Perishable Inventory System at Service Facilities with Multiple Server Vacations and Impatient Customers

This article presents a perishable inventory system under continuous review at a service facility in which a waiting area for customers is of finite size M. We assume that the replenishment of inventory is instantaneous. The items of inventory have exponential life times. It is assumed that demand for the commodity is of unit size. 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. If the server finds the customer level is zero when he returns to the system, he immediately takes another vacation. The individual customer is issued a demanded item after a random service time, which is distributed as negative exponential. Also the waiting customer independently reneges the system after an exponentially distributed amount of time. The joint probability distribution of the number customers in the system and the inventory levels is obtained in steady state case. Some measures of system performance in the steady state are derived and the total expected cost is also considered.