A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem

This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical ( , S) inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend the ( , S) inequalities to a general class of valid inequalities, called the (Q, SQ) inequalities, and we establish necessary and sufficient conditions which guarantee that the (Q, SQ) inequalities are facet-defining. A separation heuristic for (Q, SQ) inequalities is developed and incorporated into a branch and cut algorithm. A computational study verifies the usefulness of the (Q, SQ) inequalities as cuts. Key words. Stochastic Lot-Sizing

• Type: Journal
• Year: 2006
• Where: MP
• Authors: Yongpei Guan, Shabbir Ahmed, George L. Nemhauser, Andrew J. Miller
• Keywords: Inequalities, MP 2006, Multi-stage Stochastic Integer, Stochastic Integer Programming