Study on an Inventory Model with Retrial Customer and Two Heterogeneous Servers Including One with Multiple Vacations

Abstract

In this chapter, we deal with a continuous review perishable inventory system with a service facility having two heterogeneous servers (henceforth, referred to as server 1  and 2 server ) and server 2  is always available but server 1  goes on vacation when the inventory level is less than or equal to one. The individual customer is issued a demanded item after a random service time, which is distributed as negative exponential. The life time of each commodity is assumed to be exponential. The inventory is replenished according to an \(s, Q\) control policy and the replenishing times are assumed to be exponentially distributed. At the end of a vacation period, service begins if inventory level is more than one in the system. Otherwise, the server takes another vacation immediately and continuous in the same method until he finds at least two items in the system upon returning from a vacation. Any arriving primary customers who find the waiting room full are queued in the orbit. The inter-retrial times are exponentially distributed. The joint probability distribution of the number of customers in the waiting room, the number of customers in the orbit, the status of the servers and the inventory level are obtained for the steady state case. Some important system performance measures in the steady state are derived, and the long-run total expected cost rate is also calculated. The results are illustrated numerically.