Linear Programming, Sensitivity Analysis & Related Topics

Preface

Acknowledgements

1 Introduction

1.1. Modelling using Linear Programming

1.2. Solving linear programmes

1.2.1. The graphical solution and the importance of visual displays.

1.2.2. The Simplex Method and its main variants

1.2.3. Computer software packages

1.2.4. Complementary information and Sensitivity Analysis

1.3. Linear Programming: the Approach par excellence for understanding modelling

1.3.1. The variants of Linear Programming

1.3.2. LP's related topics

1.4. The Approach of the book

Part I Linear Programming and Sensitivity Analysis

2 The Geometric Approach

2.1. The founding concepts of Linear Programming

2.2. The Maximization Form

Application # 1: An advertising campaign [Aurel 2D]

2.2.1. The mathematical formulation

2.2.2. The graphical solution and the fundamental theorem of LP

- Basic vs. non-basic variables

- Basic solution vs. basic feasible solution

- The Fundamental Theorem of Linear Programming

2.2.3. Interpreting the slack and surplus variables

2.2.4. Shadow prices

Application # 2: Computer games

2.3. The Minimization Form

Application # 3: A Portfolio selection

Chapter 2 Exercises and applications

3 The Simplex Method

3.1. The Maximization Form

3.1.1. The Standard Form

3.1.2. The simplex algorithm (using tableaux)

3.1.3. Shadow prices and reduced costs.

3.1.4. The algorithm (using matrix algebra)

3.1.5. Introduction of artificial variables