Joint pricing and inventory management under minimax regret

We study the problem of jointly optimizing the price and order quantity for a perishable product in a single selling period, also known as the pricing newsvendor problem, under demand ambiguity. Specifically, the demand is a function of the selling price and a random factor of which the distribution is unknown. We employ the minimax regret decision criterion to minimize the worst-case regret, where the regret is defined as the difference between the optimal profit that could be obtained with perfect/complete information and the realized profit using the decision made with ambiguous demand information. First, given the interval in which the random factor lies with high probability, 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. We further show that the minimax regret approach avoids the high degree of conservativeness that is often incurred in the application of the commonly used max-min robust optimization approach. Second, when partial distributional information of the random factor is available, we adopt the Wasserstein distance to depict the distributional ambiguity and characterize the set of worst-case distributions and the maximum regret given the selling price and order quantity. Third, we compare the minimax regret approaches with the traditional profit-maximization approach in a data-driven setting. We show via a numerical study that the minimax regret approaches outperform the traditional profit-maximization approach, especially when the data are scarce, the demand has high volatility, and the number of exercised prices is small. Furthermore, leveraging the partial distributional information of the random factor can further improve the performance of the minimax regret approach.