A Production-Inventory System with a Service Facility and Production Interruptions for Perishable Items

Abstract

In this paper, we consider a production-inventory system with a service facility and production interruptions. Customers arrive in the system according to a Poisson process and require a random time of the service from a single service facility. The service time is assumed to be exponentially distributed. The items are produced according to an (s, S) policy. Each customer leaves the system with one item from the inventory at his service completion epoch if the inventory is available. The production is interrupted for a vacation of random time once the inventory level becomes S. The vacations are exponentially distributed. On return from a vacation, if the inventory level depletes to s, then the production is immediately switched on. It then starts production and is kept in the on mode until the inventory level becomes S. The items in stock are perishable and have exponential life times. It is assumed that no customers is allowed to join the queue when the inventory level is zero. We first derive the stability condition of the system. Then, We obtain the product form solution for the stationary joint distribution of the number of customers and the on-hand inventory level. Based on this stationary distribution, we compute explicitly some performance measures and develop a cost function. Finally, some numerical results are presented.