Model Building in Mathematical Programming

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 ProgrammingModel5.1 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 ProgrammingModel

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