This paper considers the pricing problem of a service facility when services are jointly produced by the customers and the facility. Building on the work of Mendelson, we model the facility as a GI/GI/ 1 queue with customer-chosen service rates and linear delay costs. We show that the service rates chosen by the customers, based on their self-interest, are always suboptimal for the facility due to congestion externalities. We derive optimal incentive-compatible pricing schemes that can achieve optimal arrival rates and induce customers to choose optimal service rates. For the case of system-wide net-value maximization, we show that the optimal incentive-compatible pricing scheme consists of a variable fee that is proportional to the actual service time and a fixed-rebate that is equal to a customer's expected delay cost in the queue. For the case of profit maximization of the facility, we show that the optimal pricing scheme again consists of a fixed fee and a variable fee. One insight from our analysis is that it may be appropriate for a service facility to reimburse each customer for his actual delay cost in the queue.
