The Disjunctive-Facet Problem: Formulation and Solution Techniques

Many practical operations-research problems have the form in which the objective is to select an optimal production schedule, rental policy, distribution pattern, etc., from among a variety of alternatives, each of which has an associated set of constraints that must all be satisfied if a particular alternative is chosen. The disjunctive-facet problem provides a “direct” formulation for such problems, circumventing the need to resort to artifices involving the creation of discrete variables and supporting constraints to model these problems as mixed integer programs. We provide special cutting planes that are designed to take particular advantage of the disjunctive-facet problem structure. Thus, our results not only give a more compact representation of certain classes of discrete optimization problems, but provide more powerful methods for solving these problems as well.