Mathematical Programming

, Volume 152, Issue 1–2, pp 1–32 | Cite as

Distributionally robust multi-item newsvendor problems with multimodal demand distributions

  • Grani A. HanasusantoEmail author
  • Daniel Kuhn
  • Stein W. Wallace
  • Steve Zymler
Full Length Paper Series A


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 \(\mathrm{NP}\)-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.

Mathematics Subject Classification

90C15 90C22 



We are indebted to Karthik Natarajan for valuable discussions on the topic of this paper. We also thank two anonymous reviewers whose comments led to substantial improvements of this paper. This research was supported by EPSRC under Grant EP/I014640/1.


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2014

Authors and Affiliations

  • Grani A. Hanasusanto
    • 1
    Email author
  • Daniel Kuhn
    • 2
  • Stein W. Wallace
    • 3
  • Steve Zymler
    • 1
  1. 1.Department of ComputingImperial College LondonLondonUK
  2. 2.Management of Technology and Entrepreneurship InstituteÉcole Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland
  3. 3.Department of Business and Management ScienceNorwegian School of EconomicsBergenNorway

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