INTRODUCTION TO MATHEMATICAL PROGRAMMING. PART I Anita Ciekot

Contents

INTRODUCTION 

CHAPTER 1. REVIEW OF LINEAR ALGEBRA

1.1. Matrices. Matrix operation

1.2. Systems of linear equations. Methods of solution

CHAPER 2. LINEAR PROGRAMMING

2.1. Basic concepts and notation

2.2. Linear programming problem formulation

2.3. Graphical solutions to linear problems

2.4. The Simplex Method

2.4.1. Introduction to the Simplex Method – the algebraic approach

2.4.2. The Simplex Algorithm – step by step

2.4.3. The Big M – method

2.5. Duality theory

2.5.1. Formulating the dual LP

2.5.2. The dual theorems

2.5.3. Economic interpretation of dual variables

2.6. Sensitivity analysis

2.6.1. Sensitivity to an objective coefficients

2.6.2. Sensitivity to constraint bounds

2.7. Special cases of linear programming problems

CHAPTER 3. TRANSPORTATION PROBLEM

3.1. Transportation problem – mathematical model formulating

3.1.1. Basic definitions

3.2. Initial basic feasible solution

3.2.1. Northwest Corner Method

3.2.2. Minimum Cost Method

3.2.3. Vogel’s approximation method

3.3. Optimal solution for transportation problem

3.4. Standard application of transportation problem – Transshipment problems

CHAPTER 4. INTEGER LINEAR PROGRAMMING

4.1. Formulating the integer linear problem

4.2. The branch and bound method

4.3. Binary and mixed integer linear problem

CHAPTER 5. COMPUTER IMPLEMENTATION

5.1. An introduction to using the Maple package

5.2. Linear algebra with Maple

5.3. A step-by-step Maple implementation to solve the linear programming problems

5.3.1. The graphical solution to LP

5.3.2. The Simplex method

5.3.3. Transportation problem

BIBLIOGRAPHY