A branch-and-cut method for dynamic decision making under joint chance constraints

Minjiao Zhang, Simge Küçükyavuz, Saumya Goel

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

In this paper, we consider a finite-horizon stochastic mixed-integer program involving dynamic decisions under a constraint on the overall performance or reliability of the system. We formulate this problem as a multistage (dynamic) chance-constrained program, whose deterministic equivalent is a large-scale mixed-integer program. We study the structure of the formulation and develop a branch-and-cut method for its solution. We illustrate the efficacy of the proposed model and method on a dynamic inventory control problem with stochastic demand in which a specific service level must be met over the entire planning horizon. We compare our dynamic model with a static chance-constrained model, a dynamic risk-averse optimization model, a robust optimization model, and a pseudo-dynamic approach and show that significant cost savings can be achieved at high service levels using our model.

Original languageEnglish (US)
Pages (from-to)1317-1333
Number of pages17
JournalManagement Science
Volume60
Issue number5
DOIs
StatePublished - May 2014

Keywords

  • Branch-and-cut
  • Chance constraints
  • Multistage
  • Probabilistic lot sizing
  • Service levels History

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research

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