Revenue Management Under a Mixture of Independent Demand and Multinomial Logit Models

• 成果类型: Article
• 署名作者: Cao, Yufeng; Rusmevichientong, Paat; Topaloglu, Huseyin
• 署名单位: Shanghai Jiao Tong University; University of Southern California
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2333
• 发表日期: 2023
• 页码: 603-625
• 关键词: assortment optimization; capacitated assortment; programming approach; price optimization; choice model; algorithm

摘要

We consider assortment optimization problems when customers choose under a mixture of independent demand and multinomial logit models. In the assortment optimization setting, each product has a fixed revenue associatedwith it. The customers choose among the products according to our mixture choice model. The goal is to find an assortment that maximizes the expected revenue from a customer. We show that we can find the optimal assortment by solving a linear program. We establish that the optimal assortment becomes larger as the relative size of the customer segment with the independent demand model increases. Moreover, we showthat the Pareto-efficient assortments thatmaximize aweighted average of the expected revenue and the total purchase probability are nested, in the sense that the Pareto-efficient assortments become larger as the weight on the total purchase probability increases. Considering the assortment optimization problem with a capacity constraint on the offered assortment, we show that the problem is NP-hard, even when each product consumes unit capacity, so that we have a constraint on the number of offered products. We give a fully polynomial-time approximation scheme. In the assortment-based network revenue-management problem, we have resources with limited capacities, and each product consumes a combination of resources. The goal is to find a policy for deciding which assortment of products to offer to each arriving customer tomaximize the total expected revenue over a finite selling horizon. A standard linear-programming approximation for this problem includes one decision variable for each subset of products. We show that this linear program can be reduced to an equivalent one of substantially smaller size. We give an expectation-maximization algorithm to estimate the parameters of our mixture model. Our computational experiments indicate that our mixture model can provide improvements in predicting customer purchases and identifying profitable assortments.