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New heuristics for solving the economic lot scheduling problem with reworks
Reliability optimization of component assignment problem for a multistate network in terms of minimal cuts
1.  Department of Industrial Management, National Taiwan University of Science & Technology, Taipei 106, Taiwan, Taiwan 
References:
[1] 
T. Aven, Reliability evaluation of multistate systems with multistate components,, IEEE Transactions on Reliability, 34 (1985), 473. doi: 10.1109/TR.1985.5222235. 
[2] 
S. T. Cheng, Topological optimization of a reliable communication network,, IEEE Transactions on Reliability, 47 (1998), 225. doi: 10.1109/24.740489. 
[3] 
M. L. F. Cheong, R. Bhatnagar and S. C. Graves, Logistics network design with supplier consolidation hubs and multiple shipment options,, Journal of Industrial and Management Optimization, 3 (2007), 51. 
[4] 
P. C. Chu and J. E. Beasley, A genetic algorithm for the generalized assignment problem,, Computers and Operations Research, 24 (1997), 17. doi: 10.1016/S03050548(96)000329. 
[5] 
D. Coit and A. Smith, Reliability optimization of seriesparallel systems using genetic algorithm,, IEEE Transactions on Reliability, 45 (1996), 254. doi: 10.1109/24.510811. 
[6] 
D. W. Coit and A. Smith, Penalty guided genetic search for reliability design optimization,, Computers and Industrial Engineering, 30 (1996), 895. doi: 10.1016/03608352(96)00040X. 
[7] 
C. J. Colbourn, "The Combinatorics of network Reliability,", Oxford University, (1987). 
[8] 
Z. Dzalilov, I. Ouveysi and A. Rubinov, An extended lifetime measure for telecommunication network,, Journal of Industrial and Management Optimization, 4 (2008), 329. 
[9] 
M. L. Fisher, R. Jaikumar and L. Van Wassenhove, A multiplier adjustment method for the generalised assignment problem,, Management Science, 32 (1986), 1095. doi: 10.1287/mnsc.32.9.1095. 
[10] 
L. R. Ford, and D. R. Fulkerson, "Flows in Networks,", Princeton University, (1962). 
[11] 
D. Goldberg, "Genetic Algorithms in Search, Optimization and Machine Learning,", AddisonWesley Press, (1989). 
[12] 
P. R. Harper, V. De Senna, I. T. Vieira and A. K. Shahani, A genetic algorithm for the project assignment problem,, Computers and Operations Research, 32 (2005), 1255. 
[13] 
C. C. Hsieh and Y. T. Chen, Reliable and economic resource allocation in an unreliable flow network,, Computer and Operations Research, 32 (2005), 613. doi: 10.1016/j.cor.2003.08.008. 
[14] 
C. C. Hsieh and Y. T. Chen, Resource allocation decisions under various demands and cost requirements in an unreliable flow network,, Computer and Operations Research, 32 (2005), 2771. doi: 10.1016/j.cor.2004.04.003. 
[15] 
C. C. Hsieh and M. H. Lin, Reliabilityoriented multiresource allocation in a stochasticflow network,, Reliability Engineering and System Safety, 81 (2003), 155. doi: 10.1016/S09518320(03)000826. 
[16] 
C. C. Jane and Y. W. Laih, A practical algorithm for computing multistate twoterminal reliability,, IEEE Transactions on Reliability, 57 (2008), 295. doi: 10.1109/TR.2008.920792. 
[17] 
C. C. Jane, J. S. Lin and J. Yuan, On reliability evaluation of a limitedflow network in terms of minimal cutsets,, IEEE Transactions on Reliability, 42 (1993), 354. doi: 10.1109/24.257817. 
[18] 
G. Levitin and A. Lisnianski, A new approach to solving problems of multistate system reliability optimization,, Quality Reliability Engineering International, 17 (2001), 93. doi: 10.1002/qre.388. 
[19] 
Y. K. Lin, A simple algorithm for reliability evaluation of a stochasticflow network with node failure,, Computer and Operations Research, 28 (2001), 1277. doi: 10.1016/S03050548(00)000393. 
