A polyhedral study of the static probabilistic lot-sizing problem

Xiao Liu, Simge Kucukyavuz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities subsume existing inequalities for this problem, and they are facet-defining under certain conditions. In addition, we show that they give the convex hull description of a related stochastic lot-sizing problem. We propose a new formulation that exploits the simple recourse structure, which significantly reduces the number of variables and constraints of the deterministic equivalent program. This reformulation can be applied to general chance-constrained programs with simple recourse. The computational results show that the proposed inequalities and the new formulation are effective for the static probabilistic lot-sizing problems.

Original languageEnglish (US)
Pages (from-to)233-254
Number of pages22
JournalAnnals of Operations Research
Volume261
Issue number1-2
DOIs
StatePublished - Feb 2018

Keywords

  • Branch and cut
  • Chance constraints
  • Facets
  • Lot sizing
  • Simple recourse reformulation
  • Valid inequalities

ASJC Scopus subject areas

  • Decision Sciences(all)
  • Management Science and Operations Research

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