Assortment Optimization Under the Multi-Purchase Multinomial Logit Choice Model

• Activity Number: 43 - Advances in Modeling Consumer Choice Behavior
• Type: Invited
• Date/Time: Sunday, August 7, 2022 : 4:00 PM to 5:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Jacob Feldman* and Danny Segev and Huseyin Topaloglu and Yicheng Bai and Laura Wagner
• Companies: Washington University and Tel-Aviv University and Cornell University and Cornell University and Catolica-Lisbon School of Business and Economics
• Keywords: customer choice models; multinomial logit; multi-purchase; assortment optimization; algorithms

Abstract

In this paper, we introduce the Multi-Purchase Multinomial Logit choice model, which extends the random utility maximization framework of the classical Multinomial Logit model to a multiple-purchase setting. We first provide a recursive procedure to compute the choice probabilities in this model, which in turn provides a framework to study its resulting assortment problem, where the goal is to select a subset of products to make available for purchase so as to maximize expected revenue. Our main algorithmic results consist of two distinct polynomial time approximations schemes (PTAS); the first, and simpler of the two, caters to a setting where each customer may buy only a constant number of products, whereas the second more nuanced algorithm applies to our multi-purchase model in its general form. Additionally, we study the revenue-potential of making assortment decisions that account for multi-purchase behavior in comparison to those that overlook this phenomenon. In particular, we relate both the structure and revenue performance of the optimal assortment under a traditional single-purchase model to that of the optimal assortment in the multi-purchase setting.