Abstract

In this paper, we develop a supply network model for a service facility system with perishable inventory (on hand) by considering a two dimensional stochastic process of the form (L, X) = , where L (t) is the level of the on hand inventory and X (t) is the number of customers at time t. The inter-arrival time to the service station is assumed to be exponentially distributed with mean 1/?. The service time for each customer is exponentially distributed with mean 1/ µ. The maximum inventory level is S and the maximum capacity of the waiting space is N. The replenishment process is assumed to be (S-1, S) with a replenishment of only one unit at any level of the inventory. Lead time is exponentially distributed with parameter ?. The items are replenished at a rate of ? whose mean replenishment time is 1/?. Item in inventory is perishable when it's utility drops to zero or the inventory item become worthless while in storage. Perishable of any item occurs at a rate of ?. Once entered a queue, the customer may choose to leave the queue at a rate of ? if they have not been served after a certain time (reneging). The steady state probability distributions for the system states are obtained. A numerical example is provided to illustrate the method described in the model.

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