We examine a variant of the uncapacitated lot-sizing model of Wagner-Whitin involving sales instead of fixed demands, and lower bounds on stocks. Two extended formulations are presented, as well as a dynamic programming algorithm and a complete description of the convex hull of solutions. When...

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 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 examine the single-item lot-sizing problem with Wagner-Whitin costs over an n period horizon, i.e. Pt + ht ≥ Pt+l for t = 1, ... , n - 1, where Pt, ht are the unit production and storage costs in period t respectively, so it always pays to produce as late as possible. We describe integral...

A dynamic knapsack set is a natural generalization of the 0-1 knapsack set with a continuous variable studied recently. For dynamic knapsack sets a large family of facet-defining inequalities, called dynamic knapsack inequalities, are derived by fixing variables to one and then lifting....

We consider the single item lot-sizing problem with capacities that are non-decreasing overtime. When the cost function is i) non-speculative or Wagner-Whitin (for instance, constantunit production costs and non-negative unit holding costs), and ii) the production set-upcosts are non-increasing...

We consider the single item lot-sizing problem with capacities that are non-decreasing over time. When the cost function is i) non-speculative or Wagner-Whitin (for instance, constant unit production costs and non-negative unit holding costs), and ii) the production set-up costs are...