Annals of Operations Research

, Volume 264, Issue 1–2, pp 1–40 | Cite as

Modelling and analysis of hub-and-spoke networks under stochastic demand and congestion

  • Nader Azizi
  • Navneet Vidyarthi
  • Satyaveer S. Chauhan
Original Paper
  • 106 Downloads

Abstract

Motivated by the strategic importance of congestion management, in this paper we present a model to design hub-and-spoke networks under stochastic demand and congestion. The proposed model determines the location and capacity of the hub nodes and allocate non-hub nodes to these hubs while minimizing the sum of the fixed cost, transportation cost and the congestion cost. In our approach, hubs are modelled as spatially distributed M/G/1 queues and congestion is captured using the expected queue lengths at hub facilities. A simple transformation and a piecewise linear approximation technique are used to linearize the resulting nonlinear model. We present two solution approaches: an exact method that uses a cutting plane approach and a novel genetic algorithm based heuristic. The numerical experiments are conducted using CAB and TR datasets. Analysing the results obtained from a number of problem instances, we illustrate the impact of congestion cost on the network topology and show that substantial reduction in congestion can be achieved with a small increase in total cost if congestion at hub facilities is considered at the design stage. The computational results further confirm the stability and efficiency of both exact and heuristic approaches.

Keywords

Hub-and-spoke Congestion Cutting plane approach Genetic algorithm 

References

  1. Abdinnour-Helm, S. (2001). Using simulated annealing to solve the p-hub median problem. International Journal of Physical Distribution and Logistics Management, 31(3), 203–220.CrossRefGoogle Scholar
  2. Abdinnour-Helm, S., & Venkataramanan, M. A. (1998). Solution approaches to hub location problems. Annals of Operations Research, 78, 31–50.CrossRefGoogle Scholar
  3. Alumur, S., & Kara, B. Y. (2008). Network hub location problems: The state-of-the-art. European Journal of Operational Research, 190, 1–21.CrossRefGoogle Scholar
  4. Alumur, S. A., Nickel, S., & Saldanha da Gama, F. (2012). Hub location under uncertainty. Transportation Research: Part B, 46, 529–543.CrossRefGoogle Scholar
  5. Azizi, N. (2017). Managing facility disruption in hub-and-spoke networks: Formulations and efficient solution methods. Annals of Operations Research,. doi: 10.1007/s10479-017-2517-0.Google Scholar
  6. Azizi, N., Chauhan, S., Salhi, S., & Vidyarthi, N. (2016). The impact of hub failure in hub-and-spoke networks: Mathematical formulations and solution techniques. Computers & Operations Research, 65, 74–188.CrossRefGoogle Scholar
  7. Boffey, B., Galvao, R., & Espejo, L. (2007). A review of congestion models in the location of facilities with immobile servers. European Journal of Operational Research, 178(3), 643–662.CrossRefGoogle Scholar
  8. Bryan, D. L., & O’Kelly, M. E. (1999). Hub-and-spoke networks in air transportation: An analytical review. Journal of Regional Science, 39(2), 275–295.CrossRefGoogle Scholar
  9. de Camargo, R. S., Miranda, G, Jr., & Ferreira, R. P. M. (2011). A hybrid outer approximation/benders decomposition algorithm for the single allocation hub location problem under congestion. Operations Research Letters, 39(12), 329–337.CrossRefGoogle Scholar
  10. de Camargo, R. S., Miranda, G, Jr., Ferreira, R. P. M., & Luna, H. P. (2009a). Multiple allocation hub-and-spoke network design under hub congestion. Computers and Operations Research, 36(12), 3097–3106.CrossRefGoogle Scholar
  11. de Camargo, R. S., Miranda, G, Jr., & Luna, H. P. (2009b). Benders decomposition for the hub location problems with economies of scale. Transportation Science, 43(1), 86–97.CrossRefGoogle Scholar
