A data-driven distributionally robust newsvendor model with a Wasserstein ambiguity set

Abstract

In this paper, we derive a closed-form solution and an explicit characterization of the worst-case distribution for the data-driven distributionally robust newsvendor model with an ambiguity set based on the Wasserstein distance of order p∈[1,∞). We also consider the risk-averse decision with the Conditional Value-at-Risk (CVaR) objective. For the risk-averse model, we derive a closed-form solution for the p = 1 case, and propose a tractable formulation to obtain an optimal order quantity for the p > 1 case. We conduct numerical experiments to compare out-of-sample performance and convergence results of the proposed solutions against the solutions with other distributionally robust models. We also analyze the risk-averse solutions compared to the risk-neutral solutions.