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

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Soft Computing Applications

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

Abstract

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.

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References

  1. Goldman, A.J.: Optimal location for centers in a network. Transportation Science 3, 352–360 (1969)

    Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  3. Campbell, J.F.: Integer programming formulations of discrete hub location problems. European Journal of Operational Research 72(2), 387–405 (1994)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  11. Elhedhli, S., Hu, F.X.: Hub-and-spoke network design with congestion. Computers & Operations Research 32(6), 1615–1632 (2005)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  14. Eiselt, H.A., Marianov, V.: A conditional p-hub location problem with attraction functions. Computers & Operations Research 36(12), 3128–3135 (2009)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  16. Kim, H., O’Kelly, M.E.: Reliable p-Hub Location Problems in Telecommunication Networks. Geographical Analysis 41, 283–306 (2009)

    Article  Google Scholar 

  17. Campbell, J.F.: Hub location for time definite transportation. Computers & Operations Research 36(12), 3107–3116 (2009)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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), 1047–1066

    Google Scholar 

  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)

    Article  Google Scholar 

  21. Lin, C.-C., Lee, S.-C.: The competition game on hub network design. Transportation Research Part B: Methodological 44(4), 618–629 (2010)

    Article  MathSciNet  Google Scholar 

  22. Ishfaq, R., Sox, C.R.: Hub location-allocation in intermodal logistic networks. European Journal of Operational Research 210(2), 213–230 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  24. Contreras, I., Cordeau, J.-F., Laporte, G.: Stochastic uncapacitated hub location. European Journal of Operational Research 212(3), 518–528 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  27. Yaman, H.: Allocation strategies in hub networks. European Journal of Operational Research 211(3), 442–451 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  30. Kratica, J., et al.: An evolutionary-based approach for solving a capacitated hub location problem. Applied Soft Computing 11(2), 1858–1866 (2011)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  34. Gelareh, S., Nickel, S.: Hub location problems in transportation networks. Transportation Research Part E: Logistics and Transportation Review 47(6), 1092–1111 (2011)

    Article  Google Scholar 

  35. Taghipourian, F., et al.: A fuzzy programming approach for dynamic virtual hub location problem. Applied Mathematical Modelling

    Google Scholar 

  36. Karimi, H., Bashiri, M.: Hub covering location problems with different coverage types. Scientia Iranica 18(6), 1571–1578 (2011)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. Alumur, S.A., Kara, B.Y., Karasan, O.E.: Multimodal hub location and hub network design. Omega 40(6), 927–939 (2012)

    Article  Google Scholar 

  40. Alumur, S.A., Nickel, S., Saldanha-da-Gama, F.: Hub location under uncertainty. Transportation Research Part B: Methodological 46(4), 529–543 (2012)

    Article  Google Scholar 

  41. Hwang, Y.H., Lee, Y.H.: Uncapacitated single allocation p-hub maximal covering problem. Computers & Industrial Engineering 63(2), 382–389 (2012)

    Article  MathSciNet  Google Scholar 

  42. Zhai, H., Liu, Y., Chen, W.: Applying Minimum-Risk Criterion to Stochastic Hub Location Problems. Procedia Engineering 29(0), 2313–2321 (2012)

    Article  Google Scholar 

  43. Peng, J., Liu, B.: Parallel machine scheduling models with fuzzy processing times. Information Sciences 166(1-4), 49–66 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  44. Zhao, R., Liu, B.: Standby redundancy optimization problems with fuzzy lifetimes. Computers & Industrial Engineering 49(2), 318–338 (2005)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  47. Huang, X.: Fuzzy chance-constrained portfolio selection. Applied Mathematics and Computation 177(2), 500–507 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  48. Yang, L., Liu, L.: Fuzzy fixed charge solid transportation problem and algorithm. Applied Soft Computing 7(3), 879–889 (2007)

    Article  Google Scholar 

  49. Zhou, J., Liu, B.: Modeling capacitated location-allocation problem with fuzzy demands. Computers & Industrial Engineering 53(3), 454–468 (2007)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  52. Liu, L., Gao, X.: Fuzzy weighted equilibrium multi-job assignment problem and genetic algorithm. Applied Mathematical Modelling 33(10), 3926–3935 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  55. Ke, H., Liu, B.: Fuzzy project scheduling problem and its hybrid intelligent algorithm. Applied Mathematical Modelling 34(2), 301–308 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  60. Yaman, H.: The hierarchical hub median problem with single assignment. Transportation Research Part B: Methodological 43(6), 643–658 (2009)

    Article  MathSciNet  Google Scholar 

  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. Blum, C., et al.: Hybrid metaheuristics in combinatorial optimization: A survey. Applied Soft Computing 11(6), 4135–4151 (2011)

    Article  Google Scholar 

  63. Stützle, T.: Iterated local search for the quadratic assignment problem. European Journal of Operational Research 174(3), 1519–1539 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  65. Laurent, B., Hao, J.-K.: Iterated local search for the multiple depot vehicle scheduling problem. Computers & Industrial Engineering 57(1), 277–286 (2009)

    Article  MathSciNet  Google Scholar 

  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. 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. Liu, B.: Uncertainty Theory, 3rd edn., http://orsc.edu.cn/liu/up.pdf

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Authors and Affiliations

  1. Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez Avenue, Tehran, Iran

    Soheil Davari & Mohammad Hossein Fazel Zarandi

Authors
  1. Soheil Davari
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  2. Mohammad Hossein Fazel Zarandi
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Corresponding author

Correspondence to Soheil Davari .

Editor information

Editors and Affiliations

  1. , Department of Automation & Applied Infor, Aurel Vlaicu University of Arad, Blvd. Revolutiei 77, Arad, 310130, Romania

    Valentina Emilia Balas

  2. , Institute of Intelligent Engineering, Óbuda University, Bécsi út 96/b, Budapest, 1034, Hungary

    János Fodor

  3. Dept. Measurement &, Information Systems, Technical University Budapest, Magyar tudósok körutja 2, Budapest, 1521, Hungary

    Annamária R. Várkonyi-Kóczy

  4. , Department of Informatics, University of Szeged, Arpad ter 2., Szeged, 6720, Hungary

    Joszef Dombi

  5. , School of Electrical and Information, University of South Australia, 5095, Adelaide, Australia

    Lakhmi C. Jain

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Davari, S., Fazel Zarandi, M.H. (2013). The Single-Allocation Hierarchical Hub-Median Problem with Fuzzy Flows. In: Balas, V., Fodor, J., Várkonyi-Kóczy, A., Dombi, J., Jain, L. (eds) Soft Computing Applications. Advances in Intelligent Systems and Computing, vol 195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33941-7_17

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  • DOI: https://doi.org/10.1007/978-3-642-33941-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33940-0

  • Online ISBN: 978-3-642-33941-7

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