# American Institute of Mathematical Sciences

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"

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

Received  August 2011 Revised  March 2012 Published  June 2012

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.
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 & 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, (2005).   Google Scholar [2] J. Kennedy and R. C. Eberhart, Particle swarm optimization,, in, (1995), 1942.   Google Scholar [3] J. Kennedy, R. C. Eberhart and Y. Shi, "Swarm Intelligence,", Morgan Kaufmann, (2001).   Google Scholar [4] Y. Shi and R. C. Eberhart, Parameter selection in particle swarm optimization,, Proceedings of the 7th International Conference on Evolutionary Programming, (1998), 591.   Google Scholar [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.   Google Scholar [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.   Google Scholar [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.  doi: 10.1109/59.898095.  Google Scholar

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##### References:
 [1] M. Clerc, "Particle Swarm Optimization,", Translated from the 2005 French original, (2005).   Google Scholar [2] J. Kennedy and R. C. Eberhart, Particle swarm optimization,, in, (1995), 1942.   Google Scholar [3] J. Kennedy, R. C. Eberhart and Y. Shi, "Swarm Intelligence,", Morgan Kaufmann, (2001).   Google Scholar [4] Y. Shi and R. C. Eberhart, Parameter selection in particle swarm optimization,, Proceedings of the 7th International Conference on Evolutionary Programming, (1998), 591.   Google Scholar [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.   Google Scholar [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.   Google Scholar [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.  doi: 10.1109/59.898095.  Google Scholar
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