Price Optimization Under the Finite-Mixture Logit Model

51 Pages Posted: 29 Aug 2018 Last revised: 24 Dec 2019

See all articles by Ruben van de Geer

Ruben van de Geer

VU University Amsterdam - Faculty of Science - Department of Mathematics

Arnoud den Boer

University of Amsterdam - Korteweg-de Vries Institute for Mathematics; University of Amsterdam Business School

Date Written: December 23, 2019

Abstract

We consider price optimization under the finite-mixture logit model. This model assumes that customers belong to one of a number of customer segments, where each customer segment chooses according to a multinomial logit model with segment-specific parameters. We reformulate the corresponding price optimization problem and develop a novel characterization. Leveraging this new characterization, we construct an algorithm that obtains prices at which the revenue is guaranteed to be at least (1-epsilon) times the maximum attainable revenue for any prespecified epsilon>0. Existing global optimization methods require exponential time in the number of products to obtain such a result, which practically means that the prices of only a handful of products can be optimized. The running time of our algorithm, however, is exponential in the number of customer segments and only polynomial in the number of products. This is of great practical value, since in applications the number of products can be very large, while it is has been found in various contexts that a low number of segments is sufficient to capture customer heterogeneity appropriately. The results of our numerical study show that our algorithm runs fast on a broad range of problem instances.

Keywords: price optimization; finite-mixture logit model; fully polynomial-time approximation scheme

Suggested Citation

van de Geer, Ruben and den Boer, Arnoud, Price Optimization Under the Finite-Mixture Logit Model (December 23, 2019). Available at SSRN: https://ssrn.com/abstract=3235432 or http://dx.doi.org/10.2139/ssrn.3235432

Ruben Van de Geer (Contact Author)

VU University Amsterdam - Faculty of Science - Department of Mathematics ( email )

Amsterdam
Netherlands

Arnoud Den Boer

University of Amsterdam - Korteweg-de Vries Institute for Mathematics ( email )

Netherlands

University of Amsterdam Business School ( email )

Roetersstraat 18
Amsterdam, 1018WB
Netherlands

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