A Principled Approach to Mixed Integer/Linear Problem Formulation

Abstract

We view mixed integer/linear problem formulation as a process of identifying disjunctive and knapsack constraints in a problem and converting them to mixed integer form. We show through a series of examples that following this process can yield mixed integer models that automatically incorporate some of the modeling devices that have been discovered over the years for making the formulation tighter. In one case it substantially improves on the generally accepted model. We provide a theoretical basis for the process by generalizing Jeroslow’s mixed integer representability theorem.