basic domains or dimensions of the overall problem. For example, whether to include a set for time periods is a basic and crucial decision. Similarly, whether to include spatial relations may be decided at the time of the set specification. The second role is selecting the level of aggregation, that is, the number of elements within each key set and the number and type of subsets of each key set. An example of the second role is to include in the model only those plants, commodities, processes, productive units, and so on that are crucial in providing insight into the economic problem. Moreover, it is essential to leave out of the set specification those elements that are not crucial. Any unneeded elements only add to the size of the problem and increase the cost of solving and the difficulty of understanding the model. Another example of the second role is in the specification of commodities. In the small static model the set of commodities was partitioned into three subsets: raw material, intermediate products, and final products. This worked well in that model because each commodity belonged to one and only one subset. However, in more complex models such as the large static model there are more categories of commodities and a given commodity may belong to a combination of categories. In this case the subsets of commodities do not provide a partition of the set of commodities. Then it may be useful to allow the pattern of plus and minus signs in the input-output table to determine implicitly which commodities are raw material, intermediate products, and final products and which commodities are two or more of these types. Set specification also has important implications for model size, which is discussed next. Model Size Calculations In developing high-quality industrial models it is of importance to be keenly aware of the tradeoff between (1) changes in specification of sets, variables, and equations and (2) changes in the model size. Such a consciousness enables the investigator to gain as much insight as possible from the model while keeping it small enough to be efficiently solved and readily understood. To facilitate this understanding of the tradeoff between model size and specification it is necessary to perform calculations like those shown in chapter 5 on the small static model or to have these calculations INDUSTRIAL MODELING 301 performed by the modeling language as was done for the large static model. It is useful to distinguish between increases in the model size that come from adding an additional key set or dimension, such as the addition of time to a static model, and increases from adding elements to a key set. Of course, increases in the number of key sets or domains may increase the order of the size of the model-for example, from the square of the number of elements in the key sets to the cube of the number of elements in the key sets. In contrast, changes in the number of elements in a key set increase the size of the model much less. Model Debugging Strategies There are two major steps in model debugging. The first is checking clerical errors in inputting the model to the computer and the second is finding basic specification errors. Errors in the first stage are usually numerous but relatively easy to find and correct, while errors in the second stage are few in number but difficult to locate and correct. The first stage is similar to compilation errors and the second stage is similar to solution errors in computer programming. As already indicated, the use of a modeling language greatly facilitates the discovery and correction of compilation errors. These errors are typically misspelled variable names or set elements, misplaced punc- tuation, and reversed indices. Reversed indices, for example, may be discovered by using the domain-checking facility of the GAMS language. Solution errors are more difficult to identify and correct. At the first stage they involve the use of common sense. In almost all modeling projects the first solution to the model brings great sighs of