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A fullmodifiedNewton step infeasible interiorpoint algorithm for linear optimization
A compaction scheme and generator for distribution networks
1.  Department of Industrial and Information Management, National Cheng Kung University, Tainan, 701, Taiwan 
References:
[1] 
R. K. Ahuja, T. Magnanti and J. Orlin, Network Flows: Theory, Algorithms and Applications, Prentice Hall, Englewood Cliffs, New Jersey, 1993. 
[2] 
R. J. Anderson and J. C. Setubal, Goldberg's algorithm for maximum flow in perspective: A computatioinal study, in Network flows and matching: First DIMACS implementation challenge (eds. D. S. Johnson and C. McGeoch), 12, American Mathematical Society, (1993), 117. 
[3] 
U. Bahceci and O. Feyzioglu, A network simplex based algorithm for the minimum cost proportional flow problem with disconnected subnetworks, Optimization Letters, 6 (2012), 11731184. doi: 10.1007/s1159001103565. 
[4] 
M. D. Chang, C. H. J. Chen and M. Engquist, An improved primal simplex variant for pure processing networks, ACM Transactions on Mathematical Software, 15 (1989), 6478. doi: 10.1145/62038.62041. 
[5] 
C. H. J. Chen and M. Engquist, A primal simplex approach to pure processing networks, Management Science, 32 (1986), 15821598. doi: 10.1287/mnsc.32.12.1582. 
[6] 
B. V. Cherkassky and A. V. Goldberg, On implementing pushrelabel method for the maximum flow problem, Algorithmica, 19 (1997), 390410. doi: 10.1007/PL00009180. 
[7] 
B. T. Denton, J. Forrest and R. J. Milne, Ibm solves a mixedinteger program to optimize its semiconductor supplychain, Interfaces, 36 (2006), 386399. 
[8] 
S. C. Fang and L. Qi, Manufacturing network flows: A generalized network flow model for manufacturingprocess modeling, Optimization Methods and Software, 18 (2003), 143165. doi: 10.1080/1055678031000152079. 
[9] 
D. Goldfarb and M. D. Grigoriadis, A computational comparison of the dinic and network simplex methods formaximum flow, Annals of Operations Research, 13 (1988), 83123. doi: 10.1007/BF02288321. 
[10] 
D. Klingman, A. Napier and J. Stutz, Netgen: A program for generating large scale capacitated assignment, transportation and minimum cost flow networks, Management Science, 20 (1974), 814820. 
[11] 
J. Koene, Minimal Cost Flow in Processing Networks, a Primal Approach, PhD thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 1983. 
[12] 
L.C. Kung and C.C. Chern, Heuristic factory planning algorithm for advanced planning and scheduling, Computers and Operations Research, 36 (2009), 25132530. doi: 10.1016/j.cor.2008.09.013. 
[13] 
Y.K. Lin, C.T. Yeh and C.F. Huang, Reliability evaluation of a stochasticflow distribution network with delivery spoilage, Computers and Industrial Engineering, 66 (2013), 352359. doi: 10.1016/j.cie.2013.06.019. 
[14] 
H. Lu, E. Yao and L. Qi, Some further results on minimum distribution cost flow problems, Journal of Combinatorial Optimization, 11 (2006), 351371. 
[15] 
P. Lyon, R. J. Milne, R. Orzell and R. Rice, Matching assets with demand in supplychain management at ibm microelectronics, Interfaces, 31 (2001), 108124. doi: 10.1287/inte.31.1.108.9693. 
[16] 
R. L. Sheu, M. J. Ting and I. L. Wang, Maximum flow problem in the distribution network, Journal of Industrial and Management Optimization, 2 (2006), 237254. doi: 10.3934/jimo.2006.2.237. 
[17] 
J. Shu, M. Chou, Q. Liu, C.P. Teo and I.L. Wang, Models for effective deployment and redistribution of bicycles within public bicyclesharing systems, Operations, 61 (2013), 13461359. doi: 10.1287/opre.2013.1215. 
[18] 
I. L. Wang and S. J. Lin, A network simplex algorithm for solving the minimum distribution cost problem, Journal of Industrial and Management Optimization, 5 (2009), 929950. doi: 10.3934/jimo.2009.5.929. 
