Abstract
This paper presents a method of modeling and solving a very complicated real logistic problem in the management of transportation and sales. The problem to be addressed is a large-scale multicommodity, multi-source and multi-sink network flow optimization, of 12 types of coal from 29 mines, through over 200 railway stations along 5 railroad arteries, in Chongqing Coal Industry Company of China. A minimum-cost flow model is established for the network system, and several maximal-flow algorithms are implemented to produce an optimal scheme.
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Aggarwal, A.K., Oblak, M., Vemuganti, R.R.: A heuristic solution procedure for multicommodity integer flows. Computer Operation Research 22(10), 1075–1087 (1995)
Ahuja, R.K., Kodialam, M., Mishra, A.K., Orlin, J.B.: Computational investigations of maximum flow algorithms. European J. of Operational Research 97, 509–554 (1997)
Anderson, R.J., Sctubal, J.C.: Parallel and sequential implementations of maximum flow algorithms. In: Johnson, D.S., McGeoch, C.C. (eds.) Network Flows and Matching: First DIMACS Implementation Challenge. AMS, Providence (1993)
Aringhierie, R., Cordone, R.: The Multicommodity Multilevel Bottleneck Assignment Problem. Electronic Notes in Discrete Mathematics 17, 35–40 (2004)
Asano, T., Asano, Y.: Recent developments in maximum flow algorithms. Journal of the Operations Research Society of Japan 43(1), 2–31 (2000)
Assad, A.: Multicommodity network flows, a survey. Networks 8, 37–91 (1978)
Badics, T., Boros, E., Cepek, O.: Implementing a new maximum flow algorithm. In: Johnson, D.S., McGeoch, C.C. (eds.) Network Flows and Matching: First DIMACS Implementation Challenge. AMS, Providence (1993)
Beasley, J.E., Cao, B.: A Dynamic Programming based algorithm for the Crew Scheduling Problem. Computers & Operations Research 53, 567–582 (1998)
Bertsekas, D.P.: An auction algorithm for the max-flow problem. In: IEEE Conference on the Foundations of Computer Science, pp. 118–123 (1994)
Calvete, H.I.: Network simplex algorithm for the general equal flow problem. European J. of Operational Research 150, 585–600 (2003)
Cappanera, P., Gallo, G.: On the Airline Crew Rostering Problem. European J. of Operational Research 150 (2003)
Carraresi, P., Gallo, G.: A Multi-level Bottleneck Assignment Approach to the bus drivers’ roistering problem. European J. of Operational Res. 16, 163–173 (1984)
Curet, N.D., DeVinney, J., Gaston, M.E.: An efficient network flow code for finding all minimum cost s-t cutsets. Computers & Operations Research 29, 205–219 (2002)
Derigs, U., Meier, W.: Implementing Goldberg’s max-flow algorithm: A computational investigation. Zeitschrift fur Operations Research 33, 383–403 (1989)
Dinic, E.A.: Algorithm for solution of a problem of maximum flow in networks with power estimation. Soviet Math. Doklady 11, 1277–1280 (1970)
Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM 19, 248–264 (1972)
Evans, J.R.: The simplex method for integral multicommodity networks. Naval Res. Logistics 4, 31–37 (1978)
Evans, J.R.: Reducing computational effort in detecting integral multicommodity networks. Computation Operation Research 7, 261–265 (1980)
Ford Jr., L.R., Fulkerson, D.R.: Maximal flow through a network. Canad. J. Math. 8, 399–404 (1956)
Gabrela, V., Knippelb, A., Minouxb, M.: Exact solution of multicommodity network optimization problems with general step cost functions. Operations Research Letters 25, 15–23 (1999)
Gabow, H.N.: Scaling algorithms for network flow problems. Journal of Computer and System Sciences 31, 148–168 (1985)
Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum flow problem. Journal of the ACM 35, 921–940 (1988)
Goldfarb, D., Grigoriadis, M.D.: A computational comparison of the Dinic and network simplex methods for maximum flow. Annals of Operations Research 13, 83–123 (1988)
Goldfarb, D., Hao, J.: On strongly polynomial variants of the network simplex algorithm for the maximum flow problem. Operations Res. Letters 10, 383–387 (1991)
Haghani, A., Oh, S.: Formulation and solution of a multicommodity, multi-modal network flow model for disaster relief operations. Transportation Research 30(3), 231–250 (1996)
Hassin, R.: On multicommodity flows in planar graphs. Networks 14, 225–235 (1984)
Karzanov, A.V.: Determining the maximal flow in a network by the method of preflows. Soviet Math. Doklady 15, 434–437 (1974)
Kennington, J., Helgason, R.: Algorithms for Network Programming. John Wiley & Sons, New York (1980)
Li, H.-X.: A Study on Optimization of Transportation and sale of A Variety of Coal in Chongqing Area, Master’s Degree Thesis, Xi’an Univ. of Science & Tech (1993)
Lomonosov, M.V.: On the planar integer two-flow problem. Combinatorica 3, 207–218 (1983)
Nguyen, Q.C., Venkateshwaran, V.: Implementations of the Goldberg Tarjan maximum flow algorithm. In: Johnson, D.S., McGeoch, C.C. (eds.) Network Flows and Matching: First DIMACS Implementation Challenge. AMS, Providence (1993)
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Li, H., Tian, S., Pan, Y., Zhang, X., Yu, X. (2005). Minimum-Cost Optimization in Multicommodity Logistic Chain Network. In: Li, H., Olver, P.J., Sommer, G. (eds) Computer Algebra and Geometric Algebra with Applications. IWMM GIAE 2004 2004. Lecture Notes in Computer Science, vol 3519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499251_10
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DOI: https://doi.org/10.1007/11499251_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26296-1
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