We study the convex hull of the continuous knapsack set which consists of a single inequality constraint with n non-negative integer and m non-negative bounded continuous variables. When n = 1, this set is a slight generalization of the single arc flow set studied by Magnanti, Mirchandani, and...

A separation heuristic for mixed integer programs is presented that theoretically allows one to derive several families of "strong" valid inequalities for specific models and computationally gives results as good as or better than those obtained from several existing separation routines...

A branch-and-cut mixed integer programming system, called bc-opt, is described, incorporating most of the valid inequalities that have been used or suggested for such systems, namely lifted 0-1 knapsack inequalities, 0-1 gub knapsack and integer knapsack inequalities, flow cover and continuous...

Much progress has been made in recent years in solving certain classes of production planning problems using mixed integer programming. One of the major challenges is how to make this expertise available and easy to use to the non-specialist and to the practitioners. Here we describe a modeling...

We explore one method for finding the convex hull of certain mixed integer sets. The approach is to break up the original set into a small number of subsets, find a compact polyhedral description of the convex hull of each subset, and then take the convex hull of the union of these polyhedra....

We study a capacitated network design problem arising in the design of private line networks. Given a complete graph, a subset of its node set (the "hub" set), and point-to-point traffic demands, the objective is to install capacity on the edges (using several batch sizes and nonlinear costs),...

We study further a problem that has arisen recently in the design of telecommunications transmission networks at France Telecom. Given a set of centers in a city of conglomeration linked together on a ring architecture, given the expected demands between the centers and an essentially unlimited...

We examine the polyhedral structure of the convex hull of feasible solutions of the capacitated facility location problem. In particular we derive necessary and sufficient conditions for a family of "effective capacity" inequalities to be facet-defining, and further results on a more general...

We study the polyhedral structure of variants of the discrete lot-sizing problem viewed as special cases of convex integer programs. Our approach in studying convex integer programs is to develop results for simple mixed integer sets that can be used to model integer convex objective functions....

We study different extended formulations for the set X = {x [belong] Z exp.n | Ax = Ax exp.0} in order to tackle the feasibility problem for the set X+ = X [intersection] Z+ exp.n . Here the goal is not to find an improved polyhedral relaxation of conv(X+), but rather to reformulate in such a...