A Sample-Based Approach to the Price-Setting Newsvendor Problem with Limited Demand Information

Problem definition: We consider a price-setting newsvendor problem in which the demand distribution is unknown. We assume that the retailer exercises only a few price points with a sample set of demand realizations for each exercised price. Given this limited demand information, we define an ambiguity set and study two robust optimization models that maximize the worst-case profit (maxmin profit) and minimize the maximum regret (minmax regret), respectively. Methodology/results: These two robust models are reduced to easy-to-solve optimization problems. Compared with the maximal profit under complete demand information, we find that with only a few price points, we can achieve more than 90% of the maximal profit on average and around 70% of the maximal profit in the worst case. Our method is purely data driven and model free; that is, we do not assume that the demand model follows any specific form. This approach has the advantage of avoiding model mismatches in practice. Managerial implications: We show that this new method outperforms traditional methods, such as regressions, and other model-specific methods. We also propose demand learning methods with guaranteed convergence rates when the number of exercised prices increases. Funding: R. He was supported by the National Natural Science Foundation of China [Project 72301268]. Y. Lu was supported by the Hong Kong Research Grants Council [Project 11504621] and the City University of Hong Kong [Project 9676029]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2025.0354 .