Title: Model-Free Assortment Pricing with Transaction Data
Co-authors: Ningyuan Chen, Andre A. Cire, and Saman Lagzi
Paper link: https://ssrn.com/abstract=3759397
Abstract: We study the problem when a firm sets prices for products based on the transaction data, i.e., which product past customers chose from an assortment and what were the historical prices that they observed. Our approach does not impose a model on the distribution of the customers' valuations and only assumes, instead, that purchase choices satisfy incentive-compatible constraints. The individual valuation of each past customer can then be encoded as a polyhedral set, and our approach maximizes the worst-case revenue assuming that new customers' valuations are drawn from the empirical distribution implied by the collection of such polyhedra. We study the single-product case analytically and relate it to the traditional model-based approach. Moreover, we show that the optimal prices in the general case can be approximated at any arbitrary precision by solving a compact mixed-integer linear program. We also design three approximation strategies that are of low computational complexity and interpretable. In particular, the cut-off pricing heuristic has a competent provable performance guarantee. Comprehensive numerical studies based on synthetic and real data suggest that our pricing approach is uniquely beneficial when the historical data has a limited size or is susceptible to model misspecification.
Bio: Ming Hu is the University of Toronto Distinguished Professor of Business Operations and Analytics, a professor of operations management at the Rotman School of Management, and an Amazon Scholar. He was named as one of Poets & Quants Best 40 Under 40 business school professors in 2018. He is the recipient of Wickham Skinner Early-Career Research Accomplishments Award by the POM Society (2016) and Best Operations Management Paper in Management Science Award by INFORMS (2017). He currently serves as the editor-in-chief of Naval Research Logistics, department editor of Service Science, associate editor of Management Science, Operations Research and Manufacturing & Service Operations Management, and senior editor of Production and Operations Management. He is a former chair of Revenue Management and Pricing (RMP) Section at INFORMS. For more details of his research, please visit http://ming.hu.