Title: Numerical investigation on MAP/PH(1), PH(2)/2 inventory system with multiple server vacations

Authors: C. Suganya; B. Sivakumar; G. Arivarignan

Addresses: School of Mathematics, Madurai Kamaraj University, Palkalainagar, Madurai – 625021, India ' School of Mathematics, Madurai Kamaraj University, Palkalainagar, Madurai – 625021, India ' School of Mathematics, Madurai Kamaraj University, Palkalainagar, Madurai – 625021, India

Abstract: In this paper, we consider an inventory system with two heterogeneous servers and multiple vacations. We have assumed that the customers arrive according to a Markovian arrival process and two parallel servers who provide heterogeneous phase type services to customers. The inventory is replenished according to an (s, S) policy and the replenishing time is assumed to follow exponential distribution. The vacation times of both severs are assumed to be independent and identically distributed exponential random variables. The joint probability distribution of the number of customers in the system, inventory level and server status is obtained in the steady state. Some important performance measures are obtained and the optimality of an expected total cost rate is shown through numerical illustration.

Keywords: Markovian arrival process; phase type distribution; heterogeneous servers; multiple vacations; inventory management; parallel servers; replenishment time; performance measures.

DOI: 10.1504/IJOR.2017.083173

International Journal of Operational Research, 2017 Vol.29 No.1, pp.1 - 33

Received: 19 Apr 2014
Accepted: 08 Aug 2014
Published online: 22 Mar 2017 *

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