Abstract: We consider a joint assortment optimization and customization problem under a mixture of multinomial logit models. In this problem, a firm faces customers of different types, each making a choice within an offered assortment according to the multinomial logit model with different parameters. The problem takes place in two stages. In the first stage, the firm picks an assortment of products to carry subject to a cardinality constraint. In the second stage, a customer of a certain type arrives into the system. Observing the type of the customer, the firm customizes the assortment that it carries by, possibly, dropping products from the assortment. The goal of the firm is to find an assortment to carry and a customized assortment for each customer type that can arrive in the second stage to maximize the expected revenue from a customer visit. The problem arises, for example, in online platforms, where retailers commit to a selection of products before the start of the selling season, but they can potentially customize the displayed assortments for each customer. We give an approximation algorithm that obtains 1/log m fraction of the optimal expected revenue, where m is the number of customer types. Contrasting this problem with the variant where customization is not possible, it is NP-hard to approximate the latter variant within a factor better than 1/m. Thus, from computational complexity perspective, the variant with customization is fundamentally different.

Bio: Huseyin Topaloglu is a Professor in the School of Operations Research and Information Engineering at Cornell Tech. He got his B.Sc. in Industrial Engineering from Bogazici University of Turkey and his Ph.D. in Operations Research and Financial Engineering from Princeton University. He has been a faculty member at the School of Operations Research and Information Engineering since 2002. He is currently serving as the Program Director for the Master of Engineering Program in Operations Research and Information Engineering at Cornell Tech. Professor Topaloglu works on large-scale stochastic optimization problems that arise in areas such as revenue management, inventory control, transportation logistics, and supply chain management. He is the department editor for Revenue Management Department of Product and Operations Management Journal. He serves as associate editor for the journals Management Science, Mathematical Programming C, Naval Research Logistics, Operations Research, Transportation Science, IIE Transactions, and Surveys in Operations Research and Management Science.