The mixing set with a knapsack constraint arises in deterministic equivalent of probabilistic programming problems with finite discrete distributions. We first consider the case that the probabilistic program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit inequalities for this … Read more
This paper deals with the ring star problem that consists in designing a ring that pass through a central depot, and then assigning each non visited customer to a node of the ring. The objective is to minimize the total routing and assignment costs. A new chain based formulation is proposed. Valid inequalities are proposed … Read more
An explicit description of the convex hull of solutions to the uncapacitated lot-sizing problem with backlogging, in its natural space of production, setup, inventory and backlogging variables, has been an open question for many years. In this paper, we identify facet-defining inequalities that subsume all previously known valid inequalities for this problem. We show that … Read more
We consider two (0,1)-linear programming formulations of the graph (vertex-)coloring problem, in which variables are associated to stable sets of the input graph. The first one is a set covering formulation, where the set of vertices has to be covered by a minimum number of stable sets. The second is a set packing formulation, in … Read more
We present a scheme for generating new valid inequalities for mixed integer programs by taking pair-wise combinations of existing valid inequalities. Our scheme is related to mixed integer rounding and mixing. The scheme is in general sequence-dependent and therefore leads to an exponential number of inequalities. For some important cases, we identify combination sequences that … 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