Finite source Markovian inventory system with bonus service for certain customers

Abstract: We consider a perishable inventory system with bonus service for certain customers, wherein the demand of a customer is satisfied only after performing some service on the item which is assumed to be of random duration. The maximum inventory level is S . The ordering policy is (0,S ) policy and the lead time is zero. The life time of each items is assumed to be exponential.The customers arrive according a quasi-random distribution. Arriving customers form a single waiting line based on the order of their arrivals. The first R ≥ 1 customers who arrive after the system becomes empty must wait for service to begin. We have assumed that these R customers received an additional service, called bonus service, in addition to the essential service rendered to all customers. The service times are exponentially distributed. The joint probability distribution of the number of customers in the waiting hall and the inventory level is obtained for the steady state case. Some important system performance measures and the long-run total expected cost rate are derived in the steady state.