Distributionally robust multi-item newsvendor problems with multimodal demand distributions

We present a risk-averse multi-dimensional newsvendor model for a class of products whose demands are strongly correlated and subject to fashion trends that are not fully understood at the time when orders are placed. The demand distribution is known to be multimodal in the sense that there are spat...

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Bibliographic Details
Published inMathematical programming Vol. 152; no. 1-2; pp. 1 - 32
Main Authors Hanasusanto, Grani A., Kuhn, Daniel, Wallace, Stein W., Zymler, Steve
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2015
Springer Nature B.V
Subjects
Ambiguity
Approximation
Asymmetry
Business cycles
Calculus of Variations and Optimal Control; Optimization
Clusters
Combinatorics
Costs
Demand
Fashion models
Full Length Paper
Inventory
Market entry
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Opportunity costs
Optimization
Order quantity
Production planning
Risk aversion
Studies
Texts
Theoretical
Trends
90C22
90C15
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Summary:We present a risk-averse multi-dimensional newsvendor model for a class of products whose demands are strongly correlated and subject to fashion trends that are not fully understood at the time when orders are placed. The demand distribution is known to be multimodal in the sense that there are spatially separated clusters of probability mass but otherwise lacks a complete description. We assume that the newsvendor hedges against distributional ambiguity by minimizing the worst-case risk of the order portfolio over all distributions that are compatible with the given modality information. We demonstrate that the resulting distributionally robust optimization problem is NP -hard but admits an efficient numerical solution in quadratic decision rules. This approximation is conservative and computationally tractable. Moreover, it achieves a high level of accuracy in numerical tests. We further demonstrate that disregarding ambiguity or multimodality can lead to unstable solutions that perform poorly in stress test experiments.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-014-0776-y