Title: A retrial inventory system with an unreliable server

Authors: P.V. Ushakumari

Addresses: Department of Mathematics, Amrita Vishwa Vidyapeetham University, Amritapuri Campus, Clappana P.O., Kollam, Kerala-690 525, India

Abstract: In this paper, we analyse an unreliable (s, S) inventory system with infinite capacity orbit. Customers join the retrial orbit if they are interrupted by a server breakdown and repeatedly attempt to access the server at iid intervals until it is found functioning and idle. We provide stability condition and steady state system size probabilities of the underlying stochastic process. Also, we provide several other characteristics of the system like average waiting time of a customer in the orbit, average number of breakdowns of the server, average duration of a failed service, etc. We obtained a total expected cost function which is optimal in both s and S and provided some numerical illustration.

Keywords: (s; S) inventory systems; continuous review; retrial queues; retrial inventory systems; unreliable servers; server breakdowns; Markov process; inventory management; customer waiting time; infinite capacity orbit.

DOI: 10.1504/IJMOR.2017.081924

International Journal of Mathematics in Operational Research, 2017 Vol.10 No.2, pp.190 - 210

Received: 18 Feb 2015
Accepted: 24 May 2015
Published online: 31 Jan 2017 *

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