relief from the modelers when they discover that it is indeed possible to obtain a solution-any solution-to the problem. However, the first solution is frequently nonsensical. One type of error that produces nonsensical solutions was discussed with the results of the small static model. In that solution a steel plant continued to fully utilize the older and less efficient open hearth furnaces despite unused capacity in the newer and more efficient basic oxygen furnaces. In that case the error was traced to the fact that another process was needed either to supplement or to replace the existing production activity and permit a different mix of inputs. Thus errors which appear after successful compilation but during the solution phase are an extremely important part of debugging, and ample time should be allocated for this phase of the development of any model. 302 MEXICAN CASE STUDY Industry Experts The results of a high-quality modeling exercise can be impressive. Computers can manipulate large amounts of information extremely efficiently. A skilled modeler can utilize a computer to analyze a myriad of economic factors in searching for improved operational procedures or investment patterns. However, the modeler must be on constant guard against the danger of excluding from the analysis small but crucial pieces of information which can invalidate the results. Some examples may help illustrate the point. A very careful study of transport and production costs to determine a new location for a steel mill could be organized along the lines suggested in this book. However, the analysis might overlook two small considerations: the quality of the subsoil at each potential site and the depth of the shipping channel that provides access to the site. The result might be the construction of a steel mill at a site where it would slowly but surely sink into the ground while more and more pilings were needed to keep it from doing so. Or the result might be a new steel mill located where only small ships could be loaded and unloaded, thereby greatly increasing the effective transport cost. When using impressive computers and mathematical models, how is the analyst to ensure that common sense factors are not overlooked? It is clear that subsoil conditions and channel depths and the myriad of other small but important details cannot be included in computer models. The answer lies not in making the models more complicated but rather in keeping them simple enough that their basic structure and approach can be understood by the many experts whose input is important in reaching wise operational and investment decisions. The answer also lies in the determination of the model builders to communicate clearly, crisply, and frequently with a broad range of industrial experts during the model development process. Models can indeed lead to much improved decisionmaking through the ability of the computer to do rapid calculations. But they will lead to improved decisions only if the analysts themselves develop and adhere to principles of good modeling. References Alatorre, Jaime E. 1976. "A Model for Planning Investment in the Mexican Steel Industry for the Period 1974-1986." M.A. thesis, Department of Operations Research, College of Engineering, University of Texas, Austin. Bergendorff, Hans, Peter Glenshaw, and Alexander Meeraus. 1981. "The Planning of Investment Programs in the Forestry and Forest Industry Sectors." Development Policy Staff, World Bank, Washington, D.C. Processed. Bisschop, Johannes, and Alexander Meeraus. 1982. "On the Development of a General Algebraic Modeling System in a Strategic Planning Environment." Mathematical Programming Study, vol. 20, pp. 1-29. Chenery, Hollis B. 1952. "Over-Capacity and the Acceleration Principle." Econometrica, vol. 20 (January), pp. 1-28. Choksi, Armeane M., David A. Kendrick, Alexander Meeraus, and Ardy J. Stoutjesdijk. 1981. La Programmation des investissements industriels. Paris: Economica. Choksi, Armeane M., Alexander Meeraus, and Ardy J. Stoutjesdijk. 