Two-stage newsvendor network problem: A data-driven distributionally robust optimization approach

We consider a multilocation newsvendor network in which historical data are the only available information about the joint demand distribution. To determine optimal inventory levels, we develop a novel data-driven two-stage distributionally robust optimization model that does not assume the demand support is known. Instead, we infer the support from historical data using two prediction algorithms, which yield quantile-based and Mahalanobis-distance-based support estimates and therefore either ignore or capture cross-location demand dependence. Our objective is to minimize worst-case expected cost over an ambiguity set constructed from these support estimates, consisting of all probability distributions within a prescribed type- ∞ Wasserstein ( W ∞ ) distance of the empirical distribution. To approximate the second-stage recourse decisions, we employ a multiple-linear-decision-rule approximation that is provably asymptotically optimal. This leads to tractable linear programming and second-order cone programming reformulations for the quantile-based and Mahalanobis-distance-based formulations, respectively. We also establish support-aware finite-sample guarantees for the proposed framework. Numerical results show that quantile-based support estimation is more effective at maintaining reliable service levels, whereas Mahalanobis-distance-based support estimation yields larger cost reductions, particularly under correlated demand.