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Optimal acquisition, inventory and production decisions for a closedloop manufacturing system with legislation constraint
Optimal doubleresource assignment for a distributed multistate network
1.  Department of Industrial Management, Tungnan University, New Taipei City, 222, Taiwan 
References:
[1] 
R. P. Agdeppa, N. Yamashita and M. Fukushima, An implicit programming approach for the road pricing problem with nonadditive route costs,, Journal of Industrial and Management Optimization, 4 (2008), 183. doi: 10.3934/jimo.2008.4.183. Google Scholar 
[2] 
T. Aven, Reliability evaluation of multistate systems with multistate components,, IEEE Transactions on Reliability, R34 (1985), 473. doi: 10.1109/TR.1985.5222235. Google Scholar 
[3] 
M. O. Ball, Computational complexity of network reliability analysis: An overview,, IEEE Transactions on Reliability, 35 (1986), 230. doi: 10.1109/TR.1986.4335422. Google Scholar 
[4] 
H. M. Bidhandi and R. M. Yusuff, Integrated supply chain planning under uncertainty using an improved stochastic approach,, Applied Mathematical Modelling, 35 (2011), 2618. doi: 10.1016/j.apm.2010.11.042. Google Scholar 
[5] 
S. G. Chen, Search for all minimal paths in a general directed flow network with unreliable nodes,, International Journal of Reliability and Quality Performance, 2 (2011), 63. Google Scholar 
[6] 
S.G. Chen, An optimal capacity assignment for the robust design problem in capacitated flow networks,, Applied Mathematical Modelling, 36 (2012), 5272. doi: 10.1016/j.apm.2011.12.034. Google Scholar 
[7] 
S.G. Chen, Optimal doubleresource assignment for the robust design problem in multistate computer networks,, Applied Mathematical Modelling, 38 (2014), 263. doi: 10.1016/j.apm.2013.06.020. Google Scholar 
[8] 
S.G. Chen and Y.K. Lin, Search for all minimal paths in a general large flow network,, IEEE Transactions on Reliability, 61 (2012), 949. Google Scholar 
[9] 
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. Google Scholar 
[10] 
C. J. Colbourn, The Combinatorics of Network Reliability,, Oxford University Press, (1987). Google Scholar 
[11] 
I. Correia, S. Nickel and F. S. da Gama, Hub and spoke network design with singleassignment, capacity decisions and balancing requirements,, Applied Mathematical Modelling, 35 (2011), 4841. doi: 10.1016/j.apm.2011.03.046. Google Scholar 
[12] 
L. R. Ford and D. R. Fulkerson, Flows in Networks,, NJ: Princeton University Press, (1962). Google Scholar 
[13] 
B. Gavish and I. Neuman, A system for routing and capacity assignment in computer communication networks,, IEEE Transactions on Communications, 37 (1989), 360. doi: 10.1109/26.20116. Google Scholar 
[14] 
J. D. Glover, M. Sarma and T. Overbye, Power System Analysis & Design,, 5th edition, (2008). Google Scholar 
[15] 
W. S. Griffith, Multistate reliability models,, Journal of Applied Probability, 17 (1980), 735. doi: 10.2307/3212967. Google Scholar 
[16] 
C. C. Hsieh and Y. T. Chen, Reliable and economic resource allocation in an unreliable flow network,, Computers and Operations Research, 32 (2005), 613. doi: 10.1016/j.cor.2003.08.008. Google Scholar 
[17] 
J. C. Hudson and K. C. Kapur, Reliability analysis for multistate systems with multistate components,, IIE Transactions, 15 (1983), 127. doi: 10.1080/05695558308974623. Google Scholar 
[18] 
J. C. Hudson and K. C. Kapur, Reliability bounds for multistate systems with multistate components,, Operations Research, 33 (1985), 153. doi: 10.1287/opre.33.1.153. Google Scholar 
[19] 
C. C. Jane and Y. W. Laih, A practical algorithm for computing multistate twoterminal reliability,, IEEE Transactions on Reliability, 57 (2008), 295. Google Scholar 
[20] 
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. Google Scholar 
[21] 
Y.K. Lin, System capacity for a twocommodity multistate flow network with unreliable nodes and capacity weight,, Computers and Operations Research, 34 (2007), 3043. doi: 10.1016/j.cor.2005.11.013. Google Scholar 
[22] 
Y.K. Lin and C.T. Yeh, Optimal resource assignment to maximize multistate network reliability for a computer network,, Computers & Operations Research, 37 (2010), 2229. doi: 10.1016/j.cor.2010.03.013. Google Scholar 
[23] 
Y.K. Lin and C.T. Yeh, Computer network reliability optimization under doubleresource assignments subject to a transmission budget,, Information Sciences, 181 (2011), 582. doi: 10.1016/j.ins.2010.09.036. Google Scholar 
