A Finite Source Perishable Inventory System with Retrial Demands, Server Interruptions and Multiple Vacations

This article presents a single server retrial inventory system with server interruptions, multiple server vacations and the demands originate from a finite population of N sources. The maximum storage capacity is fixed as S. It is assumed that demand for the commodity is of unit size. The individual customer is issued a demanded item after a random service time, which is distributed as negative exponential. The items of inventory have exponential life times. An (0, S) ordering policy is adopted with zero lead time. The demands that occur during the server busy period or during the server vacation period or during the server interruption period, enter into the orbit with probability p and is lost forever with probability (1-p). A retrial customer in the orbit, finding the server busy or server interruption or server vacation, returns to the orbit with probability q and is lost forever with probability (1-q). The joint probability distribution of the inventory level and the number of customers in the orbit is obtained in the steady state case. Various system performance measures are derived and the total expected cost rate is also calculated. The results are illustrated numerically. AMS Subject Classification: 90B05, 60J27.