Alper Atamturk We describe a two-stage robust optimization approach for solving network flow and design problems with demand uncertainty. We give an explicit characterization of the first-stage decisions and prove that the corresponding separation problem is NP-hard even for a network flow problem on a bipartite graph. We show, however, that if the second-stage network topology is … Read more
We describe strong mixed-integer programming formulations for robust mixed 0-1 programming with uncertainty in the objective coefficients. In particular, we focus on an objective uncertainty set described as a polytope with a budget constraint. We show that for a robust 0-1 problem, there is a tight linear programming formulation with size polynomial in the size … Read more
We investigate the polyhedral structure of the lot-sizing problem with inventory bounds. We consider two models, one with linear costs on inventory, the other with linear and fixed costs on inventory. For both models, we identify facet-defining inequalities that make use of the inventory capacities explicitly and give exact separation algorithms. We also give a … Read more
We review strong inequalities for fundamental knapsack relaxations of (mixed) integer programs. These relaxations are the 0-1 knapsack set, the mixed 0-1 knapsack set, the integer knapsack set, and the mixed integer knapsack set. Our aim is to give a unified presentation of the inequalities based on covers and packs and highlight the connections among … Read more
We study the mixed-integer knapsack polyhedron, that is, the convex hull of the mixed-integer set defined by an arbitrary linear inequality and the bounds on the variables. We describe facet-defining inequalities of this polyhedron that can be obtained through sequential lifting of inequalities containing a single integer variable. These inequalities strengthen and/or generalize known inequalities … Read more
The lot-sizing polytope is a fundamental structure contained in many practical production planning problems. Here we study this polytope and identify facet-defining inequalities that cut off all fractional extreme points of its linear programming relaxation, as well as liftings from those facets. We give a polynomial-time combinatorial separation algorithm for the inequalities when capacities are … Read more
We show that superadditive lifting functions lead to sequence independent lifting of inequalities for general mixed-integer programming. Citation Operations Research 52, 487-490, 2004