Journal
OPERATIONS RESEARCH
Volume 69, Issue 4, Pages 1077-1099Publisher
INFORMS
DOI: 10.1287/opre.2020.2091
Keywords
distributional robustness; newsvendor model; moment constraints; heavy-tailed distributions
Funding
- Learning from Common Connections in Social Networks [Ministry of Education Academic Research Fund Tier 2 grant] [MOE2017-T2-2-161]
- Design of the Last Mile Transportation System: What Does the Customer Really Want [SUTD-MIT International Design Center] [IDG2170]
- On the Interplay of Choice, Robustness and Optimization in Transportation [Ministry of Education Academic Research Fund Tier 2] [T2MOE1706]
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The study shows that for the distributionally robust newsvendor problem, the order quantity selection is optimal for heavy-tailed distributions as observed in Scarf's work, and remains valid even under information on the first and αth moments within the confidence set.
Since the seminal work of Scarf (A min-max solution of an inventory problem) in 1958 on the newsvendor problem with ambiguity in the demand distribution, there has been a growing interest in the study of the distributionally robust newsvendor problem. The model is criticized at times for being conservative because the worst-case distribution is discrete with a few support points. However, it is the order quantity prescribed by the model that is of practical relevance. Interestingly, the order quantity from Scarf's model is optimal for a heavy-tailed distribution. In this paper, we generalize this observation by showing a heavy-tail optimality property of the distributionally robust order quantity for an ambiguity set where information on the first and the ath moment is known, for any real alpha > 1. We show that the optimal order quantity for the distributionally robust newsvendor is also optimal for a regularly varying distribution with parameter alpha. In the high service level regime, when the original demand distribution is given by an exponential or a lognormal distribution and contaminated with a regularly varying distribution, the distributionally robust order quantity is shown to outperform the optimal order quantity of the original distribution, even with a small amount of contamination.
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