Joint Price and Inventory Optimization Under Minimax Regret

We study the problem of jointly optimizing the price and order quantity for a perishable product, also known as the pricing-newsvendor problem. We consider the case with demand ambiguity where the demand is a function of the price and an uncertain factor, of which only the support information is known. We employ the minimax regret decision criterion to minimize the worst-case regret, which is defined as the difference between the optimal profit that could be obtained with perfect information and the realized profit using the decision made with ambiguous information. First, we characterize the optimal pricing and ordering decisions under the minimax regret criterion and compare their properties with those in the classical models that seek to maximize the expected profit. Specifically, we explore the impact of inventory risk by comparing the optimal price and the risk-free price, and study comparative statics with respect to the degree of demand ambiguity and the unit ordering cost. Second, we compare the minimax regret approach with two other approaches that are commonly used under demand ambiguity, namely the max-min robust approach and the regression-based data-driven approach. In the demand ambiguity setting, we show that the minimax regret approach avoids the high degree of conservativeness that is often incurred in the max-min approach. In the data-driven setting, we show via a numerical study that the minimax regret approach outperforms the classical regression-based approach when data is scarce, when the demand has high volatility, or when the demand model is misspecified