Assortment Optimization under the Multi-Purchase Multinomial Logit Choice Model

Abstract

Updating a Classic: Assortment Optimization under the Multi-Purchase MNL Model In the paper “Updating a Classic: Assortment Optimization under the Multi-Purchase MNL Model,” our primary contribution resides in proposing the first multi-purchase choice model that can be fully operationalized. Our main algorithmic results consist of two distinct polynomial time approximation 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 with 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.