Newsvendor Under Ambiguity and Misspecification

Problem definition: We consider a newsvendor problem with unknown demand distribution, where we distinguish ambiguity under which the newsvendor does not differentiate demand distributions of common characteristics (e.g., mean and variance) and misspecification under which such characteristics might be misspecified (because of, e.g., estimation error and/or distribution shift). Methodology/results: The newsvendor hedges against ambiguity and misspecification by maximizing the worst-case expected profit regularized by a distribution’s distance to an ambiguity set of distributions with some specified characteristics. Focusing on the popular mean-variance ambiguity set and optimal-transport cost for the misspecification, we show that the decision criterion of misspecification aversion possesses insightful interpretations as distributional transforms. We derive the closed-form optimal order quantity that generalizes the solution of the seminal Scarf model under only ambiguity aversion. We establish finite-sample performance guarantees that consist of two parts: an in-sample optimal value and an out-of-sample effect of misspecification, which can be further decoupled into estimation error and distribution shift. We also extend the framework to multiple products, distributional characteristics specified via optimal transport, and misspecification measured by total variation distance and derive analytical optimal solutions. Managerial implications: The closed-form solution highlights the impact of misspecification aversion; the optimal order quantity under misspecification aversion can decrease as the price or variance increases, reversing the monotonicity of that under only ambiguity aversion. Hence, ambiguity and misspecification, as different layers of distributional uncertainty, can result in distinct operational consequences. The finite-sample performance guarantee theoretically justifies the need to incorporate misspecification aversion in a nonstationary environment, as demonstrated in our experiments with real-world data.

Funding: Z. Chen is supported in part by the National Natural Science Foundation of China [72422002, 72394395], the Hong Kong Research Grants Council General Research Fund [CUHK-11502422], and the Asian Institute of Supply Chains and Logistics. Ruodu Wang is supported by the Natural Sciences and Engineering Research Council of Canada [CRC-2022-00141, RGPIN-2024-03728]. S. Wang is supported by the National Natural Science Foundation of China [Grants 72471224, 72171221, 71922020, and 71988101], the Fundamental Research Funds for the Central Universities [Grant UCAS-E2ET0808X2], a grant from the MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation at UCAS, and the MOE Social Sciences Innovative Group on Complex Systems Modeling in Economic Management in the Era of Digital Intelligence, University of Chinese Academy of Sciences [E5820801].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2025.0197.