The Single-Allocation Hierarchical Hub-Median Problem with Fuzzy Flows

Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 195)


This paper addresses the problem of designing a hierarchical single-allocation hub-median (SA-H-HM) network considering fuzzy flows between nodes. The problem is modeled as a fuzzy mathematical programming model and a hybrid algorithm of population-based iterated local search (PILS) and fuzzy simulation is employed. Results clearly show that PILS is efficient in reaching solutions with virtually all the errors less than one percent to the optimal solutions. Moreover, the proposed PILS is capable to escape local optima. Finally, the results of the hybrid algorithm give insights about the problem under uncertainty.


Iterated local search Facility location Hub-and-spoke Optimization Simulation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Goldman, A.J.: Optimal location for centers in a network. Transportation Science 3, 352–360 (1969)Google Scholar
  2. 2.
    O’Kelly, M.E.: A quadratic integer program for the location of interacting hub facilities. European Journal of Operational Research 32(3), 393–404 (1987)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Campbell, J.F.: Integer programming formulations of discrete hub location problems. European Journal of Operational Research 72(2), 387–405 (1994)MATHCrossRefGoogle Scholar
  4. 4.
    Alumur, S., Kara, B.Y.: Network hub location problems: The state of the art. European Journal of Operational Research 190(1), 1–21 (2008)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    CalIk, H., et al.: A tabu-search based heuristic for the hub covering problem over incomplete hub networks. Computers & Operations Research 36(12), 3088–3096 (2009)MATHCrossRefGoogle Scholar
  6. 6.
    Cunha, C.B., Silva, M.R.: 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(3), 747–758 (2007)MATHCrossRefGoogle Scholar
  7. 7.
    Meyer, T., Ernst, A.T., Krishnamoorthy, M.: A 2-phase algorithm for solving the single allocation p-hub center problem. Computers & Operations Research 36(12), 3143–3151 (2009)MATHCrossRefGoogle Scholar
  8. 8.
    Ilic, A., et al.: A general variable neighborhood search for solving the uncapacitated single allocation p-hub median problem. European Journal of Operational Research 206(2), 289–300 (2010)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Campbell, J.F., Ernst, A.T., Krishnamoorthy, M.: Hub arc location problems: Part I – Introduction and results. Management Science 51(10), 1540–1555 (2005)MATHCrossRefGoogle Scholar
  10. 10.
    Campbell, J.F., Ernst, A.T., Krishnamoorthy, M.: Hub arc location problems: Part II – Formulations and optimal algorithms. Management Science 51(10), 1556–1571 (2005)MATHCrossRefGoogle Scholar
  11. 11.
    Elhedhli, S., Hu, F.X.: Hub-and-spoke network design with congestion. Computers & Operations Research 32(6), 1615–1632 (2005)CrossRefGoogle Scholar
  12. 12.
    Yaman, H., Kara, B.Y., Tansel, B.Ç.: The latest arrival hub location problem for cargo delivery systems with stopovers. Transportation Research Part B: Methodological 41(8), 906–919 (2007)CrossRefGoogle Scholar
  13. 13.
    Rodríguez, V., Alvarez, M.J., Barcos, L.: Hub location under capacity constraints. Transportation Research Part E: Logistics and Transportation Review 43(5), 495–505 (2007)CrossRefGoogle Scholar
  14. 14.
    Eiselt, H.A., Marianov, V.: A conditional p-hub location problem with attraction functions. Computers & Operations Research 36(12), 3128–3135 (2009)MATHCrossRefGoogle Scholar
  15. 15.
    Sim, T., Lowe, T.J., Thomas, B.W.: The stochastic p-hub center problem with service-level constraints. Computers & Operations Research 36(12), 3166–3177 (2009)MATHCrossRefGoogle Scholar
  16. 16.
