• Media type: E-Book
  • Title: A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem
  • Contributor: Guan, Yongpei [Author]; Ahmed, Shabbir [Author]; Nemhauser, George L. [Author]
  • Published: Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik, 2004-02-21
  • Language: English
  • DOI: https://doi.org/10.18452/8313
  • Keywords: Stochastic Lot-Sizing ; Multi-stage Stochastic Integer Programming ; Branch and Cut ; Polyhedral Study
  • Origination:
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  • Description: 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.
  • Access State: Open Access
  • Rights information: In Copyright