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.
Original language | English |
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Pages (from-to) | 691-710 |
Number of pages | 20 |
Journal | Production and Operations Management |
Volume | 22 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 May 2013 |
Externally published | Yes |
Keywords
- 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