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An Augmented Arborescence Formulation for the Two-Level Network Design Problem


  • Luis Gouveia


  • João Telhada



In this paper we discuss formulations for the Two Level Network Design (TLND) problem. In particular, we present an arborescence based formulation with extra constraints guaranteeing that the set of primary nodes is spanned by primary edges. This characterization suggests an arborescence based Lagrangian relaxation where the extra constraints are dualized. Although the Linear Programming (LP) value of the new formulation is proved to be theoretically weaker than the LP bound given by the flow based formulation presented by Balakrishnan, Magnanti and Mirchandani, our computational results show that for certain classes of instances the two LP bounds are quite close. Our results also show that the Lagrangian relaxation based method is quite efficient, providing a reasonable alternative to handle the problem. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Luis Gouveia & João Telhada, 2001. "An Augmented Arborescence Formulation for the Two-Level Network Design Problem," Annals of Operations Research, Springer, vol. 106(1), pages 47-61, September.
  • Handle: RePEc:spr:annopr:v:106:y:2001:i:1:p:47-61:10.1023/a:1014553523631
    DOI: 10.1023/A:1014553523631

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    Cited by:

    1. 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.
    2. 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.


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