A stochastic inventory system with two modes of service and retrial of customers

Abstract

This paper analyses an inventory model with positive service time and retrial of customers. The customers arrive according to a Markovian Arrival Process with representation ( $$D_{0} ,D_{1}$$ ). The service times are assumed to be of Phase type distribution with representation $$\left( {\eta ,U} \right)$$ . When the inventory level depletes to the reorder point s, the service is given at a reduced rate and the service time distribution has the representation $$\left( {\eta ,\alpha U} \right)$$ , where $$0 < \alpha < 1$$ . An arriving customer, who finds the inventory level zero or the server busy, enters into an orbit of infinite capacity and will retry for service from there. The lead time follows an exponential distribution with rate β. We analyze the system using Matrix Analytic Method. Some important performance measures in the steady state are obtained. A suitable cost function for the expected total cost is constructed and analyzed numerically and graphically.