Personalized Assortment Optimization under Consumer Choice Models with Local Network Effects

Abstract

In this paper, we introduce a consumer choice model in which each consumer's utility is affected by the purchase probabilities of his/her neighbors in a network. Such a consumer choice model is a general model to characterize consumer choice under network effect. We first characterize the choice probabilities under such a choice model. Then we consider the associated personalized assortment optimization problem. Particularly, the seller is allowed to offer a personalized assortment to each consumer, and the consumer chooses among the products according to the proposed choice model. We show that the problem is NP-hard even if the consumers form a star network. Despite of the complexity of the problem, we show that if the consumers form a star network, then the optimal assortment to the central consumer cannot be strictly larger than that without network effects; and the optimal assortment to each peripheral consumer must be a revenue-ordered assortment that is a subset of the optimal assortment without network effect. We also present a condition when revenue-ordered can achieve a provable performance. Then in view of the fact that each node in a network can represent a group of consumers, we propose a novel idea in which the sellers are allowed to offer assortments to each node in the network. We show that allowing for randomized may further increase the revenue, and under a mild condition, the optimal assortment for the central consumer must be a combination of two adjacent revenue-ordered and thus efficient algorithm can be developed. Finally, we extend the results to directed acyclic graphs (DAGs), showing that a mixture of adjacent revenue-ordered is optimal under certain conditions.