Estimating profitable price bounds for prescriptive price optimization

Abstract: Pricing of products and services, which has a significant impact on consumer demand, is one of the most important factors in maximizing business profits. Prescriptive price optimization is a prominent data-driven pricing methodology consisting of two phases: demand forecasting and price optimization. In the practice of prescriptive price optimization, the price of each item is typically set within a predetermined range defined by lower and upper bounds. Narrow price ranges can lead to missed opportunities, while wide price ranges run the risk of proposing unrealistic prices; therefore, determining profitable price bounds while maintaining the reliability of the suggested prices is a critical challenge that directly affects the effectiveness of prescriptive price optimization. We propose two methods for estimating price bounds in prescriptive price optimization so that future total revenue derived from the optimized prices will be maximized. Our first method for price bounds estimation uses the bootstrap procedure to estimate confidence intervals for optimal prices. Our second method uses the Nelder--Mead simplex method for black-box price bounds optimization that maximizes total revenue estimated through $K$-fold cross-validation. Experimental results with synthetic price--demand datasets demonstrate that our methods successfully narrowed down the price range while maintaining high revenues, particularly when the number of items was small or the demand noise level was low. Moreover, as more data accumulated, the comparative advantage of our methods further increased.