Title: An inventory model with negative customers and service interruptions

Authors: P. Vijaya Laxmi; M.L. Soujanya; K. Jyothsna

Addresses: Department of Applied Mathematics, Andhra University, Visakhapatnam – 530003, India ' Department of Applied Mathematics, Andhra University, Visakhapatnam – 530003, India ' Department of Applied Mathematics, Andhra University, Visakhapatnam – 530003, India

Abstract: In this paper, we consider a single server queueing system with inventory wherein customers arrive according to Poisson process. A customer turns out to be an ordinary customer or a negative customer. An ordinary customer, on arrival, joins the queue and a negative customer, on the other hand, does not join the queue but takes away one waiting customer, if any. The inventory is served at an exponential rate to the waiting customers and it is replenished according to (s; S) policy with positive lead time. Due to breakdowns the service process is subjected to interruptions, which follows an exponential distribution and the broken down server is repaired at an exponential rate. Matrix geometric solution is obtained for the steady state probability distribution of the inventory model. Finally, cost analysis is carried out.

Keywords: stochastic inventory; negative customers; service interruptions; lead times; matrix geometric method; inventory modelling; single server queueing.

DOI: 10.1504/IJMOR.2016.077556

International Journal of Mathematics in Operational Research, 2016 Vol.9 No.1, pp.1 - 14

Received: 30 Jul 2014
Accepted: 01 Oct 2014
Published online: 06 Jul 2016 *

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