AN INTRODUCTION TO LINEAR PROGRAMMING AND MATRIX GAME THEORY

This book is designed for students with only a slight knowledge of linear mathematics and aims to give a sound understanding of the technique of linear programming and of matrix game theory.

The author first introduces the ideas involved in obtaining a solution to a linear programming problem by graphical methods. The same problem is then considered in algebraic terms. The simplex tabular form and the problems of starting a simplex tabular solution and of degeneracy are discussed. This is followed by two methods of solving the transportation problem, the “stepping-stone” method and Dantzig’s method. After introducing the terminology of matrix game theory, the text deals with graphical methods for solving 2 x N two-person zero-sum matrix games. The difficult concept of duality arises quite naturally out of the game theory section and is therefore discussed int the final chapter, where the relationships between m x n zero-sum matrix games and linear programming are considered.