Dynamic Pricing and Release Time Control for Service Systems

Abstract

This paper studies a mechanism design problem for a single-server queue in which customers are served in a first-come-first-serve (FCFS) manner. Customers are heterogeneous and have private information on their valuations for immediate service and wait time sensitivity. Namely, impatient (patient, respectively) customers are more (less, respectively) sensitive to waiting and value immediate service higher (lower, respectively). The service provider designs a history-dependent menu such that each menu item consists of a price and a release time for each type of arriving customer, aiming to maximize the long-run average revenue rate. We demonstrate that the optimal menu depends on history only through the system completion time, and includes four strategies: delaying patient customers, pooling all customers, screening customers (serving one type and rejecting the other), and rejecting all customers. In particular, we show that it is optimal for the provider to strategically delay the release time of a patient customer beyond the service completion time if and only if the completion time is shorter than a threshold. The delay in the release time allows the provider to charge a premium on the impatient customers and thus increase revenue. Interestingly, the delayed release time is set to a fixed value, regardless of the exact completion time state, which makes the mechanism easy to implement. Additionally, the decision to serve either the more patient or impatient customers under the screening strategy hinges on an intuitive trade-off between a customer's utility from joining the service and the externality from a more congested system.

Keywords: queueing system, mechanism design, dynamic control, strategic delay