🤖 AI Summary
This paper addresses the challenge of setting price bounds in data-driven pricing, proposing a bi-objective optimization framework that jointly maximizes revenue and ensures price reliability. Methodologically, it introduces the first integration of Bootstrap confidence interval estimation with Nelder-Mead black-box optimization, guided by expected total revenue under K-fold cross-validation. Demand prediction uncertainty is quantified via Bootstrap resampling, and robust price upper and lower bounds are efficiently computed using the simplex method. Experimental results demonstrate that the method significantly narrows price intervals while sustaining high revenue—particularly for small product catalogs or low-noise settings. Moreover, its revenue stability and bound tightness improve consistently with increasing data volume. The approach establishes a new paradigm for interpretable, production-ready intelligent pricing.
📝 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.