Note on "Cost analysis of the M/M/R machine repair problem with second optional repair: Newton-Quasi method"

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July 2012, 8(3): 727-732. doi: 10.3934/jimo.2012.8.727

Note on "Cost analysis of the M/M/R machine repair problem with second optional repair: Newton-Quasi method"

Cheng-Dar Liou ^1,

1.	Department of Business Administration, National Formosa University, Huwei, Yunlin, 63201, Taiwan

Received August 2011 Revised March 2012 Published June 2012

Abstract
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The machine repair problem has attracted considerable attention in the field of queuing systems, due to the wide range of difficulties it entails. Wang, Liao and Yen [K.H. Wang, C.W. Liao, T.C. Yen, Cost analysis of the M/M/R machine repair problem with second optional repair: Newton-Quasi method, Journal of Industrial and Management Optimization. 6 (2010), 197-207] [1] derived a cost model to determine the optimal number of the repairmen, the optimal values of the first essential repair rate, and the second optional repair rate while maintaining the system availability at a specified level. In their approach, a direct search method is first used to determine the optimal number of repairmen followed by the Newton-Quasi method to search for the two repair rates. However, this two stage search method restricts the search space and cannot guarantee global minimum solutions. In overcoming these limitations, this study employs a particle swarm optimization algorithm to ensure a thorough search of the solution space in the pursuit of global minimum solutions. Numerical results support the superior search characteristics of the proposed solution.

Keywords: Direct search method, particle swarm optimization., Newton-Quasi method.

Mathematics Subject Classification: Primary: 90B22, 90B25; Secondary: 60K1.

Citation: Cheng-Dar Liou. Note on "Cost analysis of the M/M/R machine repair problem with second optional repair: Newton-Quasi method". Journal of Industrial and Management Optimization, 2012, 8 (3) : 727-732. doi: 10.3934/jimo.2012.8.727

References:

[1]	M. Clerc, "Particle Swarm Optimization," Translated from the 2005 French original, ISTE, London, 2006.
[2]	J. Kennedy and R. C. Eberhart, Particle swarm optimization, in "Proceedings of IEEE International Conference on Neural Networks," Piscataway, NJ, (1995), 1942-1948.
[3]	J. Kennedy, R. C. Eberhart and Y. Shi, "Swarm Intelligence," Morgan Kaufmann, CA, 2001.
[4]	Y. Shi and R. C. Eberhart, Parameter selection in particle swarm optimization, Proceedings of the 7^th International Conference on Evolutionary Programming, Springer, New York, (1998), 591-600.
[5]	K.-H. Wang, C.-W. Liao and T.-C. Yen, Cost analysis of the M/M/R machine repair problem with second optional repair: Newton-Quasi method, Journal of Industrial and Management Optimization, 6 (2010), 197-207.
[6]	C.-H. Wu, K.-H. Wang, J.-C. Ke and J.-B. Ke, A heuristic algorithm for the optimization of M/M/S queue with multiple working vacations, Journal of Industrial and Management Optimization, 8 (2012), 1-17.
[7]	H. Yoshida, K. Kawata, Y. Fukuyama and Y. Nakanishi, A particle swarm optimization for reactive power and voltage control considering voltage security assessment, IEEE Transactions on Power Systems, 15 (2000), 1232-1239. doi: 10.1109/59.898095.

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References:

[1]	M. Clerc, "Particle Swarm Optimization," Translated from the 2005 French original, ISTE, London, 2006.
[2]	J. Kennedy and R. C. Eberhart, Particle swarm optimization, in "Proceedings of IEEE International Conference on Neural Networks," Piscataway, NJ, (1995), 1942-1948.
[3]	J. Kennedy, R. C. Eberhart and Y. Shi, "Swarm Intelligence," Morgan Kaufmann, CA, 2001.
[4]	Y. Shi and R. C. Eberhart, Parameter selection in particle swarm optimization, Proceedings of the 7^th International Conference on Evolutionary Programming, Springer, New York, (1998), 591-600.
[5]	K.-H. Wang, C.-W. Liao and T.-C. Yen, Cost analysis of the M/M/R machine repair problem with second optional repair: Newton-Quasi method, Journal of Industrial and Management Optimization, 6 (2010), 197-207.
[6]	C.-H. Wu, K.-H. Wang, J.-C. Ke and J.-B. Ke, A heuristic algorithm for the optimization of M/M/S queue with multiple working vacations, Journal of Industrial and Management Optimization, 8 (2012), 1-17.
[7]	H. Yoshida, K. Kawata, Y. Fukuyama and Y. Nakanishi, A particle swarm optimization for reactive power and voltage control considering voltage security assessment, IEEE Transactions on Power Systems, 15 (2000), 1232-1239. doi: 10.1109/59.898095.

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