Optimal Pricing for a Service Facility with Congestion Penalties

Abstract

We consider the optimal pricing problem in a service facility in order to maximize its long-run average profit per unit time. We model the facility as a queueing process that may have finite or infinite capacity. Customers are admitted into the system if it is not full and if they are willing to pay the price posted by the service provider.

Moreover, the congestion level in the facility incurs penalties that greatly influence profit. We model congestion penalties in three different manners: holding costs, balking customers and impatient customers. First, we assume that congestion-dependent holding costs are incurred per unit of time. Second, we consider that each customer might be deterred by the system congestion level and might balk upon arrival. Third, customers are impatient and can leave the system with a full refund before being serviced.

We are interested in both static and dynamic pricing for all three types of congestion penalties. In the static case, we demonstrate that there is a unique optimal price that maximizes the long-run average profit per unit time. We also investigate how optimal prices vary as system parameters change. In the dynamic case, we show the existence of an optimal stationary policy in a continuous and unbounded action space that maximizes the long-run average profit per unit time. We provide explicit expressions for this policy under certain conditions. We also analyze the structure of this policy and investigate its relationship with our optimal static price.