[20] 
Y. K. Lin, Using minimal cuts to evaluate the system reliability of a stochasticflow network with failures at nodes and arcs,, Reliability Engineering and System Safety, 75 (2002), 41. doi: 10.1016/S09518320(01)001107. 
[21] 
Y. K. Lin, A stochastic model to study the system capacity for supply chains in terms of minimal cuts,, International Journal of Production Economics, 124 (2010), 181. doi: 10.1016/j.ijpe.2009.10.022. 
[22] 
J. S. Lin, C. C. Jane and J. Yuan, On reliability evaluation of a capacitatedflow network in terms of minimal pathsets,, Network, 25 (1995), 131. doi: 10.1002/net.3230250306. 
[23] 
A. Lisnianski and G. Levitin, "Multistate System Reliability: Assessment, Optimization and Application," 6th edition,, World Scientific, (2003). 
[24] 
Q. Liu, H. Zhang, X. Ma and Q. Zhao, Genetic algorithmbased study on flow allocation in a multicommodity stochasticflow network with unreliable nodes,, in, (2007), 576. doi: 10.1109/SNPD.2007.261. 
[25] 
J. Majumdar and A. K. Bhunia, Elitist genetic algorithm for assignment problem with imprecise goal,, European Journal of Operational Research, 177 (2007), 684. doi: 10.1016/j.ejor.2005.11.034. 
[26] 
R. Mookherjee, B. F. Hobbs, T. L. Friesz and M. A. Rigdon, Dynamic oligopolistic competition on an electric power network with ramping costs and joint sales constraints,, Journal of Industrial and Management Optimization, 4 (2008), 425. 
[27] 
L. Painton and J. Campbell, Genetic algorithms in optimization of system reliability,, IEEE Transactions on Reliability, 44 (1995), 172. doi: 10.1109/24.387368. 
[28] 
J. E. RamirezMarquez and C. M. Rocco, Stochastic network interdiction optimization via capacitated network reliability modeling and probabilistic solution discovery,, Reliability Engineering and System Safety, 94 (2009), 913. doi: 10.1016/j.ress.2008.10.006. 
[29] 
M. Srinivas and M. P. Lalit, Genetic algorithm: a survey,, IEEE Computer, 27 (1994), 18. 
[30] 
Y. Z. Wang, An application of genetic algorithm methods for teacher assignment problems,, Expert Systems with Applications, 22 (2002), 295. doi: 10.1016/S09574174(02)000179. 
[31] 
J. M. Wilson, A genetic algorithm for the generalized assignment problem,, Journal of the Operational Research Society, 48 (1997), 804. 
[32] 
W. Xu, S. He, R. Song and J. Li, Reliability based assignment in stochasticflow freight network,, Applied Mathematics and Computation, 211 (2009), 85. doi: 10.1016/j.amc.2009.01.024. 
[33] 
J. Xue, On multistate system analysis,, IEEE Transactions on Reliability, 34 (1985), 329. doi: 10.1109/TR.1985.5222178. 
[34] 
M. J. Yao and W. M. Chu, A genetic algorithm for determining optimal replenishment cycles to minimize maximum warehouse space requirements,, Omega, 36 (2008), 619. doi: 10.1016/j.omega.2007.01.007. 
[35] 
P. Zacharia, A. Menti and Th. Zacharias, Genetic algorithmbased optimal design of shunt compensators in the presence of harmonics,, Electric Power Systems Research, 78 (2008), 728. doi: 10.1016/j.epsr.2007.05.016. 
[36] 
A. Zeblah, Y. Massim, S. Hadjeri,A. Benaissa and H. Hamdaoui, Optimization for seriesparallel continuous power systems with buffers under reliability constraints using ant colony,, Journal of Industrial and Management Optimization, 2 (2006), 467. 