  12. Campbell, J. F. (1994). Integer programming formulations of discrete hub location problems. European Journal of Operational Research, 72, 387–405.CrossRefGoogle Scholar
  13. Campbell, J. F., & O’Kelly, M. E. (2012). Twenty-five years of hub location research. Transportation Science, 46(2), 153–169.CrossRefGoogle Scholar
  14. Carello, G., Della Croce, F., Ghirardi, M., & Tadei, R. (2004). Solving the hub location problem in telecommunication network design: A local search approach. Networks, 44(2), 94–105.CrossRefGoogle Scholar
  15. Cetiner, S., Sepil, C., & Sural, H. (2010). Hubbing and routing in postal delivery systems. Annals of Operations Research, 181, 109–124.CrossRefGoogle Scholar
  16. Cheung, R. K., & Muralidharan, B. (1999). Impact of dynamic decision making on hub-and-spoke freight transportation networks. Annals of Operations Research, 87, 49–71.CrossRefGoogle Scholar
  17. Contreras, I., Cordeau, J.-F., & Laporte, G. (2012). Exact solution of large-scale hub location problems with multiple capacity levels. Transportation Science, 46, 439–459.CrossRefGoogle Scholar
  18. Contreras, I., Díaz, J. A., & Fernández, E. (2009). Lagrangean relaxation for the capacitated hub location problem with single assigment. OR Spectrum, 31(3), 483–505.Google Scholar
  19. Contreras, I., Diaz, J. A., & Fernandez, E. (2011). Branch-and-price for large-scale capacitated problems with single assignment. INFORMS Journal on Computing, 23(1), 41–55.CrossRefGoogle Scholar
  20. 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.CrossRefGoogle Scholar
  21. Cunha, C. B., & Silva, M. R. (2007). A genetic algorithm for the problem of configuring a hub- and-spoke network for a LTL trucking company in Brazil. European Journal of Operational Research, 179, 747–758.CrossRefGoogle Scholar
  22. Ebery, J. (2001). Solving large single allocation p-hub location problems with two or three hubs. European Journal of Operational Research, 128, 447–458.CrossRefGoogle Scholar
  23. Elhedhli, S. (2005). Exact solution of a class of nonlinear knapsack problems. Operations Research Letters, 33, 615–624.CrossRefGoogle Scholar
  24. Elhedhli, S., & Hu, F. X. (2005). Hub-and-spoke network design with congestion. Computers and Operations Research, 32, 1615–1632.CrossRefGoogle Scholar
  25. Elhedhli, S., & Wu, H. (2010). A Lagrangean heuristic for hub-and-spoke system design with capacity selection and congestion. INFORMS Journal of Computing, 22(2), 282–296.CrossRefGoogle Scholar
  26. Ernst, A. T., & Krishnamoorthy, M. (1996). Efficient algorithms for the uncapacitated single allocation p-hub median problem. Location Science, 4(3), 139–154.CrossRefGoogle Scholar
  27. 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.CrossRefGoogle Scholar
  28. Ernst, A. T., & Krishnamoorthy, M. (1999). Solution algorithms for the capacitated single allocation hub location problem. Annals of Operations Research, 86, 141–159.CrossRefGoogle Scholar
  29. Grove, P. G., & O’Kelly, M. E. (1986). Hub networks and simulated schedule delay. Papers of the Regional Science Association, 59, 103–119.CrossRefGoogle Scholar
  30. Guldmann, J. M., & Shen, G. (1997). A general mixed integer nonlinear optimization model for hub network design. Working paper, Department of City and Regional Planning, The Ohio State University, Columbus, Ohio.Google Scholar
  31. Ilic, A., Urosevic, D., Brimberg, J., & Mladenovic, N. (2010). A general variable neighbourhood search for solving the uncapacitated single allocation p-hub median problem. European Journal of Operational Research, 206, 289–300.CrossRefGoogle Scholar
  32. Jeong, S.-J., Lee, C. G., & Bookbinder, J. H. (2007). The European freight railway system as a hub-and-spoke network. Transportation Research Part A, 41, 523–536.Google Scholar
