American Institute of Mathematical Sciences

Advanced
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

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 & 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

show all references

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

[1]

Min Li. A three term Polak-Ribière-Polyak conjugate gradient method close to the memoryless BFGS quasi-Newton method. Journal of Industrial & Management Optimization, 2020, 16 (1) : 245-260. doi: 10.3934/jimo.2018149
[2]

Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056
[3]

Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271
[4]

Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327
[5]

Tao Wu, Yu Lei, Jiao Shi, Maoguo Gong. An evolutionary multiobjective method for low-rank and sparse matrix decomposition. Big Data & Information Analytics, 2017, 2 (1) : 23-37. doi: 10.3934/bdia.2017006
[6]

Deren Han, Zehui Jia, Yongzhong Song, David Z. W. Wang. An efficient projection method for nonlinear inverse problems with sparsity constraints. Inverse Problems & Imaging, 2016, 10 (3) : 689-709. doi: 10.3934/ipi.2016017
[7]

Boris Kramer, John R. Singler. A POD projection method for large-scale algebraic Riccati equations. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 413-435. doi: 10.3934/naco.2016018
[8]

Petra Csomós, Hermann Mena. Fourier-splitting method for solving hyperbolic LQR problems. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 17-46. doi: 10.3934/naco.2018002
[9]

Christina Surulescu, Nicolae Surulescu. Modeling and simulation of some cell dispersion problems by a nonparametric method. Mathematical Biosciences & Engineering, 2011, 8 (2) : 263-277. doi: 10.3934/mbe.2011.8.263
[10]

Manfred Einsiedler, Elon Lindenstrauss. On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method. Journal of Modern Dynamics, 2008, 2 (1) : 83-128. doi: 10.3934/jmd.2008.2.83
[11]

Xiaomao Deng, Xiao-Chuan Cai, Jun Zou. A parallel space-time domain decomposition method for unsteady source inversion problems. Inverse Problems & Imaging, 2015, 9 (4) : 1069-1091. doi: 10.3934/ipi.2015.9.1069
[12]

Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023
[13]

Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399
[14]

Hong Seng Sim, Wah June Leong, Chuei Yee Chen, Siti Nur Iqmal Ibrahim. Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 377-387. doi: 10.3934/naco.2018024
[15]

Misha Bialy, Andrey E. Mironov. Rich quasi-linear system for integrable geodesic flows on 2-torus. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 81-90. doi: 10.3934/dcds.2011.29.81
[16]

Xiaoming Wang. Quasi-periodic solutions for a class of second order differential equations with a nonlinear damping term. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 543-556. doi: 10.3934/dcdss.2017027

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (71)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences