Dynamic Assortment Planning Without Utility Parameter Estimation

40 Pages Posted: 8 Mar 2018

See all articles by Xi Chen

Xi Chen

New York University (NYU) - Leonard N. Stern School of Business

Yining Wang

Carnegie Mellon University - School of Computer Science

Yuan Zhou

University of Illinois at Urbana-Champaign

Date Written: March 2, 2018

Abstract

We study a family of stylized dynamic assortment planning problems, where for each arriving customer, the seller offers an assortment of substitutable products and customer makes the purchase among offered products according to a discrete choice model. This paper considers two popular choice models --- the multinominal logit model (MNL) and nested logit model. Since all the utility parameters of customers are unknown, the seller needs to simultaneously learn customers' choice behavior and make dynamic decisions on assortments based on the current knowledge. The goal of the seller is to maximize the expected revenue, or equivalently, to minimize the worst-case expected regret. Although dynamic assortment planning problem has received an increasing attention in revenue management, most existing policies require the estimation of mean utility for each product and the final regret usually involves the number of products N. However, when the number of products N is large as compared to the horizon length T, the accurate estimation of mean utilities is extremely difficult. To deal with the large N case that is natural in many online applications, we propose new policies which completely avoid estimating the utility parameter for each product; and thus our regret is independent of N. In particular, for MNL model, we develop a dynamic trisection search algorithm that achieves the optimal regret (up to a log-factor). For nested logit model, we propose a lower and upper confidence bound algorithm with an aggregated estimation. There are two major advantages of the proposed policies. First, the regret of all our policies has no dependence on N. Second, our policies are almost assumption free: there is no assumption on mean utility nor any "separability'' condition on the expected revenues for different assortments. We also provide numerical results to demonstrate the empirical performance of the proposed methods.

Keywords: dynamic assortment optimization, regret analysis, lower and upper confidence bounds, nested logit models

Suggested Citation

Chen, Xi and Wang, Yining and Zhou, Yuan, Dynamic Assortment Planning Without Utility Parameter Estimation (March 2, 2018). Available at SSRN: https://ssrn.com/abstract=3133401 or http://dx.doi.org/10.2139/ssrn.3133401

Xi Chen (Contact Author)

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

Yining Wang

Carnegie Mellon University - School of Computer Science ( email )

5000 Forbes Avenue
Pittsburgh, PA 15213
United States

Yuan Zhou

University of Illinois at Urbana-Champaign ( email )

Transportation Building
University of Illinois at Urbana-Champaign
Urbana, IL 61801
United States

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