[19] 
I. L. Wang and Y. H. Yang, On solving the uncapacitated minimum cost flow problems in a distribution network, International Journal of Reliability and Quality Performance, 1 (2009), 5363. 
show all references
References:
[1] 
R. K. Ahuja, T. Magnanti and J. Orlin, Network Flows: Theory, Algorithms and Applications, Prentice Hall, Englewood Cliffs, New Jersey, 1993. 
[2] 
R. J. Anderson and J. C. Setubal, Goldberg's algorithm for maximum flow in perspective: A computatioinal study, in Network flows and matching: First DIMACS implementation challenge (eds. D. S. Johnson and C. McGeoch), 12, American Mathematical Society, (1993), 117. 
[3] 
U. Bahceci and O. Feyzioglu, A network simplex based algorithm for the minimum cost proportional flow problem with disconnected subnetworks, Optimization Letters, 6 (2012), 11731184. doi: 10.1007/s1159001103565. 
[4] 
M. D. Chang, C. H. J. Chen and M. Engquist, An improved primal simplex variant for pure processing networks, ACM Transactions on Mathematical Software, 15 (1989), 6478. doi: 10.1145/62038.62041. 
[5] 
C. H. J. Chen and M. Engquist, A primal simplex approach to pure processing networks, Management Science, 32 (1986), 15821598. doi: 10.1287/mnsc.32.12.1582. 
[6] 
B. V. Cherkassky and A. V. Goldberg, On implementing pushrelabel method for the maximum flow problem, Algorithmica, 19 (1997), 390410. doi: 10.1007/PL00009180. 
[7] 
B. T. Denton, J. Forrest and R. J. Milne, Ibm solves a mixedinteger program to optimize its semiconductor supplychain, Interfaces, 36 (2006), 386399. 
[8] 
S. C. Fang and L. Qi, Manufacturing network flows: A generalized network flow model for manufacturingprocess modeling, Optimization Methods and Software, 18 (2003), 143165. doi: 10.1080/1055678031000152079. 
[9] 
D. Goldfarb and M. D. Grigoriadis, A computational comparison of the dinic and network simplex methods formaximum flow, Annals of Operations Research, 13 (1988), 83123. doi: 10.1007/BF02288321. 
[10] 
D. Klingman, A. Napier and J. Stutz, Netgen: A program for generating large scale capacitated assignment, transportation and minimum cost flow networks, Management Science, 20 (1974), 814820. 
[11] 
J. Koene, Minimal Cost Flow in Processing Networks, a Primal Approach, PhD thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 1983. 
[12] 
L.C. Kung and C.C. Chern, Heuristic factory planning algorithm for advanced planning and scheduling, Computers and Operations Research, 36 (2009), 25132530. doi: 10.1016/j.cor.2008.09.013. 
[13] 
Y.K. Lin, C.T. Yeh and C.F. Huang, Reliability evaluation of a stochasticflow distribution network with delivery spoilage, Computers and Industrial Engineering, 66 (2013), 352359. doi: 10.1016/j.cie.2013.06.019. 
[14] 
H. Lu, E. Yao and L. Qi, Some further results on minimum distribution cost flow problems, Journal of Combinatorial Optimization, 11 (2006), 351371. 
[15] 
P. Lyon, R. J. Milne, R. Orzell and R. Rice, Matching assets with demand in supplychain management at ibm microelectronics, Interfaces, 31 (2001), 108124. doi: 10.1287/inte.31.1.108.9693. 
[16] 
R. L. Sheu, M. J. Ting and I. L. Wang, Maximum flow problem in the distribution network, Journal of Industrial and Management Optimization, 2 (2006), 237254. doi: 10.3934/jimo.2006.2.237. 
[17] 
J. Shu, M. Chou, Q. Liu, C.P. Teo and I.L. Wang, Models for effective deployment and redistribution of bicycles within public bicyclesharing systems, Operations, 61 (2013), 13461359. doi: 10.1287/opre.2013.1215. 
[18] 
I. L. Wang and S. J. Lin, A network simplex algorithm for solving the minimum distribution cost problem, Journal of Industrial and Management Optimization, 5 (2009), 929950. doi: 10.3934/jimo.2009.5.929. 
[19] 
I. L. Wang and Y. H. Yang, On solving the uncapacitated minimum cost flow problems in a distribution network, International Journal of Reliability and Quality Performance, 1 (2009), 5363. 
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