Finite Disjunctive Programming Characterizations for General Mixed-Integer Linear Programs

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.