A Perishable Inventory System with Service Facilities and Negative Customers

We consider a continuous review perishable (s, S) inventory system with a service facility consisting of a waiting line of finite capacity and a single server. Two types of customers, ordinary and negative, arrive according to a Markovian Arrival Process (MAP). An ordinary customer joins the queue and a negative customer removes some ordinary customers from the queue. Unlike the conventional method of removal rules considered in the literature, we consider the following removal rule : a negative customer at an arrival epoch removes one or more ordinary waiting customers and the number of removals is a random variable depending on the number of waiting customers in the system. The life time of each item, the service time and the lead time of the reorders are all assumed to have independent exponential distributions. The joint probability distribution of the number of customers in the system and the inventory level is obtained in both transient and steady state cases. Various stationary system performance measures are computed and the total expected cost rate is calculated. The results are illustrated numerically.