1980. The Planning of Investment Programs in the Fertilizer Industry. Baltimore, Md.: Johns Hopkins University Press. The case study has been translated into French as part of Choksi, Kendrick, Meeraus, and Stoutjesdijk (1981). Coordinating Commission for the Steel Industry. 1978. "Present Situation and Future Growth of the Steel Industry." Mexico City. Geoffrion, A. M. 1976. "The Purpose of Mathematical Programming Is Insight, Not Numbers." Interfaces, vol. 7, no. 1, pp. 81-92. Kendrick, David A., and Ardy J. Stoutjesdijk. 1978. The Planning of Industrial Investment Programs: A Methodology. Baltimore, Md.: Johns Hopkins University Press. Also translated into French as part of Choksi, Kendrick, Meeraus, and Stoutjesdijk (1981). 303 304 REFERENCES Kendrick, David A. 1967. Programming Investment in the Process Industries. Cambridge, Mass.: M.I.T. Press. Kendrick, David A., and Alexander Meeraus. 1981. "Model Reduction through Domain Restriction." Center for Economic Research Paper no. 81-12, Department of Economics, University of Texas, Austin; and Discussion Paper no. 35, Development Research Department, World Bank, Washington, D.C. Manne, Alan S., ed. 1967. Investment for Capacity Expansion: Size, Location and Time Phasing. Cambridge, Mass.: M.I.T. Press. Meeraus, Alexander. 1983. "An Algebraic Approach to Modeling." Journal of Economic Dynamics and Control, vol. 5, no. 1. Meeraus, Alexander, and David Kendrick. 1982. "Model Reduction in a Large Static Linear Programming Model." Center for Economic Research Paper no. 82-11, Department of Economics, University of Texas, Austin. Mennes, L. B. M., and Ardy J. Stoutjesdijk. 1981. "Multi-Country Investment Analysis." Development Policy Staff, World Bank, Washington, D.C. Processed. Russell, Clifford S., and William J. Vaughan. 1976. Steel Production:Processes, Products and Residuals. Baltimore, Md.: Johns Hopkins University Press. United States Steel. 1971. The Making, Shaping and Treatment of Steel. Harold E. McGannon, ed. Pittsburgh, Pa. Vietorisz, Thomas, and Alan S. Manne. 1963. "Chemical Processes, Plant Location, and Economies of Scale." In Studies in Processes Analysis. Alan S. Manne and H. M. Markowitz, eds. New York: Wiley. Wein, H. H., and V. P. Sreedharan. 1968. The Optimal Staging and Phasing of Multiproduct Capacity. Studies in Comparative and Technological Planning. East Lansing: School of Business Administration, Michigan State University. Westphal, Larry E. 1971. Planning Investments with Economies of Scale. Amsterdam: North-Holland. Index Aggregation: multiple models and, 298; Capacity utilization, interplant shipments selecting level of, 300 and,203-05 AHMSA. See Altos Hornos de Mxico S.A. Casting, 27; at AHMSA, 44; productive units Alatorre, Jaime E., 5, 54 and, 22; steel production and, 16-17, Altos Hornos de Mexico S.A. (AHMsA), 78; 110 analysis of, 43-45; capacity and shadow Coal: AHMSA and, 44; coke production and prices at, 184-85; coke production at, price of, 109; Fundidora and, 45; 108-09; commodity flows at, 182-83; importation of, 21; large static model interplant shipments and, 204,205; min- plants set and, 102; large static model ing and, 51, 179, 180; pellet imports to, results and, 176-77; mining in Mexico, 261; pig iron production at, 110; steel 51; new sites and, 29; reserves, 228, 257, production data for, 54, 56; technology 264, 272; SICARSA and, 46 at, 188; transport costs and, 75 Coke, 9,46; large static model results and, 176-77; mining reserves and, 228; price Basicogp sof, 78, 258, 271; production, 108-09 Ba.Syen ploroaces1-6 6 5 6 Commodities: exports of, 53, 203; as final 187. See also Furnaces Billets, 16, 17, 18, 19, 21, 31, 47, 110 1138-2 9, 93200mlan- Blooms, 17-1811-3118,8-2130;pln Bloos, 1-18ning model and, 24-25; set specification and, 300; small dynamic model and, Capacity: AHMSA, 44, 175; Fundidora, 76, 210-11; small static model and, 59, 60, 77, 187; HYLSA, 190, 192; increase at 61, 66-67, 72; steel production and, 7,9 SICARTSA, 259; investment variable and, Computer language. See GAMS computer 213, 216; large