Modeling of discrete/continuous optimization problems: Characterization and formulation of disjunctions and their relaxations

Abstract

This paper addresses the relaxations in alternative models for disjunctions, big-M and convex hull model, in order to develop guidelines and insights when formulating Mixed-Integer Non-Linear Programming (MINLP), Generalized Disjunctive Programming (GDP), or hybrid models. Characterization and properties are presented for various types of disjunctions. An interesting result is presented for improper disjunctions where results in the continuous space differ from the ones in the mixed-integer space. A cutting plane method is also proposed that avoids the explicit generation of equations and variables of the convex hull. Several examples are presented throughout the paper, as well as a small process synthesis problem, which is solved with the proposed cutting plane method.