17th International Symposium on Inventories, Budapest, Hungary, 20 - 24 August 2012, pp.163
In this talk we consider joint pricing and inventory decisions in a capacity constrained service system. There are M types of customers, each type arriving to a service system according to its respective Poisson process. Upon arrival, each customer demandsan item, for instance a spare part to be used for a replacement. If the item is on-hand available, then the arriving customer does not wait, whereas if the item is not available, the customer waits until the item is delivered through a possibly capacitated system. Customer types are differentiated using priorities and the waiting times of the customers for delivery depend on the priority of the type. The service system operates under an order-up-to policy and decides on the price to be charged for each customer type, and the order-up-to level for the spare parts inventory. Customers, on the other hand, decides on joining the system or not, based on their reservation price, waiting cost, and the price charged for the item. In equilibrium, the arrival rate of a customer class is such that the reservation price of the customer is equal to the sum of the price for the spare part plus the waiting cost. Based on the equilibrium arrival rates of customer types, the service system collects revenues and incurs inventory holding costs. The objective is to maximize the expected profit of the service system by choosing the best set of prices (for each type) and the best order-up-to level. Our first resultprovesthe form of the priority assignment policy. We show that customersare assigned priorities based on an ordering of the unit waiting costs of customer types. Then, we present a near explicit solution for the optimal order-up-to level, and provide conditions for obtaining the optimal price set. Finally, we show that the optimal prices are incentive compatible. That is, the price set obtained maximizes the expected profit of the service provider even if the service provider does not have information on the type of an arriving customer. Providing a menu of prices and corresponding priorities, and letting the customer choose one price from the menu is sufficient. We also provide a number of illustrations of our results through numerical examples.