Title: Optimal management policy for a single and bulk service queue

Authors: Lotfi Tadj, Chafik Abid

Addresses: School of Business Administration, Faculty of Management, Dalhousie University, Halifax, NS, B3H 3C3, Canada; Department of Finance, Information Systems and Management Science, Sobey School of Business, Saint Mary's University, Halifax, Nova Scotia, B3H 3C3, Canada. ' Department of Management, School of Business Administration, American University in Dubai, P.O. Box 28282, Dubai, United Arab Emirates

Abstract: This paper considers an organisation with a single server and single or bulk service characterised by the bilevel service discipline introduced by Baburaj (1999, pp.15-22). In this organisation, on one hand, if the queue size n is not more than a constant r then the server takes a single customer for service according to FCFS rule. On the other hand, if the size is more than r then he serves min{n, R}(R > r) units in a batch according to the same rule. While Baburaj assumes exponential service times we consider general service time distributions. The first objective is to derive the probability generating function of the number of customers in the system at a service completion epoch and at an arbitrary instant of time as well as the performance characteristics of the system. The second objective is to develop an optimal management policy, through a quick search algorithm, to obtain the optimal values of the parameters r and R which minimise a suitable cost structure. This model is useful in different real-world operational management problems to minimise the organisation costs while keeping a high customer satisfaction level.

Keywords: Markov chain; optimal policy; semi-regenerative techniques; single service queuing; bulk service queuing; general service time distributions; operations management; cost reduction; customer satisfaction.

DOI: 10.1504/IJAOM.2011.042139

International Journal of Advanced Operations Management, 2011 Vol.3 No.2, pp.175 - 187

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 28 Aug 2011 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article