Distributionally robust multi-item newsvendor problems with multimodal demand distributions

Hanasusanto, Grani A. and Kuhn, Daniel and Wallace, Stein W. and Zymler, Steve (2015) Distributionally robust multi-item newsvendor problems with multimodal demand distributions. Mathematical Programming, 152 (1-2). pp. 1-32. ISSN 0025-5610

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Abstract

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.

Item Type:
Journal Article
Journal or Publication Title:
Mathematical Programming
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
138917
Deposited By:
Deposited On:
13 Nov 2019 09:55
Refereed?:
Yes
Published?:
Published
Last Modified:
27 Mar 2020 04:27