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# SPEPS Preprint

 Author(s): Yongpei Guan, Georgia Institute of TechnologyShabbir Ahmed, Georgia Institute of TechnologyGeorge 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 Metadata export: To export the complete metadata set as Endote or Bibtex format please click to the appropriate link. Endnote   Bibtex print on demand: If you click on this icon you can order a print copy of this publication.

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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