Newsvendor under Ambiguity and Misspecification

TL;DR

This paper develops a robust newsvendor model accounting for demand distribution ambiguity and misspecification, deriving a closed-form solution and establishing performance guarantees.

Contribution

It introduces a novel framework that incorporates both ambiguity and misspecification into the newsvendor problem, with explicit solutions and theoretical guarantees.

Findings

The optimal order quantity decreases with higher price or variance under misspecification aversion.

The framework extends to multiple products and various distributional measures.

Finite-sample guarantees justify the importance of accounting for misspecification in practice.

Abstract

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 and misspecification under which such characteristics might be misspecified. 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. 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 Scarf model under only ambiguity aversion. We establish the finite-sample performance guarantee, which consists of two parts: in-sample optimal value and out-of-sample effect of misspecification that 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. 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 necessity of incorporating misspecification aversion in a non-stationary environment, which is also well demonstrated in our experiments with real-world data.