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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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.

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