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Optimal Pricing for a Service Facility

This paper investigates optimal pricing policies for a service facility modeled as a queueing system. Arriving customers are accepted if they are willing to pay the price charged by the service provider and if there is room in the waiting area. Capacity of the waiting area can be either finite or infinite. We determine expressions for the optimal prices that maximize the service provider’s long-run average profit and we prove some structural results on the optimal policies exploring their relationships with the customers’ willingness to pay and system parameters such as service speed and waiting room capacity. We show that the optimal price is not necessarily higher for systems where customers are willing to pay more and the relationship between the optimal price and waiting room capacity depends on customer demand and other system parameters. Under certain assumptions, we give necessary and sufficient conditions for the optimal price to be an increasing or decreasing function of the waiting room capacity.