Robust stochastic lot-sizing by means of histograms

Diego Klabjan, David Simchi-Levi, Miao Song

Research output: Journal article publicationJournal articleAcademic researchpeer-review

64 Citations (Scopus)


Traditional approaches in inventory control first estimate the demand distribution among a predefined family of distributions based on data fitting of historical demand observations, and then optimize the inventory control using the estimated distributions. These approaches often lead to fragile solutions whenever the preselected family of distributions was inadequate. In this article, we propose a minimax robust model that integrates data fitting and inventory optimization for the single-item multi-period periodic review stochastic lot-sizing problem. In contrast with the standard assumption of given distributions, we assume that histograms are part of the input. The robust model generalizes the Bayesian model, and it can be interpreted as minimizing history-dependent risk measures. We prove that the optimal inventory control policies of the robust model share the same structure as the traditional stochastic dynamic programming counterpart. In particular, we analyze the robust model based on the chi-square goodness-of-fit test. If demand samples are obtained from a known distribution, the robust model converges to the stochastic model with true distribution under generous conditions. Its effectiveness is also validated by numerical experiments.
Original languageEnglish
Pages (from-to)691-710
Number of pages20
JournalProduction and Operations Management
Issue number3
Publication statusPublished - 1 May 2013
Externally publishedYes


  • dynamic programming
  • optimal policy
  • robust optimization
  • stochastic inventory control

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering
  • Management Science and Operations Research
  • Management of Technology and Innovation


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