A Column Generation Scheme for Distributionally Robust Multi-Item Newsvendor Problems

Shanshan Wang () and Erick Delage ()
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Shanshan Wang: GERAD and Department of Decision Sciences, HEC Montréal, Montreal, Quebec H3T 2A7, Canada
Erick Delage: GERAD and Department of Decision Sciences, HEC Montréal, Montreal, Quebec H3T 2A7, Canada

INFORMS Journal on Computing, 2024, vol. 36, issue 3, 849-867

Abstract: This paper studies a distributionally robust multi-item newsvendor problem, where the demand distribution is unknown but specified with a general event-wise ambiguity set. Using the event-wise affine decision rules, we can obtain a conservative approximation formulation of the problem, which can typically be further reformulated as a linear program. In order to efficiently solve the resulting large-scale linear program, we develop a column generation-based decomposition scheme and speed up the computational efficiency by exploiting a special column selection strategy and stopping early based on a Karush-Kuhn-Tucker condition test. Focusing on the Wasserstein ambiguity set and the event-wise mean absolute deviation set, a computational study demonstrates both the computational efficiency of the proposed algorithm, which significantly outperforms a commercial solver and a Benders decomposition method, and the out-of-sample superiority of distributionally robust solutions relative to their sample average approximation counterparts.

Keywords: distributionally robust optimization; column generation; multi-item newsvendor problem; event-wise ambiguity set (search for similar items in EconPapers)
Date: 2024
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