    Kim, H., O’Kelly, M.E.: Reliable p-Hub Location Problems in Telecommunication Networks. Geographical Analysis 41, 283–306 (2009)CrossRefGoogle Scholar
  17. 17.
    Campbell, J.F.: Hub location for time definite transportation. Computers & Operations Research 36(12), 3107–3116 (2009)MATHCrossRefGoogle Scholar
  18. 18.
    Alumur, S.A., Kara, B.Y., Karasan, O.E.: The design of single allocation incomplete hub networks. Transportation Research Part B: Methodological 43(10), 936–951 (2009)CrossRefGoogle Scholar
  19. 19.
    Correia, I., Nickel, S., Saldanha-da-Gama, F.: Single-assignment hub location problems with multiple capacity levels. Transportation Research Part B: Methodological 44(8-9), 1047–1066Google Scholar
  20. 20.
    Gelareh, S., Nickel, S., Pisinger, D.: Liner shipping hub network design in a competitive environment. Transportation Research Part E: Logistics and Transportation Review 46(6), 991–1004 (2010)CrossRefGoogle Scholar
  21. 21.
    Lin, C.-C., Lee, S.-C.: The competition game on hub network design. Transportation Research Part B: Methodological 44(4), 618–629 (2010)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Ishfaq, R., Sox, C.R.: Hub location-allocation in intermodal logistic networks. European Journal of Operational Research 210(2), 213–230 (2011)MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Menou, A., et al.: Decision support for centralizing cargo at a Moroccan airport hub using stochastic multicriteria acceptability analysis. European Journal of Operational Research 204(3), 621–629 (2010)MATHCrossRefGoogle Scholar
  24. 24.
    Contreras, I., Cordeau, J.-F., Laporte, G.: Stochastic uncapacitated hub location. European Journal of Operational Research 212(3), 518–528 (2011)MathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    Correia, I., Nickel, S., Saldanha-da-Gama, F.: Hub and spoke network design with single-assignment, capacity decisions and balancing requirements. Applied Mathematical Modelling 35(10), 4841–4851 (2011)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Catanzaro, D., et al.: A branch-and-cut algorithm for the partitioning-hub location-routing problem. Computers & Operations Research 38(2), 539–549 (2011)MathSciNetMATHCrossRefGoogle Scholar
  27. 27.
    Yaman, H.: Allocation strategies in hub networks. European Journal of Operational Research 211(3), 442–451 (2011)MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Puerto, J., Ramos, A.B., Rodríguez-Chía, A.M.: Single-allocation ordered median hub location problems. Computers & Operations Research 38(2), 559–570 (2011)MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    Vasconcelos, A.D., Nassi, C.D., Lopes, L.A.S.: The uncapacitated hub location problem in networks under decentralized management. Computers & Operations Research 38(12), 1656–1666 (2011)MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    Kratica, J., et al.: An evolutionary-based approach for solving a capacitated hub location problem. Applied Soft Computing 11(2), 1858–1866 (2011)CrossRefGoogle Scholar
  31. 31.
    Mohammadi, M., Jolai, F., Rostami, H.: An M/M/c queue model for hub covering location problem. Mathematical and Computer Modelling 54(11-12), 2623–2638 (2011)MathSciNetMATHCrossRefGoogle Scholar
  32. 32.
    Sender, J., Clausen, U.: A new hub location model for network design of wagonload traffic. Procedia - Social and Behavioral Sciences 20(0), 90–99 (2011)CrossRefGoogle Scholar
  33. 33.
    Hansen, P., Mladenovic, N.: Design of a reliable hub-and-spoke network using an interactive fuzzy goal programming. European Journal of Operational Research 130, 449–467 (2011)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Gelareh, S., Nickel, S.: Hub location problems in transportation networks. Transportation Research Part E: Logistics and Transportation Review 47(6), 1092–1111 (2011)CrossRefGoogle Scholar
  35. 35.
