Elementary Linear Programming with Applications

Elementary Linear Programming with Applications presents a survey of the basic ideas in linear programming and related areas. It also provides students with some of the tools used in solving difficult problems which will prove useful in their professional career.

The text is comprised of six chapters. The Prologue gives a brief survey of operations research and discusses the different steps in solving an operations research problem. Chapter 0 gives a quick review of the necessary linear algebra. Chapter 1 deals with the basic necessary geometric ideas in Rn. Chapter 2 introduces linear programming with examples of the problems to be considered, and presents the simplex method as an algorithm for solving linear programming problems. Chapter 3 covers further topics in linear programming, including duality theory and sensitivity analysis. Chapter 4 presents an introduction to integer programming. Chapter 5 covers a few of the more important topics in network flows.

Students of business, engineering, computer science, and mathematics will find the book very useful.

Preface

Acknowledgments

Prologue Introduction to Operations Research

Further Readings

Chapter 0 Review of Linear Algebra (Optional)

0.1 Matrices

0.2 Gauss-Jordan Reduction

0.3 The Inverse of a Matrix

0.4 Subspaces

0.5 Linear Independence and Basis

Further Readings

Chapter 1 Geometry in Rn

1.1 Hyperplanes

1.2 Convex Sets

Further Reading

Chapter 2 Introduction to Linear Programming

2.1 The Linear Programming Problem

2.2 Matrix Notation; Geometric Solutions

2.3 The Simplex Method

2.4 Degeneracy and Cycling (Optional)

2.5 Artificial Variables

Further Readings

Chapter 3 Further Topics in Linear Programming

3.1 Duality

3.2 Computational Relations Between the Primal and Dual Problems

3.3 The Dual Simplex Method

3.4 The Revised Simplex Method

3.5 Sensitivity Analysis

3.6 Computer Aspects (Optional)

Further Readings

Chapter 4 Integer Programming

4.1 Examples

4.2 Cutting Plane Methods

4.3 Branch and Bound Methods

4.4 Computer Aspects (Optional)

Further Readings

Chapter 5 Special Types of Linear Programming Problems

5.7 The Transportation Problem

Further Readings

5.2 The Assignment Problem

Further Readings

5.3 Graphs and Networks. Basic Definitions

Further Reading

5.4 The Maximal Flow Problem

Further Readings

5.5 The Shortest Route Problem

Further Readings

5.6 The Critical Path Method

Further Readings

5.7 Computer Aspects (Optional)

Solutions to Odd-Numbered Exercises

Index