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SPEPS Preprint

Author(s): Yongpei Guan, Georgia Institute of Technology
Shabbir Ahmed, Georgia Institute of Technology
George L. Nemhauser, Georgia Institute of Technology
Title: A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem
Date of Acceptance: 21.02.2004
Submission Date: 22.01.2004
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint: pdf (urn:nbn:de:kobv:11-10059453)
Keywords (eng): Stochastic Lot-Sizing, Multi-stage Stochastic Integer Programming, Polyhedral Study, Branch and Cut
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Abstract (eng):
This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical $(\mathcal{l}, S)$ inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend the $(\mathcal{l}, S)$ inequalities to a general class of valid inequalities, called the $(Q, S_Q)$ inequalities, and we establish necessary and sufficient conditions which guarantee that the $(Q, S_Q)$ inequalities are facet-defining. A separation heuristic for $(Q, S_Q )$ inequalities is developed and incorporated into a branch and cut algorithm. A computational study verifies the usefulness of the $(Q, S_Q)$ inequalities as cuts.
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