Pricing and Prioritizing Time-Sensitive Customers with Heterogeneous Demand Rates

We consider the pricing/lead-time menu design problem for a monopoly service where time-sensitive customers have demand on multiple occasions. Customers differ in their demand rates and valuations per use. We compare a model where the demand rate is the private information of the buyers to a model where the firm has full information. The model assumes that customers queue for a finite-capacity service under a general pricing structure. Customers choose a plan from the menu to maximize their expected utility. In contrast to previous work, we assume customers do not differ in their waiting cost. Yet we show that in the private information case prioritizing customers may be optimal as a result of demand rate heterogeneity. We provide necessary and sufficient conditions for this result. In particular, we show that for intermediate capacity, more frequent-use customers that hold a lower marginal value per use should be prioritized. Further, less frequent-use customers may receive a consumer surplus. We demonstrate the applicability of these results to relevant examples. The structure of the result implies that in some cases it may be beneficial for the firm to prioritize a customer class with a lower marginal cost of waiting.