Robust personalized pricing under uncertainty of purchase probabilities

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.