Markov Decision Processes for Service Facility Systems with Perishable Inventory

We consider a service facility system with perishable inventory with finite number of servers. Each server having one perishable item for providing service. The arrival of a customer at the system according to independent Poisson Processes with rate  through a single channel. The service time of the customer is exponentially distributed with mean  1/ and the item in stock has exponential life time with perishability rate 0) (>  . The free servers are occupied by the new customer, entering for service. The maximum level of item in stock is 0 > ) (= c S . The replenishment of inventory is instantaneous, when the inventory level comes to zero. Customers can be rejected from the system only when all the servers are busy that is, there is no waiting line. Transition probabilities are obtained from the two dimensional process. The problem is modeled as a Semi Markov decision process and we use the modified Value Iteration algorithm to obtain the minimum average loss rate.