An (s, S) retrial inventory system with impatient and negative customers
by M. Rajkumar
International Journal of Mathematics in Operational Research (IJMOR), Vol. 6, No. 1, 2014

Abstract: In this paper, we consider a continuous review inventory system with an orbit of infinite size. A customer turns out to be an ordinary customer and a negative customer. On arrival, an ordinary customer joins the queue and the negative customer does not join the queue and takes away one waiting customer from the orbit if any. If there is no customer when a negative customer arrives, then the negative customer will be serviced. The customers in the orbit are assumed not only to retry for their demand, but may renege from the orbit after a random time. We consider this situation by assuming Poisson arrivals for both types of 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 and illustrated with example.

Online publication date: Sat, 28-Jun-2014

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