Multi-period hub network design problems with modular capacities

Abstract

In this paper, a modeling framework is proposed for multi-period hub location. The problems to be studied are extensions of classical hub location problems to the situation in which the hub network can be progressively built and its capacity gradually expanded over time. Both the single allocation and the multiple allocation cases are considered. For each case, a mixed-integer linear programming formulation is proposed and a set of valid inequalities is derived for enhancing the corresponding model. The results of a set of computational tests performed using the formulations proposed and their enhancements are reported. The value of the multi-period solution is discussed as a measure for evaluating the relevance of considering a multi-period model instead of a static counterpart.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2

References

  1. Alumur, S., & Kara, B. (2008). Network hub location problems: The state of the art. European Journal of Operational Research, 190, 1–21.

    Article  Google Scholar 

  2. Alumur, S., Kara, B., & Karasan, O. (2009). The design of single allocation incomplete hub networks. Transportation Research Part B, 43, 936–951.

    Article  Google Scholar 

  3. Alumur, S., Kara, B., & Karasan, O. (2012). Multimodal hub location and hub network design. Omega, 40, 927–939.

    Article  Google Scholar 

  4. Alumur, S., Nickel, S., Saldanha-da-Gama, F., & Verter, V. (2012). Multi-period reverse logistics network design. European Journal of Operational Research, 220, 67–78.

    Article  Google Scholar 

  5. Beasley, J. E. (1990). OR library: Hub location. http://people.brunel.ac.uk/mastjjb/jeb/orlib/phubinfo.html.

  6. Boland, N., Krishnamoorthy, M., Ernst, A., & Ebery, J. (2004). Preprocessing and cutting for multiple allocation hub location problems. European Journal of Operational Research, 155, 638–653.

    Article  Google Scholar 

  7. Campbell, J. (1990). Locating transportation terminals to serve an expanding demand. Transportation Research Part B, 24, 173–192.

    Article  Google Scholar 

  8. Campbell, J., Ernst, A., & Krishnamoorthy, M. (2002). Facility location, applications and theory. Berlin: Springer. ch. Hub Location Problems.

    Google Scholar 

  9. Campbell, J. F., & O’Kelly, M. E. (2012). Twenty-five years of hub location research. Transportation Science, 46, 153–169.

    Article  Google Scholar 

  10. Contreras, I., Cordeau, J.-F., & Laporte, G. (2011). The dynamic uncapacitated hub location problem. Transportation Science, 45, 18–32.

    Article  Google Scholar 

  11. Contreras, I., Fernández, E., & Marín, A. (2010). The tree of hubs location problem. European Journal of Operational Research, 202, 390–400.

    Article  Google Scholar 

  12. Cordeau, J.-F., Pasin, F., & Solomon, M. M. (2006). An integrated model for logistics network design. Annals of Operations Research, 144, 59–82.

    Article  Google Scholar 

  13. Correia, I., Nickel, S., & Saldanha-da-Gama, F. (2010). Single-assignment hub location problems with multiple capacity levels. Transportation Research Part B, 44, 1047–1066.

    Article  Google Scholar 

  14. Ebery, J., Krishnamoorthy, M., Ernst, A., & Boland, N. (2000). The capacitated multiple allocation hub location problem: Formulations and algorithms. European Journal of Operational Research, 120, 614–631.

    Article  Google Scholar 

  15. Ernst, A., & Krishnamoorthy, M. (1999). Solution algorithms for the capacitated single allocation hub location problem. Annals of Operations Research, 86, 141–159.

    Article  Google Scholar 

  16. Ernst, A. T., & Krishnamoorthy, M. (1996). Efficient algorithms for the uncapacitated single allocation p-hub median problem. Location Science, 4, 139–154.

    Article  Google Scholar 

  17. Ernst, A. T., & Krishnamoorthy, M. (1998). Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub median problem. European Journal of Operational Research, 104, 100–112.

    Article  Google Scholar 

  18. Gelareh, S. (2008). Hub location models in public transport planning. PhD thesis, Vom Fachbereich Mathematik der Technischen Universität Kaiserslautern.

  19. Gelareh, S., & Nickel, S. (2011). Hub location problems in transportation networks. Transportation Research Part E, 47, 1092–1111.

    Article  Google Scholar 

  20. Melo, M., Nickel, S., & Saldanha-da-Gama, F. (2006). Dynamic multi-commodity capacitated facility location: A mathematical modeling framwork for strategic supply chain planning. Computers & Operations Research, 33, 181–208.

    Article  Google Scholar 

  21. Melo, M., Nickel, S., & Saldanha-da-Gama, F. (2009). Facility location and supply chain management a review. European Journal of Operational Research, 196, 1–12.

    Article  Google Scholar 

  22. Nickel, S., Schöbel, A., & Sonneborn, T. (2001). Mathematics methods and optimization in transportation systems. Berlin: Springer. ch. Hub Location Problems in Urban Traffic Networks.

    Google Scholar 

  23. O’Kelly, M. (1987). A quadratic integer problem for the location of interacting hub facilities. European Journal of Operational Research, 32, 393–404.

    Article  Google Scholar 

  24. Tan, P. Z., & Kara, B. Y. (2007). A hub covering model for cargo delivery systems. Networks, 49, 28–39.

    Article  Google Scholar 

  25. Yaman, H. (2008). Star p-hub median problem with modular arc capacities. Computers & Operations Research, 35(9), 3009–3019.

    Article  Google Scholar 

  26. Yoon, M.-G., & Current, J. (2008). The hub location and network design problem with fixed and variable costs: Formulation and dual-based solution heuristic. Journal of the Operational Research Society, 59, 80–89.

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Sibel A. Alumur.

Appendix

Appendix

See Tables 7 and 8.

Table 7 Performance of the valid inequalities with single allocation problem
Table 8 Performance of the valid inequalities with multiple allocation problem

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Alumur, S.A., Nickel, S., Saldanha-da-Gama, F. et al. Multi-period hub network design problems with modular capacities. Ann Oper Res 246, 289–312 (2016). https://doi.org/10.1007/s10479-015-1805-9

Download citation

Keywords

  • Hub location
  • Hub network design
  • Multi-period planning
  • Single allocation
  • Multiple allocation