Revenue-Utility Tradeoff in Assortment Optimization Under the Multinomial Logit Model with Totally Unimodular Constraints

Mika Sumida (), Guillermo Gallego (), Paat Rusmevichientong (), Huseyin Topaloglu () and James Davis ()
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Mika Sumida: School of Operations Research and Information Engineering, Cornell Tech, New York, New York 10044
Guillermo Gallego: Department of Industrial Engineering and Decision Analytics, HKUST, Hong Kong
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
James Davis: Uber Technologies Inc., San Francisco, California 94103

Management Science, 2021, vol. 67, issue 5, 2845-2869

Abstract: We examine the revenue–utility assortment optimization problem with the goal of finding an assortment that maximizes a linear combination of the expected revenue of the firm and the expected utility of the customer. This criterion captures the trade-off between the firm-centric objective of maximizing the expected revenue and the customer-centric objective of maximizing the expected utility. The customers choose according to the multinomial logit model, and there is a constraint on the offered assortments characterized by a totally unimodular matrix. We show that we can solve the revenue–utility assortment optimization problem by finding the assortment that maximizes only the expected revenue after adjusting the revenue of each product by the same constant. Finding the appropriate revenue adjustment requires solving a nonconvex optimization problem. We give a parametric linear program to generate a collection of candidate assortments that is guaranteed to include an optimal solution to the revenue–utility assortment optimization problem. This collection of candidate assortments also allows us to construct an efficient frontier that shows the optimal expected revenue–utility pairs as we vary the weights in the objective function. Moreover, we develop an approximation scheme that limits the number of candidate assortments while ensuring a prespecified solution quality. Finally, we discuss practical assortment optimization problems that involve totally unimodular constraints. In our computational experiments, we demonstrate that we can obtain significant improvements in the expected utility without incurring a significant loss in the expected revenue.

Keywords: choice modeling; multinomial logit; revenue–utility trade-off; totally unimodular constraints (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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