static model and, 118, language 126-29, 180-81; of Mexican steel in- Constraints: binary variable, 234; convex dustry, 56; new sites and, 26, 37; small combination, 233; institutional, 175-76, static model and, 62, 68 201-02; in large static model, 115-20; Capacity expansion, 27; formulation of model size (small static) and, 70-71; in investment program and, 28-29; size small dynamic model, 230-34; in small of, 30-31; small dynamic model results static model, 66-69 and, 260-61, 262,264; timing of, 31-32, Coordinating Commission for the Steel 211 Industry, 129 305 306 INDEX Consorcio Minero Benito Juarez-Pefia namic model and, 220, 226-27, 233-34; Colorado, 50, 179 model constraints and maximum, Costs: capital, 220-21; of competing tech- 68-69; small static model and, 60, 61, nologies, 30; import, 236; investment, 78; of steel products, 53, 203 32, 33, 212, 235, 253-55; large static model and, 133, 201, 202; raw material, Foreig trade, 33-34 235; small dynamic model objective Fundidora de Monterrey SA.: analysis of, function and, 234-35; small static model 45-46; coke production and, 109; com- objective function and, 69-70; transport, modity flows at, 186-88; flat products 64-65, 75-78, 135-36, 235-36 decline and, 53; furnace technology and capacity at, 76; interplant shipments Decentralization program, 37, 40 and, 204, 205; mining and, 51, 179, 180; Demand: large static model parameters pig iron production and, 110; raw and, 129-32; market size estimation material received at, 185-86; site factors and, 56; small dynamic model para- for, 221; steel production data and, 56; meters and, 218-20; for steel products, technology at, 76, 188; transport costs 37-42 and, 75 Discount term (small dynamic model), Furnaces: at AHmsA, 44,45; basic oxygen, 221-22 14-16, 56, 75, 76, 77, 187; capacity Diseconomies of scale, 214-16, 220-21. additionsand, 31;electricarc, 15,16,21; See also Economies of scale energy prices and, 257; at Fundidora, Dynamic model. See Small dynamic model 45-46, 76, 77, 187; at HYLSA, 48; iron production and blast, 12-13, 263; open Economies of scale: capacity expansion nearth process and, 14,15,16,27,73, 76, size and, 30-31; foreign trade and, 33; 77; pig iron production and, 110;'pro- investment cost and, 32; large static duction costs and, 74, 75; production model and capacity parameters and, processes and, 24; productive units and, 128-29; replication unit for diseco- 22; at SICARTSA, 47; steel scrap and, nomies and, 216. See also Diseconomies 51-53; at TAmsA, 49; technological of scale choice and, 30 Electricity prices: constant, 257; in large GAms computer language: advantages of, static model, 133; in small dynamic 299; debugging and, 301; large static model, 226, 270-71 model notational equivalence and, Energy: prices and furnace technology 136-38; large static model statement and, 257; subsidy, 259, 271-72, 295; technological choice and, 30. See also tational equivalence and, 236-38; small Coal; Coke; Electricity; Natural gas dynamic model statement and, 238-52; Expansion units, 27; investment program small static model notational equival- formulation and, 28-29; size of, 30-31; ence and, 79-80; small static model in small dynamic model, 211, 260-61, statement and, 80-100 262, 264; timing of, 31-32 Geoffrion, A. M., 297 Experimental runs: large static model, 201-07; small dynamic model, 258-59, Hojalata y Limina S.A. (HYLsA and 267-73 RLSAP), 187; analysis of, 47-48; ca- Exports, 31, 33; of HYL technology, 47; pacity and shadow prices at, 190, 192; institutional constraints and, 175; large commodity flows at, 188-90, 191; inter- static model and, 107, 114, 119, 129, 135; plant shipments and, 204, 205; mining product flow and, 196; of raw material, and, 51, 179, 180; natural gas prices and, 52, 53; revenue from, 236; small dy- 78; site factors for, 221; steel production INDEX 307 costs and, 75; steel production data and, Large static model: 56; TAMSA pellets and, 49 -constraints, 115-19 HYL process (direct reduction of iron ores), -AMS: mathematical notational equival- 13, 47 ence