Abstract
Distributionally robust optimization is increasingly becoming a popular methodology to deal with uncertainty in optimization problems. Although the methodology optimizes for the worst-case distribution, a better understanding of the prescriptions from the models important from a practical perspective. In the paper “On the heavy-tail behavior of the distributionally robust newsvendor,” B. Das, A. Dhara, and K. Natarajan provide a novel analysis for the problem in the newsvendor setting with moment information. They show that the distributionally robust newsvendor by planning for the worst possible demand distribution with moment information will remains optimal if the true demand distribution is heavy-tailed. The prescribed optimal solution has a heavy-tail optimality’ property for free. Since the seminal work of Scarf (A min-max solution of an inventory problem) in 1958 on the newsvendor problem with ambiguity in the demand distribution, there has been a growing interest in the study of the distributionally robust newsvendor problem. The model is criticized at times for being conservative because the worst-case distribution is discrete with a few support points. However, it is the order quantity prescribed by the model that is of practical relevance. Interestingly, the order quantity from Scarf’s model is optimal for a heavy-tailed distribution. In this paper, we generalize this observation by showing a heavy-tail optimality property of the distributionally robust order quantity for an ambiguity set where information on the first and the αth moment is known, for any real α > 1. We show that the optimal order quantity for the distributionally robust newsvendor is also optimal for a regularly varying distribution with parameter α. In the high service level regime, when the original demand distribution is given by an exponential or a lognormal distribution and contaminated with a regularly varying distribution, the distributionally robust order quantity is shown to outperform the optimal order quantity of the original distribution, even with a small amount of contamination.