Assortment Optimization for the Multinomial Logit Model with Repeated Customer Interactions

This paper presents the multinomial logit model with repeated customer interactions. In each period, the same customer selects a product from the assortment recommended in that period or opts out. It captures the essence of an increasingly popular business model called the subscription box, exemplified by Stitch Fix and Wantable. From the seller's perspective, the choice probability is updated based on the purchase history. We study the adaptive assortment recommendation strategy for all the periods. Although the problem is generally NP-hard as we show, when the customer interacts with the seller for two periods, we discover the structures of the optimal assortment when the available products in the two periods are identical and develop approximation algorithms in other cases. For more than two periods, although the optimal assortments are intractable, we find that the optimal fixed assortments that are not adapted to the purchase history can achieve 68.47% or 50% of the optimal expected revenue, respectively, when the available products across periods are disjoint or not. Using two public datasets, we demonstrate that the model with repeated customer interactions can better predict the purchase behavior and generates higher revenues