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

In this chapter, we’ll look at a continuous review perishable inventory system with a service facility that has two heterogeneous servers (referred to as server and server in this chapter), one of which is always accessible but goes on vacation when the inventory level is less than or equal to one. After a random service time, which is distributed as a negative exponential, the individual customer is given the requested item. Each commodity’s life expectancy is considered to be exponential. The inventory is replenished based on a control policy, with replenishment times considered to be exponentially distributed. If there is more than one inventory level in the system at the end of a vacation period, service will begin. Otherwise, the server immediately takes another vacation and repeats the process until he finds at least two items in the system when he returns from vacation. Arriving primary customers who find the waiting room to be overcrowded will be directed to the orbit. Inter-retrial times are spread exponentially. For the steady state situation, we derive 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. In the steady state, some critical system performance measures are calculated, as well as the long-run total projected cost rate. The outcomes are represented numerically.

Author (S) Details

Dr. K. Jeganathan
Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai – 600 005, India.

Dr. C. Sugapriya
Department of Mathematics, Queen Marry’s College, Chennai, India.

M. Nithya
Department of Mathematics, Queen Marry’s College, Chennai, India.

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