Robust optimization for selective newsvendor problem with uncertain demand

In this paper, we consider the selective newsvendor problem (SNVP), where the decision maker selects the optimal set of markets to serve and the optimal order quantity to procure. We consider the case of a single product SNVP with uncertain demand data of unknown probability distributions for some of the potential markets. We present robust models for the SNVP. The demand uncertainty is characterized by an uncertainty set. We study SNVP with uncertain demand that has box, ellipsoidal, polyhedral uncertainty set or combinations of these uncertainty sets. The robust counterpart models are obtained and efficient solution algorithms are proposed. Computational experiments, discussion of results, and useful insights are provided.