Model-Free Assortment Pricing with Transaction Data

Abstract

We study a problem in which 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 show that the optimal prices in this setting can be approximated at any arbitrary precision by solving a compact mixed-integer linear program. Moreover, we study special practical cases where the program can be solved efficiently, and design three approximation strategies that are of low computational complexity and interpretable. 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.

Contextual Inverse Optimization: Offline and Online Learning

“…While we are able to leverage some ideas from this literature such as the use of ellipsoids and projected knowledge sets, we highlight, however, that the nature of the problem studied here is substantially different from the contextual pricing/search literature due to the nature of the feedback, as there is no control in our setting on the feedback one sees. The recent studies Feng et al (2018) and Chen et al (2021) study robust assortment and price optimization based on revealed preferences associated with choice data. Additional early works that focus on learning utility functions from revealed preferences include Beigman and Vohra (2006), Zadimoghaddam and Roth (2012), Balcan et al (2014), Amin et al (2015).…”