A perishable inventory system with service facilities and retrial customers

In this article, we present a continuous review perishable (s, S) inventory system with a service facility consisting of finite waiting room and a single server. The customers arrive according to a Markovian arrival process (MAP). The individual customer’s unit demand is satisfied after a random time of service which is assumed to have phase-type distribution. The life time of each item and the lead time of reorders are assumed to have independent exponential distributions. Any arriving customer, who finds the waiting room is full, enters into the orbit of infinite space. These orbiting customers compete for service by sending out signals the duration between two successive attempts are exponentially distributed. The joint probability distribution of the number of customers in the waiting room, number of customers in the orbit and the inventory level is obtained in the steady-state case. Various stationary system performance measures are computed and total expected cost rate is calculated.