Assortment Optimization under the Multinomial Logit Model with Utility-Based Rank Cutoffs

51 Pages Posted: 30 Jul 2022

See all articles by Jacob Feldman

Jacob Feldman

Washington University in St. Louis - John M. Olin Business School

Laura Wagner

University of Navarra - Management

Huseyin Topaloglu

Cornell University - School of Operations Research and Information Engineering

Yicheng Bai

Cornell University - School of Operations Research and Information Engineering

Date Written: July 19, 2022

Abstract

We study assortment optimization problems under a natural variant of the multinomial logit model where the customers are willing to focus only on a certain number of products that provide the largest utilities. In particular, each customer has a rank cutoff, characterizing the number of products that she will focus on during the course of her choice process. Given that we offer a certain assortment of products, the choice process of a customer with rank cutoff k proceeds as follows. The customer associates random utilities with all of the products as well as the no-purchase option. She ignores all alternatives whose utilities are not within the k largest utilities. Among the remaining alternatives, the customer chooses the available alternative that provides the largest utility. Under the assumption that the~utilities follow Gumbel distributions with the same scale parameter, we provide a recursion to compute the choice probabilities. Considering the assortment optimization problem to find the revenue-maximizing assortment of products to offer, we show that the problem is NP-hard and give a polynomial-time approximation scheme. Since the customers ignore the products below their rank cutoffs in our variant of the multinomial logit model, intuitively speaking, our variant captures choosier choice behavior than the standard multinomial logit model. Accordingly, we show that the revenue-maximizing assortment under our variant includes the revenue-maximizing assortment under the standard multinomial logit model, so choosier behavior leads to larger assortments offered to maximize the expected revenue. We conduct computational experiments on both synthetic and real datasets to demonstrate that incorporating rank cutoffs can yield better predictions of customer choices and yield more profitable assortment recommendations.

Keywords: customer choice, MML, PTAS

JEL Classification: C02

Suggested Citation

Feldman, Jacob and Wagner, Laura and Topaloglu, Huseyin and Bai, Yicheng, Assortment Optimization under the Multinomial Logit Model with Utility-Based Rank Cutoffs (July 19, 2022). Available at SSRN: https://ssrn.com/abstract=4167228 or http://dx.doi.org/10.2139/ssrn.4167228

Jacob Feldman (Contact Author)

Washington University in St. Louis - John M. Olin Business School ( email )

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States

Laura Wagner

University of Navarra - Management ( email )

Barcelona, 08034
Spain

Huseyin Topaloglu

Cornell University - School of Operations Research and Information Engineering ( email )

Ithaca, NY
United States

Yicheng Bai

Cornell University - School of Operations Research and Information Engineering ( email )

Ithaca, NY 14853
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
244
Abstract Views
796
Rank
255,275
PlumX Metrics