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Enhanced formulations and branch-and-cut for the two level network design problem with transition facilities

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  • Gollowitzer, Stefan
  • Gouveia, Luis
  • Ljubić, Ivana

Abstract

We consider a new combinatorial optimization problem that combines network design and facility location aspects. Given a graph with two types of customers and two technologies that can be installed on the edges, the objective is to find a minimum cost subtree connecting all customers while the primary customers are served by a primary subtree that is embedded into the secondary subtree. In addition, besides fixed link installation costs, facility opening costs, associated to each node where primary and secondary subtree connect, have to be paid. The problem is called the Two Level Network Design Problem with Transition Facilities (TLNDF).

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:225:y:2013:i:2:p:211-222
    DOI: 10.1016/j.ejor.2012.09.040
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    References listed on IDEAS

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    1. Anantaram Balakrishnan & Thomas L. Magnanti & Prakash Mirchandani, 1994. "Modeling and Heuristic Worst-Case Performance Analysis of the Two-Level Network Design Problem," Management Science, INFORMS, vol. 40(7), pages 846-867, July.
    2. Anantaram Balakrishnan & Thomas L. Magnanti & Prakash Mirchandani, 1994. "A Dual-Based Algorithm for Multi-Level Network Design," Management Science, INFORMS, vol. 40(5), pages 567-581, May.
    3. Duin, Cees & Volgenant, Anton, 1989. "Reducing the hierarchical network design problem," European Journal of Operational Research, Elsevier, vol. 39(3), pages 332-344, April.
    4. Current, John & Pirkul, Hasan, 1991. "Theory and methodologyThe hierarchical network design problem with transshipment facilities," European Journal of Operational Research, Elsevier, vol. 51(3), pages 338-347, April.
    5. 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.
    6. 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.
    7. Contreras, Ivan & Fernández, Elena, 2012. "General network design: A unified view of combined location and network design problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 680-697.
    8. Current, John R. & ReVelle, Charles S. & Cohon, Jared L., 1986. "The hierarchical network design problem," European Journal of Operational Research, Elsevier, vol. 27(1), pages 57-66, October.
    9. Gouveia, Luis & Janssen, Eric, 1998. "Designing reliable tree networks with two cable technologies," European Journal of Operational Research, Elsevier, vol. 105(3), pages 552-568, March.
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