Data-Driven Feature-Based Newsvendor: A Distributionally Robust Approach

Abstract

In this paper, we study the feature-based newsvendor problem in the context of available historical demand observations and related demand covariates. The demand distribution conditioned on these features is based on general kernel estimation methods that can incorporate machine learning algorithms, such as the random forest. To account for estimation errors, we propose a distributionally robust optimization (DRO) approach that contains all distributions close to the estimated conditional demand distribution under a discrepancy measure based on the cumulative distribution functions. Interestingly, we show that the DRO problem with such an ambiguity set admits a closed-form solution for the newsvendor loss. In addition, we show that the optimal solution produced by this approach converges to the optimal inventory decision asymptotically and provides a finite-sample performance guarantee. The results of numerical experiments with synthetic and real-world data sets show that compared with other approaches, our model performs well in terms of the out-of-sample cost and computational time.