Robust Stochastic Lot-Sizing by Means of Histograms
Name
Simchi-Levi_Robust stochastic.pdf
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1.39 MB
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Adobe PDF
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Author(s)
Klabjan, Diego
Simchi-Levi, David
Song, Miao
Date Issued
February 2013
Journal
Production and Operations Management
Publisher
Wiley Blackwell
Citation
Klabjan, Diego, David Simchi-Levi, and Miao Song. “Robust Stochastic Lot-Sizing by Means of Histograms.” Production and Operations Management (2013).
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1111/j.1937-5956.2012.01420.x