    Taghipourian, F., et al.: A fuzzy programming approach for dynamic virtual hub location problem. Applied Mathematical ModellingGoogle Scholar
  36. 36.
    Karimi, H., Bashiri, M.: Hub covering location problems with different coverage types. Scientia Iranica 18(6), 1571–1578 (2011)CrossRefGoogle Scholar
  37. 37.
    de Camargo, R.S., Miranda, G.: Single allocation hub location problem under congestion: Network owner and user perspectives. Expert Systems with Applications 39(3), 3385–3391 (2012)CrossRefGoogle Scholar
  38. 38.
    Fazel Zarandi, M.H., Davari, S., Haddad Sisakht, S.A.: The Q-coverage multiple allocation hub covering problem with mandatory dispersion. Scientia Iranica (2012)Google Scholar
  39. 39.
    Alumur, S.A., Kara, B.Y., Karasan, O.E.: Multimodal hub location and hub network design. Omega 40(6), 927–939 (2012)CrossRefGoogle Scholar
  40. 40.
    Alumur, S.A., Nickel, S., Saldanha-da-Gama, F.: Hub location under uncertainty. Transportation Research Part B: Methodological 46(4), 529–543 (2012)CrossRefGoogle Scholar
  41. 41.
    Hwang, Y.H., Lee, Y.H.: Uncapacitated single allocation p-hub maximal covering problem. Computers & Industrial Engineering 63(2), 382–389 (2012)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Zhai, H., Liu, Y., Chen, W.: Applying Minimum-Risk Criterion to Stochastic Hub Location Problems. Procedia Engineering 29(0), 2313–2321 (2012)CrossRefGoogle Scholar
  43. 43.
    Peng, J., Liu, B.: Parallel machine scheduling models with fuzzy processing times. Information Sciences 166(1-4), 49–66 (2004)MathSciNetMATHCrossRefGoogle Scholar
  44. 44.
    Zhao, R., Liu, B.: Standby redundancy optimization problems with fuzzy lifetimes. Computers & Industrial Engineering 49(2), 318–338 (2005)CrossRefGoogle Scholar
  45. 45.
    Zheng, Y., Liu, B.: Fuzzy vehicle routing model with credibility measure and its hybrid intelligent algorithm. Applied Mathematics and Computation 176(2), 673–683 (2006)MathSciNetMATHCrossRefGoogle Scholar
  46. 46.
    Liu, L., Li, Y.: The fuzzy quadratic assignment problem with penalty: New models and genetic algorithm. Applied Mathematics and Computation 174(2), 1229–1244 (2006)MathSciNetMATHCrossRefGoogle Scholar
  47. 47.
    Huang, X.: Fuzzy chance-constrained portfolio selection. Applied Mathematics and Computation 177(2), 500–507 (2006)MathSciNetMATHCrossRefGoogle Scholar
  48. 48.
    Yang, L., Liu, L.: Fuzzy fixed charge solid transportation problem and algorithm. Applied Soft Computing 7(3), 879–889 (2007)CrossRefGoogle Scholar
  49. 49.
    Zhou, J., Liu, B.: Modeling capacitated location-allocation problem with fuzzy demands. Computers & Industrial Engineering 53(3), 454–468 (2007)CrossRefGoogle Scholar
  50. 50.
    Erbao, C., Mingyong, L.: A hybrid differential evolution algorithm to vehicle routing problem with fuzzy demands. Journal of Computational and Applied Mathematics 231(1), 302–310 (2009)MathSciNetMATHCrossRefGoogle Scholar
  51. 51.
    Lan, Y.-F., Liu, Y.-K., Sun, G.-J.: Modeling fuzzy multi-period production planning and sourcing problem with credibility service levels. Journal of Computational and Applied Mathematics 231(1), 208–221 (2009)MathSciNetMATHCrossRefGoogle Scholar
  52. 52.
