Optimal Pricing under Mixed Logit Choice

TL;DR

This paper develops a method for optimal pricing of multiple differentiated products using the mixed logit choice model, which captures customer heterogeneity and substitution patterns to maximize revenue.

Contribution

It introduces a revenue-maximization framework under the mixed logit model and proves log-concavity in the single-product case, with extensive numerical validation for multiple products.

Findings

Mixed logit model improves revenue by capturing customer heterogeneity.

Log-concavity of the optimization problem established for single-product case.

Numerical experiments show significant revenue gains with the mixed logit model.

Abstract

In this paper we consider the problem of pricing multiple differentiated products. This is challenging as a price change in one product, not only changes the demand of that particular product, but also the demand for the other products. To address this problem, customer choice models have recently been introduced as these are capable of describing customer choice behavior across differentiated products. In the present paper the objective is to obtain the revenue-maximizing prices when the customer's decision making process is modelled according to a particular customer choice model, namely the mixed logit model. The main advantage of using the mixed logit model, also known as the random coefficients logit model, for this purpose is its flexibility. In the single-product case we establish log-concavity of the optimization problem under certain regularity conditions. In addition, in the multi-product case, we present the results of our extensive numerical experiments. These suggest that the mixed logit model, by taking unobserved customer heterogeneity and flexible substitution patterns into account, can significantly improve the attainable revenue.