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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/11499251_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26296-1
Online ISBN: 978-3-540-32119-4
eBook Packages: Computer ScienceComputer Science (R0)