Model Building in Mathematical Programming

H. Paul Williams, London School of Economics, UK.

• Preface PART 11 Introduction1.1 The Concept of a Model1.2 Mathematical Programming Models2 Solving Mathematical Programming Models2.1 Algorithms and Packages2.2 Practical Considerations2.3 Decision Support and Expert Systems2.4 Constraint Programming 3 Building Linear Programming Models3.1 The Importance of Linearity3.2 Defining Objectives3.3 Defining Constraints3.4 How to Build a Good Model3.5 The Use of Modelling Languages4 Structured Linear Programming Models4.1 Multiple Plant, Product, and Period Models4.2 Stochastic Programming Models4.3 Decomposing a Large Model5 Applications and Special Types of Mathematical Programming Model5.1 Typical Applications5.2 Economic Models5.3 Network Models5.4 Converting Linear Programs to Networks6 Interpreting and Using the Solution of a Linear Programming Model6.1 Validating a Model6.2 Economic Interpretations6.3 Sensitivity Analysis and the Stability of a Model6.4 Further Investigations Using a Model6.5 Presentation of the Solutions7 Non-linear Models7.1 Typical Applications7.2 Local and Global Optima7.3 Separable Programming7.4 Converting a Problem to a Separable Model8 Integer Programming8.1 Introduction8.2 The Applicability of Integer Programming8.3 Solving Integer Programming Models9 Building Integer Programming Models I9.1 The Uses of Discrete Variables9.2 Logical Conditions and Zero—One Variables9.3 Special Ordered Sets of Variables9.4 Extra Conditions Applied to Linear Programming Models9.5 Special Kinds of Integer Programming Model9.6 Column Generation10 Building Integer Programming Models II10.1 Good and Bad Formulations10.2 Simplifying an Integer Programming Model10.3 Economic Information Obtainable by Integer Programming10.4 Sensitivity Analysis and the Stability of a Model10.5 When and How to Use Integer Programming11 The Implementation of a Mathematical Programming System of Planning11.1 Acceptance and Implementation11.2 The Unification of Organizational Functions11.3 Centralization versus Decentralization11.4 The Collection of Data and the Maintenance of a ModelPART 212 The Problems12.1 Food Manufacture 1When to buy and how to blend12.2 Food Manufacture 2Limiting the number of ingredients and adding extra conditions12.3 Factory Planning 1What to make, on what machines, and when12.4 Factory Planning 2When should machines be down for maintenance12.5 Manpower PlanningHow to recruit, retrain, make redundant, or overman12.6 Refinery OptimizationHow to run an oil refinery12.7 MiningWhich pits to work and when to close them down12.8 Farm PlanningHow much to grow and rear12.9 Economic PlanningHow should an economy grow12.10 DecentralizationHow to disperse offices from the capital12.11 Curve FittingFitting a curve to a set of data points12.12 Logical DesignConstructing an electronic system with a minimum number of components12.13 Market SharingAssigning retailers to company divisions12.14 Opencast MiningHow much to excavate12.15 Tariff Rates (Power Generation)How to determine tariff rates for the sale of electricity12.16 Hydro PowerHow to generate and combine hydro and thermal electricity generation12.17 Three-dimensional Noughts and CrossesA combinatorial problem12.18 Optimizing a ConstraintReconstructing an integer programming constraint more simply12.19 Distribution 1Which factories and depots to supply which customers12.20 Depot Location (Distribution 2)Where should new depots be built12.21 Agricultural PricingWhat prices to charge for dairy products12.22 Efficiency AnalysisHow to use data envelopment analysis to compare efficiencies of garages12.23 Milk CollectionHow to route and assign milk collection lorries to farms12.24 Yield ManagementWhat quantities of airline tickets to sell at what prices and what times12.25 Car Rental 1How many cars to own and where to locate them12.26 Car Rental 2Where should repair capacity be increased12.27 Lost Baggage DistributionWhich vehicles should go to which customers and in what order12.28 Protein FoldingHow a string of Amino Acids is likely to fold12.29 Protein ComparisonHow similar are two proteinsPART 313 Formulation and Discussion of Problems13.1 Food Manufacture 113.2 Food Manufacture 213.3 Factory Planning 113.4 Factory Planning 213.5 Manpower Planning13.6 Refinery Optimization13.7 Mining13.8 Farm Planning13.9 Economic Planning13.10 Decentralization13.11 Curve Fitting13.12 Logical Design13.13 Market Sharing13.14 Opencast Mining13.15 Tariff Rates (Power Generation)13.16 Hydro Power13.17 Three-dimensional Noughts and Crosses13.18 Optimizing a Constraint13.19 Distribution 113.20 Depot Location (Distribution 2)13.21 Agricultural Pricing13.22 Efficiency Analysis13.23 Milk Collection13.24 Yield Management13.25 Car Rental 113.26 Car Rental 213.27 Lost Baggage Distribution13.28 Protein Folding13.29 Protein ComparisonPART 414 Solutions to Problems14.1 Food Manufacture 114.2 Food Manufacture 214.3 Factory Planning 114.4 Factory Planning 214.5 Manpower Planning14.6 Refinery Optimization14.7 Mining14.8 Farm Planning14.9 Economic Planning14.10 Decentralization14.11 Curve Fitting14.12 Logical Design14.13 Market Sharing14.14 Opencast Mining14.15 Tariff Rates (Power Generation)14.16 Hydro Power14.17 Three-dimensional Noughts and Crosses14.18 Optimizing a Constraint14.19 Distribution 114.20 Depot Location (Distribution 2)14.21 Agricultural Pricing14.22 Efficiency Analysis14.23 Milk Collection14.24 Yield Management14.25 Car Rental 114.26 Car Rental 214.27 Lost Baggage Distribution14.28 Protein Folding14.29 Protein ComparisonReferencesAuthor IndexSubject Index