[37] 
M. J. Zuo, Z. Tian and H. Z. Huang, An efficient method for reliability evaluation of multistate networks given all minimal path vectors,, IIE Transactions, 39 (2007), 811. doi: 10.1080/07408170601013653. 
show all references
References:
[1] 
T. Aven, Reliability evaluation of multistate systems with multistate components,, IEEE Transactions on Reliability, 34 (1985), 473. doi: 10.1109/TR.1985.5222235. 
[2] 
S. T. Cheng, Topological optimization of a reliable communication network,, IEEE Transactions on Reliability, 47 (1998), 225. doi: 10.1109/24.740489. 
[3] 
M. L. F. Cheong, R. Bhatnagar and S. C. Graves, Logistics network design with supplier consolidation hubs and multiple shipment options,, Journal of Industrial and Management Optimization, 3 (2007), 51. 
[4] 
P. C. Chu and J. E. Beasley, A genetic algorithm for the generalized assignment problem,, Computers and Operations Research, 24 (1997), 17. doi: 10.1016/S03050548(96)000329. 
[5] 
D. Coit and A. Smith, Reliability optimization of seriesparallel systems using genetic algorithm,, IEEE Transactions on Reliability, 45 (1996), 254. doi: 10.1109/24.510811. 
[6] 
D. W. Coit and A. Smith, Penalty guided genetic search for reliability design optimization,, Computers and Industrial Engineering, 30 (1996), 895. doi: 10.1016/03608352(96)00040X. 
[7] 
C. J. Colbourn, "The Combinatorics of network Reliability,", Oxford University, (1987). 
[8] 
Z. Dzalilov, I. Ouveysi and A. Rubinov, An extended lifetime measure for telecommunication network,, Journal of Industrial and Management Optimization, 4 (2008), 329. 
[9] 
M. L. Fisher, R. Jaikumar and L. Van Wassenhove, A multiplier adjustment method for the generalised assignment problem,, Management Science, 32 (1986), 1095. doi: 10.1287/mnsc.32.9.1095. 
[10] 
L. R. Ford, and D. R. Fulkerson, "Flows in Networks,", Princeton University, (1962). 
[11] 
D. Goldberg, "Genetic Algorithms in Search, Optimization and Machine Learning,", AddisonWesley Press, (1989). 
[12] 
P. R. Harper, V. De Senna, I. T. Vieira and A. K. Shahani, A genetic algorithm for the project assignment problem,, Computers and Operations Research, 32 (2005), 1255. 
[13] 
C. C. Hsieh and Y. T. Chen, Reliable and economic resource allocation in an unreliable flow network,, Computer and Operations Research, 32 (2005), 613. doi: 10.1016/j.cor.2003.08.008. 
[14] 
C. C. Hsieh and Y. T. Chen, Resource allocation decisions under various demands and cost requirements in an unreliable flow network,, Computer and Operations Research, 32 (2005), 2771. doi: 10.1016/j.cor.2004.04.003. 
[15] 
C. C. Hsieh and M. H. Lin, Reliabilityoriented multiresource allocation in a stochasticflow network,, Reliability Engineering and System Safety, 81 (2003), 155. doi: 10.1016/S09518320(03)000826. 
[16] 
C. C. Jane and Y. W. Laih, A practical algorithm for computing multistate twoterminal reliability,, IEEE Transactions on Reliability, 57 (2008), 295. doi: 10.1109/TR.2008.920792. 
[17] 
C. C. Jane, J. S. Lin and J. Yuan, On reliability evaluation of a limitedflow network in terms of minimal cutsets,, IEEE Transactions on Reliability, 42 (1993), 354. doi: 10.1109/24.257817. 
[18] 
G. Levitin and A. Lisnianski, A new approach to solving problems of multistate system reliability optimization,, Quality Reliability Engineering International, 17 (2001), 93. doi: 10.1002/qre.388. 
[19] 
Y. K. Lin, A simple algorithm for reliability evaluation of a stochasticflow network with node failure,, Computer and Operations Research, 28 (2001), 1277. doi: 10.1016/S03050548(00)000393. 
