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Yongpei Guan1 Shabbir Ahmed1

Summary: Yongpei Guan1
Shabbir Ahmed1
George L. Nemhauser1
Andrew J. Miller2
A Branch-and-Cut Algorithm for the Stochastic
Uncapacitated Lot-Sizing Problem
December 12, 2004
Abstract. 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 Multi-stage Stochastic Integer Programming Polyhe-
dral Study Branch-and-Cut
1. Introduction
The deterministic uncapacitated lot-sizing problem is to determine a minimum
cost production and inventory holding schedule for a product so as to satisfy its


Source: Ahmed, Shabbir - School of Industrial and Systems Engineering, Georgia Institute of Technology


Collections: Engineering