Optimal Policy for Dynamic Assortment Planning Under Multinomial Logit Models

• 成果类型: Article
• 署名作者: Chen, Xi; Wang, Yining; Zhou, Yuan
• 署名单位: New York University; State University System of Florida; University of Florida; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1133
• 发表日期: 2021
• 页码: 1639-1657
• 关键词: revenue management; choice model; optimization

摘要

We study the dynamic assortment planning problem, where for each arriving customer, the seller offers an assortment of substitutable products and the customer makes the purchase among offered products according to an uncapacitated multinomial logit (MNL) model. Because all the utility parameters of theMNLmodel are unknown, the seller needs to simultaneously learn customers' choice behavior and make dynamic decisions on assortments based on the current knowledge. The goal of the seller is to maximize the expected revenue, or, equivalently, to minimize the expected regret. Although dynamic assortment planning problem has received an increasing attention in revenue management, most existing policies require the estimation of mean utility for each product and the final regret usually involves the number of products N. The optimal regret of the dynamic assortment planning problem under the most basic and popular choice model-the MNL model-is still open. By carefully analyzing a revenue potential function, we develop a trisection-based policy combined with adaptive confidence bound construction, which achieves an item-independent regret bound of O(root T), where T is the length of selling horizon. We further establish the matching lower bound result to show the optimality of our policy. There are two major advantages of the proposed policy. First, the regret of all our policies has no dependence on N. Second, our policies are almost assumption-free: there is no assumption on mean utility nor any separability condition on the expected revenues for different assortments. We also extend our trisection search algorithm to capacitated MNL models and obtain the optimal regret (O) over tilde (root NT) (up to logrithmic factors) without any assumption on themean utility parameters of items.