On Mixing Sets Arising in Chance-Constrained Programming

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

An O(n^2) Algorithm for Lot Sizing with Inventory Bounds and Fixed Costs

Lot-sizing problems with inventory bounds and fixed charges have not received much attention in the literature, even though there are many emerging applications in which highly specialized storage is the main activity of interest. The traditional infinite capacity and variable cost assumptions on inventory that have been prevalent in the literature are inappropriate in situations … Read more

Uncapacitated Lot Sizing with Backlogging: The Convex Hull

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

Lot Sizing with Inventory Bounds and Fixed Costs: Polyhedral Study and Computation

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