A Stochastic Inventory Model with Multiple Vacations and N - Policy

Abstract

We consider a perishable inventory system under continuous review at a service facility in which a waiting area for customers is of finite size. We assume that the replenishment of inventory is instantaneous. The items of inventory have exponential life times. The service starts only when the customer level reaches a prefixed level, starting from the epoch at which no customer is left behind in the system. The arrivals of customers to the service station form a Poisson process. The server goes for a vacation of an exponentially distributed duration whenever the waiting area is zero. The service process is subject to interruptions, which occurs according to a Poisson process. The interrupted server is repaired at an exponential rate. Also the waiting customer independently reneges the system after an exponentially distributed amount of time. The joint probability distribution of the number of customers in the system and the inventory levels is obtained in steady state case. The results are illustrated with numerical examples.