Optimal management policy for a single and bulk service queue
by Lotfi Tadj, Chafik Abid
International Journal of Advanced Operations Management (IJAOM), Vol. 3, No. 2, 2011

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.

Online publication date: Tue, 30-Sep-2014

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