Model Building in Mathematical Programming (1999)
CONTENTS  
1 Introduction 3
1.1 The Concept of a Model 3

1.2 Mathematical Programming Models5

2 Solving Mathematical Programming Models 10
2.1 Algorithms and Packages10

2.2 Practical Considerations12

2.3 Decision Support and Expert Systems15

2.4 Constraint Logic Programming (CLP)15

3 Building Linear Programming Models 17
3.1 The Importance of Linearity17

3.2 Defining Objectives19

3.3 Defining Constraints
3.4 How to Build a Good Model32

3.5 The Use of Modelling Languages36

4 Structured Linear Programming Models 39
4.1 Multiple Plant, Product, and Period Models39

4.2 Decomposing a Large Model48

5 Applications and Special Types of Mathematical Programming Model 59
5.1 Typical Applications59

5.2 Economic Models65

5.3 Network Models72

5.4 Converting Linear Programs to Networks90

6 Interpreting and Using the Solution of a Linear Programming Model 93
6.1 Validating a Model93

6.2 Economic Interpretations97
111

6.3 Sensitivity Analysis and the Stability of a Model
6.4 Further Investigations Using a Model122

6.5 Presentation of the Solutions124

7 Non-linear Models 126
7.1 Typical Applications126



7.2 Local and Global Optima129



7.3 Separable Programming136



7.4 Converting a Problem to a Separable Model142



8 Integer Programming 144
8.1 Introduction144



8.2 The Applicability of Integer Programming145



8.3 Solving Integer Programming Models151



9 Building Integer Programming Models I 154
9.1 The uses of Discrete Variables154



9.2 Logical Conditions and Zero-One Variables160



9.3 Special Ordered Sets of Variables165



9.4 Extra Conditions Applied to Linear Programming Models169



9.5 Special Kinds of Integer Programming Model176



10 Building Integer Programming Models II 187
10.1 Good and Bad Formulations187



10.2 Simplifying an Integer Programming Model197



10.3 Economic Information Obtainable by Integer Programming209



10.4 Sensitivity Analysis and the Stability of a Model216



10.5 When and How to Use Integer Programming219



11 The Implementation of a Mathematical Programming System of Planning 221
11.1 Acceptance and Implementation221



11.2 The Unification of Organizational Functions223



11.3 Centralization versus Decentralization225



11.4 The Collection of Data and the Maintenance of a Model227