Constrained Pricing under Finite Mixtures of Logit

2026-02-08

AI Summary

This study addresses the challenging problem of pricing optimization under business or regulatory constraints in settings with multiple customer segments, where customer choices follow a finite mixture of logit models. The authors propose an optimization framework based on the finite mixture logit model and, for the first time, develop a polynomial-time approximation scheme (PTAS) for this problem by leveraging exponential cone programming and bilinear modeling within a branch-and-bound algorithm. The approach guarantees scalability when the number of customer segments is bounded. Numerical experiments demonstrate that the proposed method significantly outperforms state-of-the-art baselines in both solution quality and computational efficiency.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• constrained pricing
• mixed logit model
• multinomial logit
• finite mixture
• revenue management

Innovation

• constrained pricing
• mixed logit model
• polynomial-time approximation scheme
• exponential cone programming
• branch-and-bound