Abstract
The following chapter deals with flow problems in transportation networks in terms of fuzziness. Literature review considering flows and basic problem statements is given. The task of maximum flow finding in transportation network with lower flow bounds in fuzzy conditions is described and solved. The necessity of considering dynamic transportation networks is explained. The task of maximum flow finding with lower flow bounds in fuzzy conditions in dynamic network is solved. Peculiarity of the considered task is in fuzzy and transit nature of the network parameters.
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References
Bozhenyuk, A., Gerasimenko, E., Rozenberg, I.: Algorithm of maximum dynamic flow finding in a fuzzy transportation network. In: Proceedings of East West Fuzzy Colloquium 2012 19th Fuzzy Colloquium 5–7 September, pp. 125–132 (2012)
Bozhenyuk, A., Gerasimenko, E., Rozenberg, I.: The task of minimum cost flow finding in transportation networks in fuzzy conditions. In: 10th International FLINS Conference on Uncertainty Modeling in Knowledge Engineering and Decision Making 26–29 August 2012, pp. 354–359. Word Scientific, Istanbul (2012)
Chabini, I., Abou-Zeid, M.: The minimum cost flow problem in capacitated dynamic networks. In: Annual Meeting of the Transportation Research Board, pp. 1–30. Washington (2003)
Christofides, N.: Graph Theory: An Algorithmic Approach. Academic Press, New York (1975)
Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. J. Assoc. Comput. Mach. 19(2), 248–264 (1972)
Fonoberova, M., Lozovanu, D.: The maximum flow in dynamic networks. Comput. Sci. J. Moldova. 12, 3(36), 387–396 (2004)
Ford, L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton (1962)
Goldberg, A.V., Rao, S.: Beyond the flow decomposition barrier. J. Assoc. Comput. Mach. 45, 753–782 (1998)
Hu, T.C.: Integer Programming and Network Flows. Addison-Wesley Publishing Company, Ontario (1970)
Melkonian, V.: Flows in dynamic networks with aggregate arc capacities. Inf. Process. Lett. 101(1), 30–35 (2007)
Minieka, E.: Optimization Algorithms for Networks and Graphs. Marcel Dekker Inc, New York (1978)
Murty, K.G.: Network Programming. Prentice Hall, NJ (1992)
Nasrabadi, E., Hashemi, S.M.: Minimum cost time-varying network flow problems. Optim. Methods Softw. 25(3), 429–447 (2010)
Powell, W., Jaillet, P., Odoni, A.: Stochastic and Dynamic Networks and Routing. In: Ball, M.O., Magnanti, T.L., Monma C.L., Nemhauser, G.L. (eds.) Handbook in Operations Research and Management Science, 8, pp. 141–296. Network Routing, Elsevier, Amsterdam (1995)
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Bozhenyuk, A., Gerasimenko, E. (2014). Flows Finding in Networks in Fuzzy Conditions. In: Kahraman, C., Öztayşi, B. (eds) Supply Chain Management Under Fuzziness. Studies in Fuzziness and Soft Computing, vol 313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53939-8_12
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DOI: https://doi.org/10.1007/978-3-642-53939-8_12
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