Newsvendor problem with discrete demand and constrained first moment under ambiguity

We study a single period newsvendor problem under ambiguity in the presence of a discrete random demand. Ambiguity is introduced in the model by $\epsilon$-contaminating the newsvendor’s prior probability measure with respect to two suitable classes of probability measures, assuring that the lower expected demand and the upper expected demand are both equal to the prior expected demand. Assuming that the newsvendor has a pessimistic attitude towards ambiguity, we characterize the order quantity that either maximizes the lower expected profit or minimizes the upper expected loss. Since the two contamination classes are cores of two distinct belief functions, we show that the maximin and minimax problems translate in the maximization and minimization of two distinct Choquet integrals.