Model Building in Mathematical Programming

Transcription

1 Model Building in Mathematical Programming Fourth Edition H. PAUL WILLIAMS Faculty of Mathematical Studies University of Southampton JOHN WILEY & SONS, LTD Chichester New York Brisbane Toronto Singapore

2 Contents Preface xi PART Introduction The Concept of a Model Mathematical Programming Models 5 2 Solving Mathematical Programming Models Algorithms and Packages Practical Considerations Decision Support and Expert Systems Constraint Logic Programming (CLP) 15 3 Building Linear Programming Models The Importance of Linearity Defining Objectives Defining Constraints How to Build a Good Model The Use of Modelling Languages 36 4 Structured Linear Programming Models Multiple Plant, Product, and Period Models Decomposing a Large Model 48 5 Applications and Special Types of Mathematical Programming Model Typical Applications Economic Models Network Models Converting Linear Programs to Networks 90 6 Interpreting and Using the Solution of a Linear Programming Model Validating a Model Economic Interpretations Sensitivity Analysis and the Stability of a Model Further Investigations Using a Model Presentation of the Solutions 124

3 7 Non-linear Models Typical Applications Local and Global Optima Separable Programming Converting a Problem to a Separable Model Integer Programming Introduction The Applicability of Integer Programming Solving Integer Programming Models Building Integer Programming Models I The Uses of Discrete Variables Logical Conditions and Zero-One Variables Special Ordered Sets of Variables Extra Conditions Applied to Linear Programming Models Special Kinds of Integer Programming Model Building Integer Programming Models II Good and Bad Formulations Simplifying an Integer Programming Model Economic Information Obtainable by Integer Programming Sensitivity Analysis and the Stability of a Model When and How to Use Integer Programming The Implementation of a Mathematical Programming System of Planning Acceptance and Implementation The Unification of Organizational Functions Centralization versus Decentralization The Collection of Data and the Maintenance of a Model 227 PART The Problems Food Manufacture When to buy and how to blend 12.2 Food Manufacture Limiting the number of ingredients and adding extra conditions 12.3 Factory Planning What to make, on what machines, and when 12.4 Factory Planning When should machines be down for maintenance

4 12.5 Manpower Planning 234 How to recruit, retrain, make redundant, or overman 12.6 Refinery Optimization 236 How to run an oil refinery 12.7 Mining 238 Which pits to work and when to dose them down 12.8 Farm Planning 239 How much to grow and rear 12.9 Economic Planning 240 How should an economy grow Decentralization 242 How to disperse officesfrom the capital CurveFitting 242 Fitting a curve to a sei of data points Logical Design 243 Constructing an electronic System with a minimum number of components Market Sharing 244 Assigning retailers to Company divisions Opencast Mining 245 How much to excavate Tariff Rates (Power Generation) 247 How to determine tariff rates for the sale of electricity Hydro Power 247 How to generate and combine hydro and thermal electricity generation Three-dimensional Noughts and Crosses 248 A combinatorial problem Optimizing a Constraint 249 Reconstructing an integer programming constraint more simply Distribution Which factories and depots to supply which customers Depot Location (Distribution 2) 251 Where should new depots be built Agricultural Pricing 252 What prices to charge for dairy products Efficiency Analysis 253 How to use data envelopment analysis to compare efficiencies ofgarages Milk Collection 255 How to route and assign milk collection lorries tofarms Yield Management 256 What quantities of airline tickets to seil at what prices and what times vn

5 PART Formulation and Discussion of Problems Food Manufacture Food Manufacture Factory Planning Factory Planning Manpower Planning Refinery Optimization Mining Farm Planning Economic Planning Decentralization CurveFitting Logical Design Market Sharing Opencast Mining Tariff Rates (Power Generation) Hydro Power Three-dimensional Noughts and Crosses Optimizing a Constraint Distribution Depot Location (Distribution 2) Agricultural Pricing Efficiency Analysis Milk Collection Yield Management 302 PART Solutions to Problems Food Manufacture Food Manufacture Factory Planning Factory Planning Manpower Planning Refinery Optimization Mining Farm Planning Economic Planning Decentralization CurveFitting Logical Design Market Sharing Opencast Mining Tariff Rates (Power Generation) 322

6 14.16 Hydro Power Three-dimensional Noughts and Crosses Optimizing a Constraint Distribution Depot Location (Distribution 2) Agricultural Pricing Efficiency Analysis Milk Collection Yield Management 331 References 335 AuthorIndex 345 Subject Index 348