FINITE DISJUNCTIVE PROGRAMMING CHARACTERIZATIONS FOR GENERAL MIXED-INTEGER LINEAR PROGRAMS BINYUAN CHEN, S ˙ IMGE K ¨ UC ¸ ¨ UKYAVUZ, SUVRAJEET SEN 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 which 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. Key words: Mixed-integer programming, disjunctive programming, convex hull, finite convergence. 1. Introduction Mixed-integer linear programming (MILP) has come a long way. Advanced software (e.g. XPRESS, CPLEX etc.) are routinely solving MILP problems with thousands of variables with very reasonable computational demands. The area is now growing towards mixed-integer nonlinear programming, as well as stochastic MILP. In both cases, impres- sive computational results have been reported by Bonami et al. (2008) and Yuan and Sen (2009), respectively. One of the more important lessons learned from MILP and related literature is that valid inequalities are indispensable in robust MILP software. Thus, it is common for Date : March 7, 2010. Binyuan Chen: Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85720, USA. bychen@email.arizona.edu. Supported, in part, by Air Force Office of Scientific Research (AFOSR) Grant F49620-03-1-0377 Simge K¨ u¸ c¨ ukyavuz: Department of Integrated Systems Engineering, Ohio State University, Columbus, OH 43210, USA. kucukyavuz.2@osu.edu. Supported, in part, by NSF-CMMI Grant 0917952. Suvrajeet Sen: (corresponding author) Department of Integrated Systems Engineering, Ohio State Uni- versity, Columbus, OH 43210, USA. sen.22@osu.edu. Supported, in part, by AFOSR Grants: FA9950- 08-1-0154 and FA9550-08-1-0117. 1