Abstract:

In this paper, we introduce a new vacation strategy. We consider an queueing-inventory system with lost sales and (s, S) strategy under the vacation strategy. When inventory level is zero, the server goes to a working vacation in which if the replenishment is successful, the server immediately begins to serve the customer normally. When the working vacation is over, if the inventory level is still zero, the server will take multiple vacations, otherwise he/she will return to the normal working state. We analyze the stationary distributions of the queueing-inventory system under the vacation strategy by using Markov process method. On this basis, some performance indices and average cost function are obtained. Finally, the optimal inventory policy and the optimal expected cost are also discussed by numerical examples.

Key words: queueing-inventory system, lost sale, (s, S) strategy, working vacation, Markov process