Characterization and Formulation of Disjunctions and their Relaxations

A. R. VECCHIETTI; S. LEE; I. E. GROSSMANN

Santa Fe

Congreso; ENPROMER 2001; 2001

The formulation of discrete decisions in mathematical programs is not an easy task. The modeler has several alternatives using mathematical inequalities involving binary/integer variables: Big-M, Beaumont surrogates or the convex hull. The decisions about which representation is more  appropriate is not always clear to the modeler. In this paper we analyze the use of disjunction for modeling discrete decision. Then, we present the disjunction properties. We compare the possible relaxation of a disjunctive set: convex hull, Big-M or Beaumont surrogate. We provide some general guidelines and a preprocessing algorithm to help and clarify, which could be the best relaxation for a discrete decision and therefore the best possible formulation.