[24] 
Y.K. Lin and C.T. Yeh, Determine the optimal doublecomponent assignment for a stochastic computer network,, Omega, 40 (2012), 120. doi: 10.1016/j.omega.2011.04.002. Google Scholar 
[25] 
K. Murakami and H. S. Kim, Joint optimization of capacity and flow assignment for selfhealing ATM networks,, in IEEE International Conference on Communications, 1 (1995), 216. doi: 10.1109/ICC.1995.525168. Google Scholar 
[26] 
D. W. Pentico, Assignment problems, a golden anniversary survey,, European Journal of Operational Research, 176 (2007), 774. doi: 10.1016/j.ejor.2005.09.014. Google Scholar 
[27] 
Y. Shen, A new simple algorithm for enumerating all minimal paths and cuts of a graph,, Microelectronics and Reliability, 35 (1995), 973. doi: 10.1016/00262714(94)001214. Google Scholar 
[28] 
E. D. Sykas, On the capacity assignment problem in packetswitching computer networks,, Applied Mathematical Modelling, 10 (1986), 346. doi: 10.1016/0307904X(86)900946. Google Scholar 
[29] 
W. L. Winston, Introduction to Mathematical Programming: Application and Algorithms,, Duxbury Press, (1995). Google Scholar 
[30] 
J. Xue, On multistate system analysis,, IEEE Transactions on Reliability, 34 (1985), 329. Google Scholar 
[31] 
Q. Yang, S. Song and C. Wu, Inventory policies for a partially observed supply capacity model,, Journal of Industrial and Management Optimization, 9 (2013), 13. doi: 10.3934/jimo.2013.9.13. Google Scholar 
[32] 
W. C. Yeh, Search for minimal paths in modified networks,, Reliability Engineering & System Safety, 75 (2002), 389. doi: 10.1016/S09518320(01)001284. Google Scholar 
[33] 
W. C. Yeh, A new approach to evaluating reliability of multistate networks under the cost constraint,, Omega, 33 (2005), 203. doi: 10.1016/j.omega.2004.04.005. Google Scholar 
[34] 
A. F. Zantuti, Algorithms for capacities and flow assignment problem in computer networks,, in 19th International Conference on Systems Engineering, (2008), 315. doi: 10.1109/ICSEng.2008.24. Google Scholar 
[35] 
X. Zhang, D. Wang, H. Sun and K. S. Trivedi, A BDDbased algorithm for analysis of multistate systems with multistate components,, IEEE Transactions on Computers, 52 (2003), 1608. Google Scholar 
[36] 
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. Google Scholar 
show all references
References:
[1] 
R. P. Agdeppa, N. Yamashita and M. Fukushima, An implicit programming approach for the road pricing problem with nonadditive route costs,, Journal of Industrial and Management Optimization, 4 (2008), 183. doi: 10.3934/jimo.2008.4.183. Google Scholar 
[2] 
T. Aven, Reliability evaluation of multistate systems with multistate components,, IEEE Transactions on Reliability, R34 (1985), 473. doi: 10.1109/TR.1985.5222235. Google Scholar 
[3] 
M. O. Ball, Computational complexity of network reliability analysis: An overview,, IEEE Transactions on Reliability, 35 (1986), 230. doi: 10.1109/TR.1986.4335422. Google Scholar 
[4] 
H. M. Bidhandi and R. M. Yusuff, Integrated supply chain planning under uncertainty using an improved stochastic approach,, Applied Mathematical Modelling, 35 (2011), 2618. doi: 10.1016/j.apm.2010.11.042. Google Scholar 
[5] 
S. G. Chen, Search for all minimal paths in a general directed flow network with unreliable nodes,, International Journal of Reliability and Quality Performance, 2 (2011), 63. Google Scholar 
[6] 
S.G. Chen, An optimal capacity assignment for the robust design problem in capacitated flow networks,, Applied Mathematical Modelling, 36 (2012), 5272. doi: 10.1016/j.apm.2011.12.034. Google Scholar 
[7] 
S.G. Chen, Optimal doubleresource assignment for the robust design problem in multistate computer networks,, Applied Mathematical Modelling, 38 (2014), 263. doi: 10.1016/j.apm.2013.06.020. Google Scholar 
[8] 
S.G. Chen and Y.K. Lin, Search for all minimal paths in a general large flow network,, IEEE Transactions on Reliability, 61 (2012), 949. Google Scholar 
[9] 
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. Google Scholar 
[10] 
C. J. Colbourn, The Combinatorics of Network Reliability,, Oxford University Press, (1987). Google Scholar 
[11] 
I. Correia, S. Nickel and F. S. da Gama, Hub and spoke network design with singleassignment, capacity decisions and balancing requirements,, Applied Mathematical Modelling, 35 (2011), 4841. doi: 10.1016/j.apm.2011.03.046. Google Scholar 
