Mathematical Conditions for Profitability of Simple Logistic System Transformation to the Hub and Spoke Structure

  • Barbara Mażbic-Kulma
  • Jan W. OwsińskiEmail author
  • Jarosław Stańczak
  • Aleksy Barski
  • Krzysztof Sȩp
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1081)


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.


Hub and spoke Logistics Graphs Transportation systems Profitability 


  1. 1.
    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
  2. 2.
    Bailey, E.E.: Airline deregulation confronting the paradoxes. Regul. Cato Rev. Bus. Gover. 15(3), 18 (1992)Google Scholar
  3. 3.
    Cascetta, E.: Transportation Systems Analysis: Models and Applications, p. 742. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  4. 4.
    Cohen, R., Havin, S.: Complex Networks: Structure, Robustness and Function. Cambridge University Press, Cambridge (2010)CrossRefGoogle Scholar
  5. 5.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein. C.: Introduction to algorithms. The Massachusetts Institute of Technology (2009)Google Scholar
  6. 6.
    Erciyes, K.: Complex Networks: An Algorithmic Perspective, p. 320. CRC Press, Boca Raton (2014)CrossRefGoogle Scholar
  7. 7.
    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)zbMATHGoogle Scholar
  8. 8.
    Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graph. Computer Science and Mathematics, p. 284. New York University (1980)Google Scholar
  9. 9.
    Kaveh, A.: Optimal Analysis of Structures by Concepts of Symmetry and Regularity, p. 463. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    Möller, D.P.F.: Introduction to Transportation Analysis, Modeling and Simulation. Computational Foundations and Multimodal Applications, p. 343. Springer, Heidelberg (2014)zbMATHGoogle Scholar
  11. 11.
    O’Kelly, M.E.: A quadratic integer program for the location of interacting hub facilities. Eur. J. Oper. Res. 32, 392–404 (1987)MathSciNetzbMATHGoogle Scholar
  12. 12.
    O’Kelly, M.E., Bryan, D.: Interfacility interaction in models of hubs and spoke networks. J. Reg. Sci. 42(1), 145–165 (2002)CrossRefGoogle Scholar
  13. 13.
    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)Google Scholar
  14. 14.
    Schöbel, A.: Optimization in Public Transportation, Optimization and Its Applications . Springer, Heidelberg (2006)Google Scholar
  15. 15.
    Stańczak, J., Potrzebowski, H., Sȩp, K.: Evolutionary approach to obtain graph covering by densely connected subgraphs. Control Cybern. 41(3), 80–107 (2011)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Takes, F.W.: Algorithms for Analyzing and Mining Real-World Graphs, PhD thesis at Leiden University (2014)Google Scholar
  17. 17.
    Wilson, R.J.: Introduction to Graph Theory. Pearson Education, London (2012)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2021

Authors and Affiliations

  • Barbara Mażbic-Kulma
    • 1
  • Jan W. Owsiński
    • 1
    • 2
    Email author
  • Jarosław Stańczak
    • 1
    • 2
  • Aleksy Barski
    • 1
    • 2
  • Krzysztof Sȩp
    • 1
    • 2
  1. 1.Warsaw School of Information TechnologyWarszawaPoland
  2. 2.Systems Research InstitutePolish Academy of SciencesWarszawaPoland

Personalised recommendations