    Liu, L., Gao, X.: Fuzzy weighted equilibrium multi-job assignment problem and genetic algorithm. Applied Mathematical Modelling 33(10), 3926–3935 (2009)MathSciNetMATHCrossRefGoogle Scholar
  53. 53.
    Davari, S., Fazel Zarandi, M.H., Hemmati, A.: Maximal Covering Location Problem (MCLP) with fuzzy travel times. Expert Systems with Applications 38(12), 14535–14541 (2011)CrossRefGoogle Scholar
  54. 54.
    Li, X., et al.: A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns. Journal of Computational and Applied Mathematics 233(2), 264–278 (2009)MathSciNetMATHCrossRefGoogle Scholar
  55. 55.
    Ke, H., Liu, B.: Fuzzy project scheduling problem and its hybrid intelligent algorithm. Applied Mathematical Modelling 34(2), 301–308 (2010)MathSciNetMATHCrossRefGoogle Scholar
  56. 56.
    Wen, M., Kang, R.: Some optimal models for facility location-allocation problem with random fuzzy demands. Applied Soft Computing 11(1), 1202–1207 (2011)CrossRefGoogle Scholar
  57. 57.
    Fazel Zarandi, M.H., Hemmati, A., Davari, S.: The multi-depot capacitated location-routing problem with fuzzy travel times. Expert Systems with Applications 38(8), 10075–10084 (2011)CrossRefGoogle Scholar
  58. 58.
    Davari, S., Fazel Zarandi, M.H.: The single-allocation hierarchical hub median location problem with fuzzy demands. African Journal of Business Manegement 6(1), 347–360 (2012)Google Scholar
  59. 59.
    Lau, H.C.W., et al.: A credibility-based fuzzy location model with Hurwicz criteria for the design of distribution systems in B2C e-commerce. Computers & Amp; Industrial Engineering 59(4), 873–886 (2010)CrossRefGoogle Scholar
  60. 60.
    Yaman, H.: The hierarchical hub median problem with single assignment. Transportation Research Part B: Methodological 43(6), 643–658 (2009)MathSciNetCrossRefGoogle Scholar
  61. 61.
    Kara, B.Y.: Modeling and analysis of issues in hub location problems. Ph.D. Thesis, in Industrial Engineering Department, Bilkent University (1999)Google Scholar
  62. 62.
    Blum, C., et al.: Hybrid metaheuristics in combinatorial optimization: A survey. Applied Soft Computing 11(6), 4135–4151 (2011)CrossRefGoogle Scholar
  63. 63.
    Stützle, T.: Iterated local search for the quadratic assignment problem. European Journal of Operational Research 174(3), 1519–1539 (2006)MathSciNetMATHCrossRefGoogle Scholar
  64. 64.
    Hashimoto, H., Yagiura, M., Ibaraki, T.: An iterated local search algorithm for the time-dependent vehicle routing problem with time windows. Discrete Optimization 5(2), 434–456 (2008)MathSciNetMATHCrossRefGoogle Scholar
  65. 65.
    Laurent, B., Hao, J.-K.: Iterated local search for the multiple depot vehicle scheduling problem. Computers & Industrial Engineering 57(1), 277–286 (2009)MathSciNetCrossRefGoogle Scholar
  66. 66.
    Josef Geiger, M.: Decision support for multi-objective flow shop scheduling by the Pareto Iterated Local Search methodology. Computers & Industrial Engineering. Corrected Proof (in press)Google Scholar
  67. 67.
    Derbel, H., et al.: An Iterated Local Search for Solving A Location-Routing Problem. Electronic Notes in Discrete Mathematics 36, 875–882 (2010)Google Scholar
  68. 68.
    Liu, B.: Uncertainty Theory, 3rd edn.,

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Soheil Davari
    • 1
  • Mohammad Hossein Fazel Zarandi
    • 1
  1. 1.Department of Industrial EngineeringAmirkabir University of TechnologyTehranIran

Personalised recommendations