An Inventory System with Retrial Demands and Multiple Server Vacation

Abstract

In this article, we consider a continuous review inventory system with Markovian demand. The operating policy is (s, S) policy, that is, the maximum inventory level is S and whenever the inventory level drops to s, an order for Q (= S − s) units is placed. The ordered items are received after a random time which is assumed to be exponential distribution. The server goes for a vacation of an exponentially distributed duration whenever the inventory level reaches zero. If the server finds empty stock when he returns to the system, he immediately takes another vacation. The demands that occur during stock out period or during the server vacation period enter into the orbit of infinite size. These orbiting demands retry for their demand after a random time, which is assumed to be exponential distribution. 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 in the steady state are derived and the long-run total expected cost rate is calculated. Several instances of a numerical example, which provide insight into the behaviour of the system, are presented.