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research article

Distributionally Robust Multi-Item Newsvendor Problems with Multimodal Demand Distributions

Hanasusanto, Grani A.
•
Kuhn, Daniel  
•
Wallace, Stein W.
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2015
Mathematical Programming

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.

  • Details
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Type
research article
DOI
10.1007/s10107-014-0776-y
Web of Science ID

WOS:000358292600001

Author(s)
Hanasusanto, Grani A.
Kuhn, Daniel  
Wallace, Stein W.
Zymler, Steve
Date Issued

2015

Publisher

Springer Verlag

Published in
Mathematical Programming
Volume

152

Issue

1-2

Start page

1

End page

32

Subjects

Distributionally robust optimization

•

Multi-item newsvendor

•

Multimodal demand distribution

Note

Available from Optimization Online

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
RAO  
Available on Infoscience
January 22, 2014
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/100101
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