  33. Klincewicz, J. G. (1992). Avoiding local optima in the p-hub location problem using tabu search and GRASP. Annals of Operations Research, 40, 283–302.CrossRefGoogle Scholar
  34. Klincewicz, J. G. (1998). Hub location in backbone/tributary network design: A review. Location Science, 6, 307–335.CrossRefGoogle Scholar
  35. Koksalan, M., & Soylu, B. (2010). Bicriteria p-hub location problems and evolutionary algorithms. INFORMS Journal of Computing, 22(4), 528–542.CrossRefGoogle Scholar
  36. Kratica, J., Stanimirovic, Z., Tosic, D., & Filipovic, V. (2007). Two genetic algorithms for solving the uncapacitated single allocation p-hub median problem. European Journal of Operational Research, 182(1), 15–28.CrossRefGoogle Scholar
  37. Lapierre, S. D., Ruiz, A. B., & Soriano, P. (2004). Designing distribution networks: Formulations and solution heuristic. Transportation Science, 38, 174–187.CrossRefGoogle Scholar
  38. Marianov, V., & Serra, D. (2003). Location models for airline hubs behaving as M/D/c queues. Computer and Operations Research, 30, 983–1003.CrossRefGoogle Scholar
  39. Martin, J. C., & Roman, C. (2004). Analyzing competition for hub location in intercontinental aviation markets. Transportation Research Part E, 40, 135–150.CrossRefGoogle Scholar
  40. Mayer, C., & Sinai, T. (2003). Network effects, congestion externalities, and air traffic delays: Or why not all delays are evil. American Economic Review, 93(4), 1194–1215.CrossRefGoogle Scholar
  41. Nickel, S., Schobel, A., & Sonneborn, T. (2001). Hub location problems in urban traffic networks. In J. Niittymaki & M. Pursula (Eds.), Mathematical methods and optimization in transportation systems (pp. 95–107). Dordrecht: Kluwer Academic Publisher.CrossRefGoogle Scholar
  42. O’Kelly, M. E. (1986). The location of interacting hub facilities. Transportation Science, 20, 92–106.CrossRefGoogle Scholar
  43. O’Kelly, M. E. (1987). A quadratic integer program for the location of interacting hub facilities. European Journal of Operational Research, 32, 393–404.CrossRefGoogle Scholar
  44. O’Kelly, M. E., Skorin-Kapov, D., & Skorin-Kapov, S. (1995). Lower bounds for the hub location problem. Management Science, 41(4), 713–721.CrossRefGoogle Scholar
  45. Salhi, S. (2017). Heuristic search: The emerging science of problem solving. Berlin: Springer.CrossRefGoogle Scholar
  46. Skorin-Kapov, D., & Skorin-Kapov, J. (1994). On tabu search for the location of interacting hub facilities. European Journal of Operational Research, 73(3), 501–508.CrossRefGoogle Scholar
  47. Skorin-Kapov, D., Skorin-Kapov, J., & O’Kelly, M. E. (1996). Tight linear programming relaxations of uncapacitated p-hub median problems. European Journal of Operational Research, 94, 582–593.CrossRefGoogle Scholar
  48. Smith, K., Krishnamoorthy, M., & Palaniswami, M. (1996). Neural versus traditional approaches to the location of interacting hub facilities. Location Science, 4(3), 155–171.CrossRefGoogle Scholar
  49. Vidyarthi, N. K., Elhedhli, S., & Jewkes, E. M. (2009). Response time reduction in make-to-order and assemble-to-order supply chain design. IIE Transactions, 41(5), 448–466.CrossRefGoogle Scholar
  50. Yaman, H., & Carello, G. (2005). Solving the hub location problem with modular link capacities. Computers and Operations Research, 32, 3227–3245.CrossRefGoogle Scholar
  51. Yaman, H., Kara, B. Y., & Tansel, B. C. (2007). The latest arrival hub location problem for cargo delivery systems with stopovers. Transportation Research B, 41(8), 906–919.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Kent Business SchoolUniversity of KentCanterburyUK
  2. 2.John Molson School of BusinessConcordia UniversityMontrealCanada

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