Constrained Pricing under Finite Mixtures of Logit

TL;DR

This paper develops efficient algorithms for constrained pricing problems under mixed logit demand models, providing polynomial-time approximation schemes and practical algorithms for multiple customer segments.

Contribution

It introduces a PTAS for constrained pricing under multinomial logit and extends it to finite mixed logit models with multiple segments, using exponential cone programming reformulations.

Findings

PTAS for multinomial logit constrained pricing

Efficient Branch-and-Bound algorithm for mixed logit

Strong empirical performance against baselines

Abstract

The mixed logit model is a flexible and widely used demand model in pricing and revenue management. However, existing work on mixed-logit pricing largely focuses on unconstrained settings, limiting its applicability in practice where prices are subject to business or regulatory constraints. We study the constrained pricing problem under multinomial and mixed logit demand models. For the multinomial logit model, corresponding to a single customer segment, we show that the constrained pricing problem admits a polynomial-time approximation scheme (PTAS) via a reformulation based on exponential cone programming, yielding an $\varepsilon$-optimal solution in polynomial time. For finite mixed logit models with $T$ customer segments, we reformulate the problem as a bilinear exponential cone program with $O(T)$ bilinear terms. This structure enables a Branch-and-Bound algorithm whose complexity is exponential only in $T$. Consequently, constrained pricing under finite mixtures of logit admits a PTAS when the number of customer segments is bounded. Numerical experiments demonstrate strong performance relative to state-of-the-art baselines.