Abstract
Optimization of logistic systems is one of the most important challenges in the modern world. Fast, cheap and reliable transportation systems are necessary to warrant stable development of global economy. To optimize the transportation system it is necessary to build a model of it. Transportation systems are usually modeled using graphs. In such graphs the nodes are equivalents of railway stations, bus stops, airports, etc., and the edges model connections or transfers among them. Graph models of logistic systems are often unstructured with accidental connections between nodes. However, optimization of such irregular connection structure can be done by conversion to a hub & spoke network structure. After this conversion a new shape of the logistic network is created, where the identified main nodes - hubs have direct, fast and high capacity connections among themselves, and the secondary nodes - spokes are connected only with their hubs. In this new graph there are only a few types of connections, having often very similar properties. It is possible to maintain almost equal transportation parameters across the whole network. This means a great progress compared to the traditional “peer-to-peer" network. In return, it is possible to improve the frequency and/or duration of journeys in the modified graph. First of all, though, it is necessary to establish the profitability conditions for such a transformation. This subject is discussed in the present work.
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References
Bast, H., Delling, D., Goldberg, A., Müller-Hannemann, M., Pajor, T., Sanders, P., Wagner, D., Werneck, R.F.: Route planning in transportation networks. Cornell University Library (2015). arXiv:1504.05140
Bailey, E.E.: Airline deregulation confronting the paradoxes. Regul. Cato Rev. Bus. Gover. 15(3), 18 (1992)
Cascetta, E.: Transportation Systems Analysis: Models and Applications, p. 742. Springer, Heidelberg (2009)
Cohen, R., Havin, S.: Complex Networks: Structure, Robustness and Function. Cambridge University Press, Cambridge (2010)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein. C.: Introduction to algorithms. The Massachusetts Institute of Technology (2009)
Erciyes, K.: Complex Networks: An Algorithmic Perspective, p. 320. CRC Press, Boca Raton (2014)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness, p. 344. W.H. Freeman and Company, New York (1979)
Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graph. Computer Science and Mathematics, p. 284. New York University (1980)
Kaveh, A.: Optimal Analysis of Structures by Concepts of Symmetry and Regularity, p. 463. Springer, Heidelberg (2013)
Möller, D.P.F.: Introduction to Transportation Analysis, Modeling and Simulation. Computational Foundations and Multimodal Applications, p. 343. Springer, Heidelberg (2014)
O’Kelly, M.E.: A quadratic integer program for the location of interacting hub facilities. Eur. J. Oper. Res. 32, 392–404 (1987)
O’Kelly, M.E., Bryan, D.: Interfacility interaction in models of hubs and spoke networks. J. Reg. Sci. 42(1), 145–165 (2002)
Owsiński, J.W., Stańczak, J., Barski, A., Sȩp, K., Sapiecha, P.: Graph based approach to the minimum hub problem in transportation network. Proc. FEDCSiS 2015, 1641–1648 (2015)
Schöbel, A.: Optimization in Public Transportation, Optimization and Its Applications . Springer, Heidelberg (2006)
Stańczak, J., Potrzebowski, H., Sȩp, K.: Evolutionary approach to obtain graph covering by densely connected subgraphs. Control Cybern. 41(3), 80–107 (2011)
Takes, F.W.: Algorithms for Analyzing and Mining Real-World Graphs, PhD thesis at Leiden University (2014)
Wilson, R.J.: Introduction to Graph Theory. Pearson Education, London (2012)
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Mażbic-Kulma, B., Owsiński, J.W., Stańczak, J., Barski, A., Sȩp, K. (2021). Mathematical Conditions for Profitability of Simple Logistic System Transformation to the Hub and Spoke Structure. In: Atanassov, K., et al. Uncertainty and Imprecision in Decision Making and Decision Support: New Challenges, Solutions and Perspectives. IWIFSGN 2018. Advances in Intelligent Systems and Computing, vol 1081. Springer, Cham. https://doi.org/10.1007/978-3-030-47024-1_37
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