A production inventory model with server breakdown and customer impatience

In this paper, we consider a single server production inventory model with server breakdown and customer impatience while server is down. We assume that customer arrivals are according to a Markovian Arrival Process. If the server is busy at the time of arrival of a customer, the customer joins a queue of infinite capacity. The server is subjected to breakdowns, which occur according to a Poisson process. The service time of customers follows independent and identical phase type distribution and one unit of the inventory is required for each service. Repair starts immediately after a breakdown and the time taken for repair follows phase type distribution. The customer whose service was interrupted waits for the remaining service while the server is under repair. When repair is completed, the service of the interrupted customer is resumed from the interrupted stage. When the server is under repair, loss of customers from the infinite queue due to impatience occurs at exponentially distributed intervals. Such impatient customers go to a buffer of finite capacity, provided waiting space is available, else such customers leave the system for ever. The production of each inventory occurs in k stages of production and production time of each stage follows independent phase type distributions. The production of inventory is according to (s, S) policy. Here the steady state analysis has been done. Various performance measures have been evaluated and we derived distributions of certain important performance characteristics. We analysed the model numerically and graphically.