Journal Published Online: 26 March 2013
Volume 41, Issue 3

Analysis of the Machine Repair Models With Multi-Threshold Synchronous Vacations



In this paper, we present an analysis of a machine repair problem with M operating machines and S standbys, in which c repairmen are responsible for supervising these machines and follow a multi-threshold, synchronous vacation policy. With such a policy, at a repair completion instant, if the number of the failed machines in the system is less than a preset threshold value, partial idle servers together take a single vacation (or leave for a random amount of time doing other secondary job). At the end of a vacation, they return to repair the failed machines (or waits for the arrival). The steady-state probabilities are solved by using the matrix-analytic method, and formulae of system performance measures are thereby obtained. A cost model is then developed to formulate an optimization problem to find the minimum cost. The direct search and quasi-Newton methods are implemented to determine the optimal number of servers, the optimal threshold policy and the optimal repair rate.

Author Information

Wu, Chia-Huang
Dept. of Industrial Engineering and Management, National Chiao Tung Univ., Taiwan, TW
Ke, Jau-Chuan
Dept. of Applied Statistics, National Taichung Univ. of Science and Technology, Taichung, TW
Choudhury, Gautam
Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Assam, India National Taichung University of Science and Technology Taichung, TW
Pages: 8
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Stock #: JTE20120061
ISSN: 0090-3973
DOI: 10.1520/JTE20120061