Regret in the Newsvendor Model with Demand and Yield Randomness

Abstract

We study the fundamental stochastic newsvendor model that considers both demand and yield randomness. It is usually difficult in practice to describe precisely the joint demand and yield distribution, although partial statistical information and empirical data about this ambiguous distribution are often accessible. We combat the issue of distributional ambiguity by taking a data-driven distributionally robust optimization approach to hedge against all distributions that are sufficiently close to a uniform and discrete distribution of empirical data, where closeness is measured by the type-infinity Wasserstein distance. We adopt the minimax regret decision criterion to assess the optimal order quantity that minimizes the worst-case regret. Several properties about the minimax regret model, including optimality condition, regret bound, and the worst-case distribution, are presented. The optimal order quantity can be determined via an efficient golden section search. We extend the analysis to the Hurwicz criterion model, which generalizes the popular albeit pessimistic maximin model (maximizing the worst-case expected profit) and its (less noticeable) more optimistic counterpart—the maximax model (maximizing the best-case expected profit). Finally, we present numerical comparisons of our data-driven minimax regret model with data-driven models based on the Hurwicz criterion and with a minimax regret model based on partial statistical information on moments.