Robust price optimization of multiple products under interval uncertainties

In this paper, we solve a multi-product price optimization problem under interval uncertainty of the price sensitivity parameter in the demand function. The objective of the problem is to maximize the revenue of the firm where the decision variables are the prices of the products supplied by the firm. We propose an approach that yields solutions that remain optimal 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 research 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 demonstrate that although robust optimization is deemed to be conservative, the results of the proposed approach indicate little lost revenue compared to those from the simulation.