A Robust Framework for Modeling Preferences and its Applications in Revenue Management

Columbia University, New York NY

Investigators

Abstract

Modeling customer preferences is a fundamental challenge in estimating demand in revenue management problems since the uncertain demand crucially depends on the substitution behavior of the customers. Such modeling is especially difficult as the preferences are latent and unobservable. The broad goal of this project is to develop a tractable data-driven approach for modeling preferences that is robust to model selection errors, and develop efficient algorithms for related decision problems. This research aims at developing foundational theory for preference modeling that has potential of significant impact in practice. To facilitate the dissemination of this work to maximize societal impact, the PI will focus on: i) training of students through research and integration of the results from this research into core graduate curriculum, ii) increasing the involvement of undergraduate students in research through summer REU projects, iii) increasing the societal impact through outreach programs for local high-schools including Society for Women in Engineering (SWE) and Harlem School Partnership (HSP) for STEM Education with particular focus on increasing the participation of underrepresented minorities and iv) working with industry towards application of this research in practice. The main focus of this project is to study a Markovian framework for modeling preferences. This framework of modeling choice is simple yet very powerful and amenable to strong generalizations to capture a rich class of preference models. The PI aims to consider two broad directions in this project including: i) using the framework of Markov chain transitions to model a rich class of substitution behavior, and ii) using a Markov chain over an exponentially large state space of preferences to model a class of distribution over permutations such as Mallows and maximum entropy distributions more generally. Efficient estimation and optimization algorithms over these models would result in the theoretical foundations for a tractable data-driven approach to choice modeling. With the availability of large amount of data in today's world, such an approach has the potential of significant impact in many applications.