Robust personalized pricing under uncertainty of purchase probabilities

TL;DR

This paper introduces a robust optimization approach for personalized pricing that accounts for uncertainty in purchase probability predictions, improving revenue reliability under prediction errors.

Contribution

It develops a mixed-integer linear robust optimization model and a Lagrangian decomposition algorithm for large-scale personalized pricing problems.

Findings

The robust model improves revenue stability under prediction errors.

The decomposition algorithm enhances computational efficiency.

Experimental results validate the effectiveness of the approach.

Abstract

This paper is concerned with personalized pricing models aimed at maximizing the expected revenues or profits for a single item. While it is essential for personalized pricing to predict the purchase probabilities for each consumer, these predicted values are inherently subject to unavoidable errors that can negatively impact the realized revenues and profits. To address this issue, we focus on robust optimization techniques that yield reliable solutions to optimization problems under uncertainty. Specifically, we propose a robust optimization model for personalized pricing that accounts for the uncertainty of predicted purchase probabilities. This model can be formulated as a mixed-integer linear optimization problem, which can be solved exactly using mathematical optimization solvers. We also develop a Lagrangian decomposition algorithm combined with line search to efficiently find high-quality solutions for large-scale optimization problems. Experimental results demonstrate the effectiveness of our robust optimization model and highlight the utility of our Lagrangian decomposition algorithm in terms of both computational efficiency and solution quality.