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Model Building in Mathematical Programming

The 5th edition of Model Building in Mathematical Programming discusses the general principles of model building in mathematical programming and demonstrates how they can be applied by using several simplified but practical problems from widely different contexts. Suggested formulations and solutions are given together with some computational experience to give the reader a feel for the computational difficulty of solving that particular type of model. Furthermore, this book illustrates the scope and limitations of mathematical programming, and shows how it can be applied to real situations. By emphasizing the importance of the building and interpreting of models rather than the solution process, the author attempts to fill a gap left by the many works which concentrate on the algorithmic side of the subject. In this article, H.P. Williams explains his original motivation and objectives in writing the book, how it has been modified and updated over the years, what is new in this edition and why it has maintained its relevance and popularity over the years:
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Table of Contents

Preface PART 1 1 Introduction 1.1 The Concept of a Model 1.2 Mathematical Programming Models 2 Solving Mathematical Programming Models 2.1 Algorithms and Packages 2.2 Practical Considerations 2.3 Decision Support and Expert Systems 2.4 Constraint Programming 3 Building Linear Programming Models 3.1 The Importance of Linearity 3.2 Defining Objectives 3.3 Defining Constraints 3.4 How to Build a Good Model 3.5 The Use of Modelling Languages 4 Structured Linear Programming Models 4.1 Multiple Plant, Product, and Period Models 4.2 Stochastic Programming Models 4.3 Decomposing a Large Model 5 Applications and Special Types of Mathematical Programming Model 5.1 Typical Applications 5.2 Economic Models 5.3 Network Models 5.4 Converting Linear Programs to Networks 6 Interpreting and Using the Solution of a Linear Programming Model 6.1 Validating a Model 6.2 Economic Interpretations 6.3 Sensitivity Analysis and the Stability of a Model 6.4 Further Investigations Using a Model 6.5 Presentation of the Solutions 7 Non-linear Models 7.1 Typical Applications 7.2 Local and Global Optima 7.3 Separable Programming 7.4 Converting a Problem to a Separable Model 8 Integer Programming 8.1 Introduction 8.2 The Applicability of Integer Programming 8.3 Solving Integer Programming Models 9 Building Integer Programming Models I 9.1 The Uses of Discrete Variables 9.2 Logical Conditions and Zero One Variables 9.3 Special Ordered Sets of Variables 9.4 Extra Conditions Applied to Linear Programming Models 9.5 Special Kinds of Integer Programming Model 9.6 Column Generation 10 Building Integer Programming Models II 10.1 Good and Bad Formulations 10.2 Simplifying an Integer Programming Model 10.3 Economic Information Obtainable by Integer Programming 10.4 Sensitivity Analysis and the Stability of a Model 10.5 When and How to Use Integer Programming 11 The Implementation of a Mathematical Programming System of Planning 11.1 Acceptance and Implementation 11.2 The Unification of Organizational Functions 11.3 Centralization versus Decentralization 11.4 The Collection of Data and the Maintenance of a Model PART 2 12 The Problems 12.1 Food Manufacture 1 When to buy and how to blend 12.2 Food Manufacture 2 Limiting the number of ingredients and adding extra conditions 12.3 Factory Planning 1 What to make, on what machines, and when 12.4 Factory Planning 2 When should machines be down for maintenance 12.5 Manpower Planning How to recruit, retrain, make redundant, or overman 12.6 Refinery Optimization How to run an oil refinery 12.7 Mining Which pits to work and when to close them down 12.8 Farm Planning How much to grow and rear 12.9 Economic Planning How should an economy grow 12.10 Decentralization How to disperse offices from the capital 12.11 Curve Fitting Fitting a curve to a set of data points 12.12 Logical Design Constructing an electronic system with a minimum number of components 12.13 Market Sharing Assigning retailers to company divisions 12.14 Opencast Mining How much to excavate 12.15 Tariff Rates (Power Generation) How to determine tariff rates for the sale of electricity 12.16 Hydro Power How to generate and combine hydro and thermal electricity generation 12.17 Three-dimensional Noughts and Crosses A combinatorial problem 12.18 Optimizing a Constraint Reconstructing an integer programming constraint more simply 12.19 Distribution 1 Which factories and depots to supply which customers 12.20 Depot Location (Distribution 2) Where should new depots be built 12.21 Agricultural Pricing What prices to charge for dairy products 12.22 Efficiency Analysis How to use data envelopment analysis to compare efficiencies of garages 12.23 Milk Collection How to route and assign milk collection lorries to farms 12.24 Yield Management What quantities of airline tickets to sell at what prices and what times 12.25 Car Rental 1 How many cars to own and where to locate them 12.26 Car Rental 2 Where should repair capacity be increased 12.27 Lost Baggage Distribution Which vehicles should go to which customers and in what order 12.28 Protein Folding How a string of Amino Acids is likely to fold 12.29 Protein Comparison How similar are two proteins PART 3 13 Formulation and Discussion of Problems 13.1 Food Manufacture 1 13.2 Food Manufacture 2 13.3 Factory Planning 1 13.4 Factory Planning 2 13.5 Manpower Planning 13.6 Refinery Optimization 13.7 Mining 13.8 Farm Planning 13.9 Economic Planning 13.10 Decentralization 13.11 Curve Fitting 13.12 Logical Design 13.13 Market Sharing 13.14 Opencast Mining 13.15 Tariff Rates (Power Generation) 13.16 Hydro Power 13.17 Three-dimensional Noughts and Crosses 13.18 Optimizing a Constraint 13.19 Distribution 1 13.20 Depot Location (Distribution 2) 13.21 Agricultural Pricing 13.22 Efficiency Analysis 13.23 Milk Collection 13.24 Yield Management 13.25 Car Rental 1 13.26 Car Rental 2 13.27 Lost Baggage Distribution 13.28 Protein Folding 13.29 Protein Comparison PART 4 14 Solutions to Problems 14.1 Food Manufacture 1 14.2 Food Manufacture 2 14.3 Factory Planning 1 14.4 Factory Planning 2 14.5 Manpower Planning 14.6 Refinery Optimization 14.7 Mining 14.8 Farm Planning 14.9 Economic Planning 14.10 Decentralization 14.11 Curve Fitting 14.12 Logical Design 14.13 Market Sharing 14.14 Opencast Mining 14.15 Tariff Rates (Power Generation) 14.16 Hydro Power 14.17 Three-dimensional Noughts and Crosses 14.18 Optimizing a Constraint 14.19 Distribution 1 14.20 Depot Location (Distribution 2) 14.21 Agricultural Pricing 14.22 Efficiency Analysis 14.23 Milk Collection 14.24 Yield Management 14.25 Car Rental 1 14.26 Car Rental 2 14.27 Lost Baggage Distribution 14.28 Protein Folding 14.29 Protein Comparison References Author Index Subject Index

About the Author

H. Paul Williams, London School of Economics, UK

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