Assortment Optimization and Pricing Under the Multinomial Logit Model with Impatient Customers: Sequential Recommendation and Selection

Pin Gao (), Yuhang Ma (), Ningyuan Chen (), Guillermo Gallego (), Anran Li (), Paat Rusmevichientong () and Huseyin Topaloglu ()
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Pin Gao: School of Data Science, The Chinese University of Hong Kong, Shenzhen, China
Yuhang Ma: School of Operations Research and Information Engineering, Cornell Tech, New York, New York 10044
Ningyuan Chen: Department of Management, University of Toronto Mississauga, Mississauga, Ontario L5L 1C6, Canada
Guillermo Gallego: HKUST Industrial Engineering and Decision Analytics, Clear Water Bay, Hong Kong
Anran Li: Department of Management, London School of Economics, London, WC2A 2AE, United Kingdom
Paat Rusmevichientong: Marshall School of Business, University of Southern California, Los Angeles, California 90089
Huseyin Topaloglu: School of Operations Research and Information Engineering, Cornell Tech, New York, New York 10044

Operations Research, 2021, vol. 69, issue 5, 1509-1532

Abstract: We develop a variant of the multinomial logit model with impatient customers and study assortment optimization and pricing problems under this choice model. In our choice model, a customer incrementally views the assortment of available products in multiple stages. The patience level of a customer determines the maximum number of stages in which the customer is willing to view the assortments of products. In each stage, if the product with the largest utility provides larger utility than a minimum acceptable utility, which we refer to as the utility of the outside option, then the customer purchases that product right away. Otherwise, the customer views the assortment of products in the next stage as long as the customer’s patience level allows the customer to do so. Under the assumption that the utilities have the Gumbel distribution and are independent, we give a closed-form expression for the choice probabilities. For the assortment-optimization problem, we develop a polynomial-time algorithm to find the revenue-maximizing sequence of assortments to offer. For the pricing problem, we show that, if the sequence of offered assortments is fixed, then we can solve a convex program to find the revenue-maximizing prices, with which the decision variables are the probabilities that a customer reaches different stages. We build on this result to give a 0.878-approximation algorithm when both the sequence of assortments and the prices are decision variables. We consider the assortment-optimization problem when each product occupies some space and there is a constraint on the total space consumption of the offered products. We give a fully polynomial-time approximation scheme for this constrained problem. We use a data set from Expedia to demonstrate that incorporating patience levels, as in our model, can improve purchase predictions. We also check the practical performance of our approximation schemes in terms of both the quality of solutions and the computation times.

Keywords: utility/preference: applications; choice functions; programming:integer: algorithms; marketing: choice models; Market Analytics and Revenue Management; choice model; multinomial logit; impatient customer; sequential recommendation (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:69:y:2021:i:5:p:1509-1532

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