Title: On the distribution of an (r, Q) inventory with lead time via multi server queues

Authors: Anoop N. Nair; M.J. Jacob

Addresses: Department of Mathematics, National Institute of Technology Calicut, Kerala, Calicut 673601, India ' Department of Mathematics, National Institute of Technology Calicut, Kerala, Calicut 673601, India

Abstract: We consider a multi-server Markovian queuing model where the servers can be considered as an inventory with standard (r, Q) policy and positive lead time. The demands are considered as arrivals and the time for serving the inventory is considered as the service time. Here we consider the model in which a fixed order quantity Q is ordered each time when the on hand inventory reaches the reorder point r. Behaviour of this system is studied using a two state quasi birth and death (QBD) process. Condition for checking ergodicity, the steady state solutions, the distribution of inventory recycle time and an optimisation problem are presented. Numerical illustrations are also given.

Keywords: Markovian queues; inventory modelling; (r, Q) inventory policy; matrix analytic methods; lead times; multi server queues; ergodicity; steady state solutions; inventory recycle time; optimisation.

DOI: 10.1504/IJIE.2015.073448

International Journal of Intelligent Enterprise, 2015 Vol.3 No.1, pp.3 - 18

Received: 02 Jan 2014
Accepted: 16 Sep 2014
Published online: 09 Dec 2015 *

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