Abstract
Problem definition: In this paper, we study the newsvendor problem under some distributional ambiguity sets and explore their relations. Additionally, we explore the benefits of implementing this robust solution in the feature-based newsvendor problem. Methodology and results: We propose a new type of discrepancy-based ambiguity set, the JW ambiguity set, and analyze it within the framework of first-order stochastic dominance. We show that the distributionally robust optimization (DRO) problem with this ambiguity set admits a closed-form solution for the newsvendor loss. This result also implies that the newsvendor problem under the well-known infinity-Wasserstein ambiguity set and Lévy ball ambiguity set admit closed-form inventory levels as a by-product. In the application of feature-based newsvendor, we adopt general kernel methods to estimate the conditional demand distribution and apply our proposed DRO solutions to account for the estimation error. Managerial implications: The closed-form solutions enable an efficient computation of optimal inventory levels. In addition, we explore the property of optimal robust inventory levels with respect to the nonrobust version via concepts of perceived critical ratio and mean repulsion. The results of numerical experiments and the case study indicate that the proposed model outperforms other state-of-the-art approaches, particularly in environments where demand is influenced by covariates and difficult to estimate. Funding: X. Li is supported by the Singapore Ministry of Education [Tier 1 Grant 23-0619-P0001, 24-0500-A0001] and National Natural Science Foundation of China [Grant 72331004]. L. Zhang is partially supported by the National Natural Science Foundation of China [Grants 72171156 and 72231002] and the Hong Kong Research Grants Council [Grant 16212419]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0159 .
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