of, 136-38; statement of, 138-74 HYLSA. See Hojalata y Lamina S.A. -objective function, 120-21 HYLSAP. See Hojalata y Limina S.A. -parameters: capacity, 126-29; demand, Imports: capacity expansion and price of, 122-2; prcot 35-36 31; of coal, 21; of coke, 258, 271; costs 12resultofepert runs, 201-07 and, 236; institutional constraints and, insution conrints and,21-7; 176; large staticmodeland, 115, 133-35; m arke ts and, 1 pa (t model and question of, 33; new sites and, mills and, 1-2; w atrial 29; of ores, 21, 37; of pellets, 29, 261; 176-80 product flow and, 196; of raw material, set specification: of commodities, 52, 53; small dynamic model and 60, 61, 111-13; of markets, 106-07; of plants, 226-27; of steel ingots (TAMSA), 48-49; 102-06; of processes, 108-Il; of pro- of steel products, 53 ductive units 107-08 Input and output coefficients: commo- -variables, 114-15 dities set specifications and, 24; large Linear programming: small static model static model and, 122-25; shipment pat- results and, 71, 75-79; to study industry, terns and, 76-77; small static model and, 5 56-58, 62 Linz-Donawitz BOF process, 14. See also Institutional constraints, 175-76, 201-02 Furnaces Interplant shipments. See under Shipments Location: energy subsidy and, 271-72; Investment analysis: model construction export possibilities and, 33; markets and planning, 4; modeling limitations and, 26; natural gas and, 267-68, 270 and, 4-5; models and, 3-6; technology and,5 Markets: estimating size of, 56; large static Investment cost function, 212-17 model and, 106-07, 118, 193-201; Investment cost (small dynamic model), modeling and, 3; planning model and, 220-21, 235; derivation of, 253-55 26; small dynamic model and, 210, 233, Investment program: dynamic models 266-67; small static model and, 59, 63, and, 256, 260-64; formulating, 28-34; 68 model methodology and, 295; planning Material balance constraints: in large sta- model for, 20-28; static capacity expan- tic model, 115-18; in small dynamic sion and, 293 model, 230-31; in small static model, Iron ore: AHMSA and, 43-44; domestic 66-69. See also Constraints inputs and, 50-51; Fundidora and, 45; Mines: large static model and, 102, 107, HYLSA and, 47; imports of, 21, 37; large 108, 115-16, 118, 126, 133, 177-78; plan- static model and, 102, 126, 176-80; mines set specification, 21; new sites and, model and, 21; smal dynamic 29; processes and, 108; reserves, 228-29, Mining: AHM'A and, 43-44; domestic in- 257, 261-62, 264, 272; SICARTSA and, 46; puts and, 50-51; Fundidora and, 45; steel production and, 9, 11; TAMSA and, prices ofproducts in, 222; processesand, 49 108; SICARTSA and, 46; small dynamic, Iron production, 8, 9, 12-13; large static model and, 231; steel production and, model and, 110; limit on, 234; small 11-12; TAMSA and, 49 dynamic model and, 262-63 Models: common sense factors and, 302; Kendrick, David, 3, 4, 5, 222 currency and weight units used in, 35, 308 INDEX 133; debugging, 301; extensions of, sites and, 26-27; planning model and, 293-94; formulating an investment pro- 21-22; small dynamic model and, gram and, 28-34; investment analysis 208-09, 231, 232-33, 265-66; subsoil and, 3-5; multiple, 298-99; planning an quality and construction of, 264, 302; investment program and, 20-28; plants types of, 21-22, 42-43 and, 26; purpose of, 208, 297; size of, Prices: coke, 78, 222-23, 258, 271; coke 70-71, 300-01; time periods and dy- production and coal, 109; differing ac- namic, 26. See also Large static model; ross markets, 201; electricity, 133, 226, Small dynamic model; Small static 257, 270-71, 295; energy subsidy, 259; model large static model parameters and, 133-35; markets and shadow, 200-01; Natural gas: capacity expansion and, 27; of mining products, 222; natural gas, 37, domestic price rise and, 256-57,258-59; 77, 78, 133, 224-26, 256-57, 258-59, location factors and, 267-68, 270; 263, 269-70, 295; pellet, 223-24; scrap prices, 37, 77, 78, 133, 224-26, 263; small and domestic, 206; small dynamic model dynamic model experimental run and and export and