A Markov Chain Approximation to Choice Modeling

Jose Blanchet (), Guillermo Gallego () and Vineet Goyal ()
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Jose Blanchet: Industrial Engineering and Operations Research, Columbia University, New York, New York
Guillermo Gallego: Industrial Engineering and Logistics Management, Hong Kong University of Science and Technology, Kowloon, Hong Kong
Vineet Goyal: Industrial Engineering and Operations Research, Columbia University, New York, New York

Operations Research, 2016, vol. 64, issue 4, 886-905

Abstract: Assortment planning is an important problem that arises in many industries such as retailing and airlines. One of the key challenges in an assortment planning problem is to identify the “right” model for the substitution behavior of customers from the data. Error in model selection can lead to highly suboptimal decisions. In this paper, we consider a Markov chain based choice model and show that it provides a simultaneous approximation for all random utility based discrete choice models including the multinomial logit (MNL), the probit, the nested logit and mixtures of multinomial logit models. In the Markov chain model, substitution from one product to another is modeled as a state transition in the Markov chain. We show that the choice probabilities computed by the Markov chain based model are a good approximation to the true choice probabilities for any random utility based choice model under mild conditions. Moreover, they are exact if the underlying model is a generalized attraction model (GAM) of which the MNL model is a special case. We also show that the assortment optimization problem for our choice model can be solved efficiently in polynomial time. In addition to the theoretical bounds, we also conduct numerical experiments and observe that the average maximum relative error of the choice probabilities of our model with respect to the true probabilities for any offer set is less than 3% where the average is taken over different offer sets. Therefore, our model provides a tractable approach to choice modeling and assortment optimization that is robust to model selection errors. Moreover, the state transition primitive for substitution provides interesting insights to model the substitution behavior in many real-world applications.

Keywords: choice modeling; assortment optimization; model selection (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (73)

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