Joint inventory and pricing decisions when customers are delay sensitive

We consider the joint pricing and inventory problem of a capacity constrained service facility with several classes of customers. The customers are differentiated with their sensitivity for waiting and their willingness to pay for the service. We model the problem using an M/M/1 queueing system with non-preemptive priorities. We give closed form solutions for the inventory decisions. We also show that the prices given by the first order conditions are also incentive compatible in the sense that they optimize the profit of the firm even if the firm does not know the type of an arriving customer and let the customer choose a price from the menu of prices. We approximate the problem and provide simple and explicit solutions when there is a single customer type. In numerical illustrations, we show that the customers, who are more sensitive to wait, do not enter the system until the base stock level is above a threshold. We provide extensions of our results for M/G/1 and M/M/m systems.