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The Hierarchical Network Design Problem: A New Formulation and Solution Procedures

Author

Listed:
  • Hasan Pirkul

    (College of Business, The Ohio State University, Columbus, Ohio 43210-1399)

  • John Current

    (College of Business, The Ohio State University, Columbus, Ohio 43210-1399)

  • V. Nagarajan

    (College of Business, The Ohio State University, Columbus, Ohio 43210-1399)

Abstract

In this paper we develop a new heuristic for the hierarchical network design problem. The heuristic is based upon Lagrangian relaxation of a reformulation of the problem. In addition, we develop a branch and bound algorithm to identify the optimal solution for the 5% of the test problems for which the new heuristic failed to do so. This algorithm proved to be very efficient due to the tight bounds generated by the heuristic.

Suggested Citation

  • Hasan Pirkul & John Current & V. Nagarajan, 1991. "The Hierarchical Network Design Problem: A New Formulation and Solution Procedures," Transportation Science, INFORMS, vol. 25(3), pages 175-182, August.
    • Handle: RePEc:inm:ortrsc:v:25:y:1991:i:3:p:175-182
    DOI: 10.1287/trsc.25.3.175
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    Citations

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    Cited by:

    1. J. Beasley & E. Nascimento, 1996. "The Vehicle Routing-Allocation Problem: A unifying framework," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 65-86, June.
    2. Eusebio Angulo & Ricardo García-Ródenas & José Luis Espinosa-Aranda, 2016. "A Lagrangian relaxation approach for expansion of a highway network," Annals of Operations Research, Springer, vol. 246(1), pages 101-126, November.
    3. Obreque, Carlos & Donoso, Macarena & Gutiérrez, Gabriel & Marianov, Vladimir, 2010. "A branch and cut algorithm for the hierarchical network design problem," European Journal of Operational Research, Elsevier, vol. 200(1), pages 28-35, January.
    4. Eduardo Álvarez-Miranda & Ivana Ljubić & S. Raghavan & Paolo Toth, 2015. "The Recoverable Robust Two-Level Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 1-19, February.
    5. Sancho, N. G. F., 1995. "A suboptimal solution to a hierarchial network design problem using dynamic programming," European Journal of Operational Research, Elsevier, vol. 83(1), pages 237-244, May.
    6. Balakrishnan, Anantaram. & Magnanti, Thomas L. & Mirchandani, Prakash., 1991. "A dual-based algorithm for multi-level network design," Working papers 3365-91., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. Miyagawa, Masashi, 2011. "Hierarchical system of road networks with inward, outward, and through traffic," Journal of Transport Geography, Elsevier, vol. 19(4), pages 591-595.
    8. Mesa, Juan A. & Brian Boffey, T., 1996. "A review of extensive facility location in networks," European Journal of Operational Research, Elsevier, vol. 95(3), pages 592-603, December.
    9. Masashi Miyagawa, 2014. "Optimal allocation of area in hierarchical road networks," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 53(2), pages 617-630, September.
    10. Gollowitzer, Stefan & Gouveia, Luis & Ljubić, Ivana, 2013. "Enhanced formulations and branch-and-cut for the two level network design problem with transition facilities," European Journal of Operational Research, Elsevier, vol. 225(2), pages 211-222.
    11. Sancho, N. G. F., 1997. "The hierarchical network design problem with multiple primary paths," European Journal of Operational Research, Elsevier, vol. 96(2), pages 323-328, January.

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