Linear Programming

This text is based on a course of about 16 hours lectures to students of mathematics, statistics, and/or operational research. It is intended to introduce readers to the very wide range of applicability of linear programming, covering problems of manage- ment, administration, transportation and a number of other uses which are mentioned in their context. The emphasis is on numerical algorithms, which are illustrated by examples of such modest size that the solutions can be obtained using pen and paper. It is clear that these methods, if applied to larger problems, can also be carried out on automatic (electronic) computers. Commercially available computer packages are, in fact, mainly based on algorithms explained in this book. The author is convinced that the user of these algorithms ought to be knowledgeable about the underlying theory. Therefore this volume is not merely addressed to the practitioner, but also to the mathematician who is interested in relatively new developments in algebraic theory and in some combinatorial theory as well. The chapters on duality, and on flow in networks, are particularly directed towards this aim and they contain theorems which might not be directly relevant to methods of computation. The application of the concept of duality to the theory of games is of historical interest. It is hoped that the figures, which illustrate the results, will be found illuminating by readers with active geometrical imagination.