[12] 
L. R. Ford and D. R. Fulkerson, Flows in Networks,, NJ: Princeton University Press, (1962). Google Scholar 
[13] 
B. Gavish and I. Neuman, A system for routing and capacity assignment in computer communication networks,, IEEE Transactions on Communications, 37 (1989), 360. doi: 10.1109/26.20116. Google Scholar 
[14] 
J. D. Glover, M. Sarma and T. Overbye, Power System Analysis & Design,, 5th edition, (2008). Google Scholar 
[15] 
W. S. Griffith, Multistate reliability models,, Journal of Applied Probability, 17 (1980), 735. doi: 10.2307/3212967. Google Scholar 
[16] 
C. C. Hsieh and Y. T. Chen, Reliable and economic resource allocation in an unreliable flow network,, Computers and Operations Research, 32 (2005), 613. doi: 10.1016/j.cor.2003.08.008. Google Scholar 
[17] 
J. C. Hudson and K. C. Kapur, Reliability analysis for multistate systems with multistate components,, IIE Transactions, 15 (1983), 127. doi: 10.1080/05695558308974623. Google Scholar 
[18] 
J. C. Hudson and K. C. Kapur, Reliability bounds for multistate systems with multistate components,, Operations Research, 33 (1985), 153. doi: 10.1287/opre.33.1.153. Google Scholar 
[19] 
C. C. Jane and Y. W. Laih, A practical algorithm for computing multistate twoterminal reliability,, IEEE Transactions on Reliability, 57 (2008), 295. Google Scholar 
[20] 
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. Google Scholar 
[21] 
Y.K. Lin, System capacity for a twocommodity multistate flow network with unreliable nodes and capacity weight,, Computers and Operations Research, 34 (2007), 3043. doi: 10.1016/j.cor.2005.11.013. Google Scholar 
[22] 
Y.K. Lin and C.T. Yeh, Optimal resource assignment to maximize multistate network reliability for a computer network,, Computers & Operations Research, 37 (2010), 2229. doi: 10.1016/j.cor.2010.03.013. Google Scholar 
[23] 
Y.K. Lin and C.T. Yeh, Computer network reliability optimization under doubleresource assignments subject to a transmission budget,, Information Sciences, 181 (2011), 582. doi: 10.1016/j.ins.2010.09.036. Google Scholar 
[24] 
Y.K. Lin and C.T. Yeh, Determine the optimal doublecomponent assignment for a stochastic computer network,, Omega, 40 (2012), 120. doi: 10.1016/j.omega.2011.04.002. Google Scholar 
[25] 
K. Murakami and H. S. Kim, Joint optimization of capacity and flow assignment for selfhealing ATM networks,, in IEEE International Conference on Communications, 1 (1995), 216. doi: 10.1109/ICC.1995.525168. Google Scholar 
[26] 
D. W. Pentico, Assignment problems, a golden anniversary survey,, European Journal of Operational Research, 176 (2007), 774. doi: 10.1016/j.ejor.2005.09.014. Google Scholar 
[27] 
Y. Shen, A new simple algorithm for enumerating all minimal paths and cuts of a graph,, Microelectronics and Reliability, 35 (1995), 973. doi: 10.1016/00262714(94)001214. Google Scholar 
[28] 
E. D. Sykas, On the capacity assignment problem in packetswitching computer networks,, Applied Mathematical Modelling, 10 (1986), 346. doi: 10.1016/0307904X(86)900946. Google Scholar 
[29] 
W. L. Winston, Introduction to Mathematical Programming: Application and Algorithms,, Duxbury Press, (1995). Google Scholar 
[30] 
J. Xue, On multistate system analysis,, IEEE Transactions on Reliability, 34 (1985), 329. Google Scholar 
[31] 
Q. Yang, S. Song and C. Wu, Inventory policies for a partially observed supply capacity model,, Journal of Industrial and Management Optimization, 9 (2013), 13. doi: 10.3934/jimo.2013.9.13. Google Scholar 
[32] 
W. C. Yeh, Search for minimal paths in modified networks,, Reliability Engineering & System Safety, 75 (2002), 389. doi: 10.1016/S09518320(01)001284. Google Scholar 
[33] 
W. C. Yeh, A new approach to evaluating reliability of multistate networks under the cost constraint,, Omega, 33 (2005), 203. doi: 10.1016/j.omega.2004.04.005. Google Scholar 
[34] 
A. F. Zantuti, Algorithms for capacities and flow assignment problem in computer networks,, in 19th International Conference on Systems Engineering, (2008), 315. doi: 10.1109/ICSEng.2008.24. Google Scholar 
[35] 
X. Zhang, D. Wang, H. Sun and K. S. Trivedi, A BDDbased algorithm for analysis of multistate systems with multistate components,, IEEE Transactions on Computers, 52 (2003), 1608. Google Scholar 
[36] 
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. Google Scholar 
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