A retrial inventory system with single and modified multiple vacation for server

This paper considers a continuous review stochastic (s,S) inventory system with Poisson demand and exponentially distributed delivery time. The demands that occur during the stock out period or during the server vacation period enter into an orbit of infinite size. These orbiting demands retry to get satisfied by sending out signals so that the time durations are exponentially distributed. We consider two models which differ in the way that server go for vacation. The joint probability distribution of the inventory level, the number of demands in the orbit and the server status is obtained in the steady state case. Various system performance measures in the steady state is derived and the long-run total expected cost rate is calculated. Several numerical examples, which provide insight into the behaviour of the cost function, are presented.