Dynamic pricing and quick response of a retailer in the presence of strategic consumers: A distributionally robust optimization approach

A distributionally robust optimization approach is developed for the two-period pricing and initial ordering decisions for a retailer with quick response capability in the presence of strategic consumers. The consumers have heterogeneous tastes for the product valuation, and the consumer taste is assumed to follow a uniform distribution. The market size is uncertain with its mean and standard deviation as the only known information. The product value decreases over time, and the selling season is divided into a regular period and a discount period. Two distributionally robust dynamic pricing models with and without quick response are developed and are transformed into tractable mathematical programming models. The closed-form solutions are derived, and the effects of the parameter values on the optimal decisions and on the expected profits are examined analytically, for the model with quick response. The conditions for dynamic pricing to benefit the retailer with quick response are discussed. Two model extensions are provided with the consumer taste following a general distribution in one extension and the discount factor being stochastic in the other. Numerical experiments are conducted to verify the effectiveness and practicality of the proposed approach in coping with market size uncertainty. The effects of the parameter values on the retailer optimal decisions and on the expected profit are further examined through sensitivity analyses. The optimal decisions and the expected profits are compared for the retailer with and without quick response, and managerial insights are provided.