Introduction

Abstract

A disjunctive program is an optimization problem where the constraints represent logical conditions. In this monograph we are concerned with such conditions expressed as linear constraints. The methods associated with disjunctive programming are by no means novel. Some of the methods proposed over two decades ago to solve integer programming problems used cutting planes derived from logical statements implying integrality. It can be shown that these problems can be viewed as disjunctive programs and the cutting planes used in integer programming are special applications of the principal theorem in disjunctive programming. As amply demonstrated by the recent works of Balas, Glover and Jeroslow, the disjunctive programming approach has provided a powerful unifying theory of all cutting plane solution strategies. Furthermore, it has provided a completely different perspective to examine this theory and has enabled one to derive deeper insights into existing knowledge. In the exposition that follows, we will be presenting the existing and new thoughts on disjunctive programming so that a reader can readily understand the developments thus far, and appreciate the potentials for research in this area.