[20] 
Y. K. Lin, Using minimal cuts to evaluate the system reliability of a stochasticflow network with failures at nodes and arcs,, Reliability Engineering and System Safety, 75 (2002), 41. doi: 10.1016/S09518320(01)001107. 
[21] 
Y. K. Lin, A stochastic model to study the system capacity for supply chains in terms of minimal cuts,, International Journal of Production Economics, 124 (2010), 181. doi: 10.1016/j.ijpe.2009.10.022. 
[22] 
J. S. Lin, C. C. Jane and J. Yuan, On reliability evaluation of a capacitatedflow network in terms of minimal pathsets,, Network, 25 (1995), 131. doi: 10.1002/net.3230250306. 
[23] 
A. Lisnianski and G. Levitin, "Multistate System Reliability: Assessment, Optimization and Application," 6th edition,, World Scientific, (2003). 
[24] 
Q. Liu, H. Zhang, X. Ma and Q. Zhao, Genetic algorithmbased study on flow allocation in a multicommodity stochasticflow network with unreliable nodes,, in, (2007), 576. doi: 10.1109/SNPD.2007.261. 
[25] 
J. Majumdar and A. K. Bhunia, Elitist genetic algorithm for assignment problem with imprecise goal,, European Journal of Operational Research, 177 (2007), 684. doi: 10.1016/j.ejor.2005.11.034. 
[26] 
R. Mookherjee, B. F. Hobbs, T. L. Friesz and M. A. Rigdon, Dynamic oligopolistic competition on an electric power network with ramping costs and joint sales constraints,, Journal of Industrial and Management Optimization, 4 (2008), 425. 
[27] 
L. Painton and J. Campbell, Genetic algorithms in optimization of system reliability,, IEEE Transactions on Reliability, 44 (1995), 172. doi: 10.1109/24.387368. 
[28] 
J. E. RamirezMarquez and C. M. Rocco, Stochastic network interdiction optimization via capacitated network reliability modeling and probabilistic solution discovery,, Reliability Engineering and System Safety, 94 (2009), 913. doi: 10.1016/j.ress.2008.10.006. 
[29] 
M. Srinivas and M. P. Lalit, Genetic algorithm: a survey,, IEEE Computer, 27 (1994), 18. 
[30] 
Y. Z. Wang, An application of genetic algorithm methods for teacher assignment problems,, Expert Systems with Applications, 22 (2002), 295. doi: 10.1016/S09574174(02)000179. 
[31] 
J. M. Wilson, A genetic algorithm for the generalized assignment problem,, Journal of the Operational Research Society, 48 (1997), 804. 
[32] 
W. Xu, S. He, R. Song and J. Li, Reliability based assignment in stochasticflow freight network,, Applied Mathematics and Computation, 211 (2009), 85. doi: 10.1016/j.amc.2009.01.024. 
[33] 
J. Xue, On multistate system analysis,, IEEE Transactions on Reliability, 34 (1985), 329. doi: 10.1109/TR.1985.5222178. 
[34] 
M. J. Yao and W. M. Chu, A genetic algorithm for determining optimal replenishment cycles to minimize maximum warehouse space requirements,, Omega, 36 (2008), 619. doi: 10.1016/j.omega.2007.01.007. 
[35] 
P. Zacharia, A. Menti and Th. Zacharias, Genetic algorithmbased optimal design of shunt compensators in the presence of harmonics,, Electric Power Systems Research, 78 (2008), 728. doi: 10.1016/j.epsr.2007.05.016. 
[36] 
A. Zeblah, Y. Massim, S. Hadjeri,A. Benaissa and H. Hamdaoui, Optimization for seriesparallel continuous power systems with buffers under reliability constraints using ant colony,, Journal of Industrial and Management Optimization, 2 (2006), 467. 
[37] 
M. J. Zuo, Z. Tian and H. Z. Huang, An efficient method for reliability evaluation of multistate networks given all minimal path vectors,, IIE Transactions, 39 (2007), 811. doi: 10.1080/07408170601013653. 
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