On the Heavy-Tail Behavior of the Distributionally Robust Newsvendor

31 Pages Posted: 20 Jun 2018

See all articles by Bikramjit Das

Bikramjit Das

Singapore University of Technology and Design (SUTD)

Anulekha Dhara

University of Michigan at Ann Arbor

Karthik Natarajan

Singapore University of Technology and Design (SUTD)

Date Written: June 15, 2018

Abstract

Since the seminal work of Scarf (1958) [A min-max solution of an inventory problem, Studies in the Mathematical Theory of Inventory and Production, pages 201-209] 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 optimal order quantity is computed by accounting for the worst possible distribution from a set of demand distributions that is characterized by partial information, such as moments. 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 from the model that is typically of practical relevance. A simple observation shows that the optimal order quantity in Scarf’s model with known first and second moment is also optimal for a heavy-tailed censored student-t distribution with degrees of freedom 2. In this paper, we generalize this “heavy- tail optimality” property of the distributionally robust newsvendor to a more general ambiguity set where information on the first and the nth moment is known, for any real number n > 1. We provide a characterization of the optimal order quantity under this ambiguity set by showing that for high critical ratios, the order quantity is optimal for a regularly varying distribution with an approximate power law tail with tail index n. We illustrate the applicability of the model by calibrating the ambiguity set from data and comparing the performance of the order quantities computed via various methods in a dataset.

Suggested Citation

Das, Bikramjit and Dhara, Anulekha and Natarajan, Karthik, On the Heavy-Tail Behavior of the Distributionally Robust Newsvendor (June 15, 2018). Available at SSRN: https://ssrn.com/abstract=3197291 or http://dx.doi.org/10.2139/ssrn.3197291

Bikramjit Das (Contact Author)

Singapore University of Technology and Design (SUTD) ( email )

20 Dover Drive
Singapore, 138682
Singapore

Anulekha Dhara

University of Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

Karthik Natarajan

Singapore University of Technology and Design (SUTD) ( email )

20 Dover Drive
Singapore, 138682
Singapore

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
62
Abstract Views
586
Rank
632,837
PlumX Metrics