A two heterogeneous servers perishable inventory system of a finite population with one unreliable server and repeated attempts

In this paper,we consider a continuous review perishable inventory system with a service facility having two heterogeneous servers,server 1 and server 2,and the demands originate from a finite population of n sources. in such systems,the customers demand is satisfied only after some service is completed by any one of the two servers. compared to most inventory models in which inventory is depleted at the demand rate,here it is depleted at the rate that the service is completed. it is assumed that server 1 is perfectly reliable and server 2 is subject to interruptions. the interrupted server is repaired at an exponential rate. the primary customer who finds either both servers are busy or there is no item (excluding those in service) in the stock,enters into an orbit with probability p and is lost forever with probability 1 - p. a retrial customer in the orbit,finding the stock level (excluding those in service) is zero or both servers are busy,returns to the orbit with probability q and is lost forever with probability 1 - q. the interval between two successive repeated attempts is exponentially distributed. the items of inventory have exponential life times. as and when the on-hand inventory level drops to a prefixed level s(≥ 2),an order for q(= s - s > s) units is placed. the ordered items are received after a random time which is distributed as exponential. the joint probability distribution of the number of customers in the orbit and the inventory level is obtained in the steady state case. the measures of system performance in the steady state are derived and the total expected cost rate is also calculated. the results are illustrated numerically. © 2015 pakistan journal of statistics.