Constrained Pricing in Choice-based Revenue Management

TL;DR

This paper develops an approximation method for constrained pricing in choice-based revenue management, effectively handling non-concavity and constraints on prices and probabilities in static and dynamic settings.

Contribution

It introduces a novel approximation mechanism using bisection and MILP to solve constrained pricing problems with non-concave objectives, extending to dynamic scenarios.

Findings

Outperforms existing methods in static pricing accuracy

Effective in handling complex price and probability constraints

Scalable to larger problem instances with resource decomposition

Abstract

We consider a dynamic pricing problem in network revenue management where customer behavior is predicted by a choice model, i.e., the multinomial logit (MNL) model. The problem, even in the static setting (i.e., customer demand remains unchanged over time), is highly non-concave in prices. Existing studies mostly rely on the observation that the objective function is concave in terms of purchasing probabilities, implying that the static pricing problem with linear constraints on purchasing probabilities can be efficiently solved. However, this approach is limited in handling constraints on prices, noting that such constraints could be highly relevant in some real business considerations. To address this limitation, in this work, we consider a general pricing problem that involves constraints on both prices and purchasing probabilities. To tackle the non-concavity challenge, we develop an approximation mechanism that allows solving the constrained static pricing problem through bisection and mixed-integer linear programming (MILP). We further extend the approximation method to the dynamic pricing context. Our approach involves a resource decomposition method to address the curse of dimensionality of the dynamic problem, as well as a MILP approach to solving sub-problems to near-optimality. Numerical results based on generated instances of various sizes indicate the superiority of our approximation approach in both static and dynamic settings.