Assortment Optimization for the Multinomial Logit Model with Repeated Customer Interactions

Abstract

This paper presents the multinomial logit model with repeated customer interactions. In each period, the same customer selects a product from the recommended assortment or opts out. From the seller’s perspective, the choice probability in the current period is updated based on the purchase history of the customer. We derive this conditional choice probability and study the adaptive assortment recommendation strategy. Although the problem is generally intractable, we discover the structures of the optimal assortment when the customer interacts with the seller for two periods and the available products to recommend are identical in the two periods. For a general number of periods, we find that the optimal fixed assortments that are not adapted to the purchase history can achieve 50% of the optimal expected revenue, and the approximation ratio increases to 68.47% when the available products across periods are disjoint. Using real-world data sets, we demonstrate that the model with repeated customer interactions can better predict the purchase behavior and generate higher revenues. This paper was accepted by Chung Piaw Teo, optimization. Funding: The authors gratefully acknowledge the funding support from Meituan. C. Wang’s research was supported by the National Science Foundation of China [Grants 72495133, 72172104] and China Postdoctoral Science Foundation [Grant 2025M780760]. P. Gao’s research was supported by the National Natural Science Foundation of China [Grants 72522026, 72201234, and 72192805], Collaborative Research Funding [Grant C6032-21G] of the Hong Kong Research Grants Council, and the Guangdong Provincial Key Laboratory of Mathematical Foundations for Artificial Intelligence [Grant 2023B1212010001]. Y. Wang’s research was supported by the National Natural Science Foundation of China [Grant 12371513] and the Major Program of National Fund of Philosophy and Social Science of China [Grant 23&ZD135]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.02419 .