Robust Price Optimization of Multiple Products under Interval Uncertainties

TL;DR

This paper presents a robust optimization method for multi-product pricing under demand uncertainty, providing reliable price intervals and maintaining near-optimal revenue despite parameter estimation errors.

Contribution

It introduces a data-driven robust optimization framework that accounts for interval uncertainties in demand parameters for multi-product pricing.

Findings

The method effectively captures demand uncertainty in price decisions.

Optimal price intervals are derived with minimal revenue loss.

Robust solutions perform comparably to simulation-based approaches.

Abstract

In this paper, we solve the multiple product price optimization problem under interval uncertainties of the price sensitivity parameters in the demand function. The objective of the price optimization problem is to maximize the overall revenue of the firm where the decision variables are the prices of the products supplied by the firm. We propose an approach that yields optimal solutions under different variations of the estimated price sensitivity parameters. We adopt a robust optimization approach by building a data-driven uncertainty set for the parameters, and then construct a deterministic counterpart for the robust optimization model. The numerical results show that two objectives are fulfilled: the method reflects the uncertainty embedded in parameter estimations, and also an interval is obtained for optimal prices. We also conducted a simulation study to which we compared the results of our approach. The comparisons show that although robust optimization is deemed to be conservative, the results of the proposed approach show little loss compared to those from the simulation.