import, 226-27; small constant price of, 267-70; steel pro- static model parameters and, 63-64; duction and, 9, 12, 13 steel mills and shadow, 184-85,187,190, Nonnegativity constraints: large static mo- 192; timing of capacity expansion and, del, 119-20; small dynamic model, 234; 31 small static model, 69. See also Processes: large static model and, 108-11, Constraints 114, 116-17, 118; planning model and, Notational equivalence (between 23-24; smalt dynamic model and, 210, mathematical and GAMS terms): in large 213, 217; small static model and, 59, static model, 136-38; in small dynamic 60-61, 72-75; steel industry data and, model, 236-38; in small static model, 58; steel production and, 7-9 79-80 Production: large static model parameters Objective function: in large static model, and, 122-26; model preparation and, 120-1, 22; n smll dnamc moel, 23-24;- small static model and, 60-61, 120-21, 202; in small dynamic model, 72-75; upper bound on, 272-73 234-36; in small static model, 69-70 Open hearth process, 14, 15, 16, 27, 73, 76, Productive units: expansion and, 27, 29; 77. See also Furnaces investment variables and, 214; labor as, Ore. See Iron ore 25; large static model and, 107-08, 126; Ownership, 113, 119, 179 modeling and, 3-4; planning model and, 22-23; small dynamic model sets and, Parameters: of large static model, 210; small static model sets and, 59, 60; 122-36; large static model notational steel industry data and, 58; steel pro- equivalence and, 137-38; of small dy- duction and, 7-9, 13-14 namic model, 218-29; of small static Productivity: models and increases in, 299; model, 62-65 strikes at Fundidora and, 46 Pellets: HYLSA and, 47-48; imported, 29, Product mix, 32-33 261; large static model and, 102-05, 177-80; mining reserves and, 228; small Raw material: commodities and, 112-13; dynamic model and prices of, 223-24; costs and, 235; domestic inputs and, steel production and, 11; TAMSA and, 49 49-53; domestic prices and, 133; Pefia Colorado, 50, 179 Fundidora and, 185-86; importing, 33; Plants: data on, 54-55; expansion units large static model and, 106, 107, 108, and, 27; large static model and, 102-06, 118; material balance constraints and, 107, 108, 116-18; modeling and, 3; new 68, 116-17; small dynamic model results INDEX 309 and, 264; small static model set variables Sites: capital costs and, 221 ; characteristics and, 60, 61; transport and, 33. See also affecting choice of, 29, 264, 302; green Coal; Coke; Iron ore field, 209; investment program formu- Reserves (mineral): classifying, 50; dy- lation and new, 29; limit on iron pro- namic model and, 257, 272; exhaustion duction at, 234; limit on steel production of domestic, 264; pattern of use of, at, 272-73; planning model and new, 261-62; small dynamic model and, 26-27 228-29, 232 Small dynamic model: Results: large static model, 175-207; linear -constraints, 230-34 programming (small static model), 71, -GAms: notational equivalence of, 75-79; small dynamic model, 71, 72-75, 236-38; statement of, 238-52 256-73; small dynamic model summary -methodology and, 295 tables and, 273-92 -objective function, 234-36 Rogers, J. Scott, 297n -parameters: capital costs, 220-21; ca- Rolling mills, 21; AHMSA, 44-45; pital recovery, 222; demand, 218-20; Fundidora, 46; HYLSA, 48; large static discount term, 221-22; exports, 220; model capacity parameters and, 128; interplant shipment, 227; mining re- nonflat products and, 22; production serve, 228-29; prices, 222-27; shipment, processes and, 110-11; steel production 227; transport cost, 227 and, 9,16,17-19 -results: assumptions and, 256-58; base Russell, Clifford S., 5 solution, 259-67; conclusions concern- ing, 273; experimental runs and, 258-59, Scrap, 21, 49; analysis of, 51-53; domestic 267-73; summary tables of, 273-92 price of, 206; institutional constraints -set specification, 208-12 and, 175 -variables in, 212; new investment, Set specification: choice of elements in, 24; 213-17 good model building and, 299-300; Small static model: large static model and, 101-14, 137; -constraints, 66-69 