Finite Disjunctive Programming Characterizations for General Mixed-Integer Linear Programs

Authors:
Binyuan Chen;Simge Küçükyavuz;Suvrajeet Sen
Affiliations:
Department of Systems and Industrial Engineering, University of Arizona, Tucson, Arizona 85721;Department of Integrated Systems Engineering, The Ohio State University, Columbus, Ohio 43210;Department of Integrated Systems Engineering, The Ohio State University, Columbus, Ohio 43210
Venue:
Operations Research
Year:
2011

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Abstract

In this paper, we give a finite disjunctive programming procedure to obtain the convex hull of general mixed-integer linear programs (MILP) with bounded integer variables. We propose a finitely convergent convex hull tree algorithm that constructs a linear program that has the same optimal solution as the associated MILP. In addition, we combine the standard notion of sequential cutting planes with ideas underlying the convex hull tree algorithm to help guide the choice of disjunctions to use within a cutting plane method. This algorithm, which we refer to as the cutting plane tree algorithm, is shown to converge to an integral optimal solution in finitely many iterations. Finally, we illustrate the proposed algorithm on three well-known examples in the literature that require an infinite number of elementary or split disjunctions in a rudimentary cutting plane algorithm.