On the Heavy-Tail Behavior of the Distributionally Robust Newsvendor

Karthink Natarajan
Singapore University of Technology and Design

Friday, Oct 18, 2019
3:15 - 4:15 PM
Location: Spilker 143



Abstract:

Since the seminal work of Scarf (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 overly conservative since the worst-case distribution is discrete with a few support points. However, it is the order quantity prescribed from the model that is of practical relevance. A simple calculation shows that the optimal order quantity in Scarf's model with known first and second moment is also optimal for a censored student-t distribution with parameter 2. In this paper, we generalize this "heavy-tail optimality" property of the distributionally robust newsvendor to an ambiguity set where information on the first and the αth moment is known, for any real number α> 1. We show that the optimal order quantity for the distributionally robust newsvendor problem is also optimal for a regularly varying distribution with roughly a power law tail with tail index α.

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