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

In this paper, we study the feature-based newsvendor problem in the presence of historical demand and related demand covariates. We adopt general kernel methods to estimate the true demand distributions conditioned on the given demand features. To account for estimation errors, we propose a distributionally robust optimization (DRO) approach with the ambiguity set containing all of the distributions close to the estimated conditional demand distribution under a discrepancy measure based on the cumulative distribution function (CDF). Interestingly, we show that the DRO problem with this ambiguity set admits a closed-form solution for the newsvendor loss. This result implies that the newsvendor problem under the well-known infinity-Wasserstein ambiguity set admits a closed-form inventory level as a byproduct. In addition, we show that the solution produced by our proposed approach converges to the optimal inventory decision asymptotically at a provable convergence rate. The results of numerical experiments with synthetic and real-world data sets show that our model performs well in terms of its out-of-sample cost and computational time compared with other state-of-the-art approaches.