An (S - 1, S) Inventory System with Negative Arrivals and Multiple Vacations

In this paper, we consider a continuous review one-to-one ordering policy inventory system with multiple vacations and negative customers. The maximum storage capacity is S. The customers arrive according to a Poisson process with finite waiting hall. There are two types of customers: ordinary and negative. An ordinary customer, on arrival, joins the queue and the negative customer does not join the queue and takes away any one of the waiting customers. When the waiting hall is full, the arriving primary customer is considered to be lost. The service time and lead time are assumed to have independent exponential distribution. When the inventory becomes empty, the server takes a vacation and the vacation duration is exponentially distributed. The stationary distribution of the number of customers in the waiting hall, the inventory level and the server status for the steady state case. Some system performance measures and numerical illustrations are discussed.