Title: A continuous review retrial inventory system with impatient customers

Authors: M. Rajkumar

Addresses: Department of Mathematics, Devanga Arts College, Aruppukottai-626101, Virudhunagar District, Tamilnadu, India

Abstract: This paper examines a retrial inventory system with an orbit of infinite size. An arriving customer, finding the stock out in the system, proceeds to the orbit with probability a and is lost forever with probability (1 - a). The customers in the orbit are assumed not only to retry for their demand, may renege from the orbit at random time. We model this situation by assuming Poisson arrivals for customers, exponential lead time for orders placed under (s, S) ordering policy, exponential time between successive attempts of retrial of a customer and exponential times for reneging by customers at the orbit. The condition for ergodicity of the system is obtained. The joint probability distribution of the number of customers in the system and the inventory level is obtained in steady state case. The measures of system performance in the steady state are derived and the long run total expected cost rate is derived. The results are illustrated with numerical examples.

Keywords: stochastic inventory; poisson demands; lead times; retrial demands; reneging; continuous review; retrial inventory systems; impatient customers; ergodicity.

DOI: 10.1504/IJCSYSE.2013.052589

International Journal of Computational Systems Engineering, 2013 Vol.1 No.3, pp.193 - 199

Published online: 26 Jul 2014 *

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