A Robust Price-Setting Newsvendor Problem

The price-setting newsvendor problem is well studied in the literature. However, it is commonly assumed that retailers have complete demand information modeled as a function of price and random noise. In reality, a retailer may have very limited information on a demand model because a retailer who has exercised only a few prices does not have sufficient information to accurately estimate a demand model. This creates a gap between academic research and practical applications. In this study, we consider the price-setting newsvendor problem in which the retailer knows the expected demand on a few exercised price points and the distribution of the random noise. Both additive and multiplicative demand models are studied. The retailer makes price and inventory decisions to minimize the maximum regret, which is defined as the difference between the expected profit based on limited demand information and that based on complete demand information. We show that this robust optimization problem can be reduced to a one-dimensional optimization problem, and we derive the optimal price and inventory decisions. We also provide a demand learning policy that can reduce the minmax regret to any delta within O(1 delta) steps. We also study the problem in which the retailer maximizes the worst-case profit, and we obtain similar results. Extensive numerical studies show that our method has a great performance that dominates that of the regression method.

Automated summary

The study addresses the price-setting newsvendor problem where retailers may have limited information on demand models, which creates a gap between academic research and practical applications. A robust optimization approach is proposed to minimize maximum regret, and extensive numerical studies demonstrate its superior performance compared to the regression method.