Inequalities from Group Relaxations

Abstract

This article provides a review of the group‐theoretic approach to the generation of cutting planes in mixed integer programming. After motivating the notion of corner relaxation graphically, we give a definition of master group problems. We then present a hierarchy of valid inequalities for master group problems that can be used as cutting planes for mixed integer programs. We describe next various procedures that can be used to obtain the “strongest” valid inequalities for master group problems. We conclude by commenting on the computational possibilities of group‐theoretic cuts in mixed integer programming.