17th International Symposium on Inventories, Budapest, Macaristan, 20 - 24 Ağustos 2012, ss.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.