planning model and, 20-28; small dy- -GAMS: mathematical notational equival- namic model and, 208-12; small static ence of, 79-80; statement of, 80-100 model and, 59-62 -methodology and, 294-95 Shipments: interplant, 28, 45, 175, 189, -model size, 70-71 203-06, 227, 295; large static model and, -objective function, 69-70 114, 193-200; small dynamic model and, -parameters: capacity, 62; input-output 213, 217, 227, 266; small static model coefficients, 62;marketingrequirements, and, 60, 61, 75-78; transport problems 63; prices, 63-64; transport cost, 64-65 and, 33 -results: linear programming, 71, 75-79; SICARTSA. See Siderurgia Lazaro primary, 71, 72-75 Cdrdenas-Las Truchas S.A. -set specification, 59-60; variables relat- SIDERMEX (national steel company), 110 ing to, 60-62 Siderurgia Lzaro Cdrdenas-Las Truchas -steel plant data recapitulation and, S.A. (slCARTSA), 78, 271; analysis of, 54-59 46-47; capacity expansion at, 259, 261; Sreedharan, V. P., 5 coke production and, 109; commodity Static models. See Large static model; flows and, 181-82; location subsidy and, Small static model 271-72; mining and, 51; pellet imports Steel industry: data on, 54-55; formula- and, 261; pig iron production and, 110; tion of investment program for, 28-34; steel production data and, 56; transport investment analysis and models of, 3-5; costs and, 75 planning model for investment in, 310 INDEX 20-28; small static model and, 59-79. large static model and, 128-29; location See also Large static model; Models; and timing and, 271; natural gas prices Small dynamic model; Small static and, 37, 257; open hearth, 14, 15, 16; model rolling, 17-19; small static model and, Steel mills. See Plants 72; static capacity expansion model and, Steel production, 8, 9, 13-17; institutional 293; steel production and, 7, 9, 14-16, constraints and, 176; limiting, 272-73; 188; steel production data and, 56 no upper bounds on, 257 Time periods: capacity additions and, Steel products: categories of, 39; demand 31-32; planning model and, 26; small for, 37-42; domestic supply of, 42-49; dynamic model, 211, 213 export of, 53, 203; investment program Transport, 27-28, 33; of coal, 51; large formulation and, 32-33; large static static model and cost of, 135-36; plan- model and, 112-13, 129-32; small static ning model and, 27-28; size of capacity model and, 66-68 expansion and cost of, 30; small dy- Steel sector in Mexico: analysis of data on, namic model and cost of, 227, 235-36; 54- -59; demand for steel products and, small static model and cost of, 64-65, 37-42; domestic inputs and raw material 75-78 and, 49-53; steel producers in, 42-49 Tubos de Acero de M6ico SA. (TAMSA): Stoutjesdijk, Ardy J., 3, 4, 222 anaJysis of, 48-49; commodity flows at, Strikes, 46, 175, 206 191 -92; mining and, 51, 179 Subsidy for energy, 259, 271-72, 295 Variables: binary constraint, 234; in large TAMSA. See Tubos de Acero de Mexico static model, 114-15; large static model S.A.notational equivalence and, 137; in Technology: at AHMSA, 44, 188; casting, small staic model, 2 16-17; dynamic models and, 264, 295; expansion units and, 27; HYL process, 13, Vaughan, William J., 5 47; investment analysis and, 5; invest- Wein, H. H., 5 ment program formulation and, 30; Westphal, Larry E., 5 The full range of World Bank publications, both free and for sale, is described in the Catalog of Publications; the continuing research program is outlined in Abstracts of Current Studies. Both booklets are updated annually; the most recent edition of each is available without charge from the Publications Sales Unit, Department B, The World Bank, 1818 H Street, N.W., Washington, D.C. 20433, U.S.A. David A. Kendrick is professor of economics at the University of Texas. Alexander Meeraus is chief of the Analytic Support Unit in the Development Research Department of the World Bank. Jaime Alatorre is director of national accounting and economic statistics at the National Institute of Statistics, Geography, and Information of the Mexican Ministry of Programming and Budgeting.   0 8018 3197 0