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A branch and cut algorithm for the hierarchical network design problem

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  • Obreque, Carlos
  • Donoso, Macarena
  • Gutiérrez, Gabriel
  • Marianov, Vladimir

Abstract

The Hierarchical Network Design Problem consists of locating a minimum cost bi-level network on a graph. The higher level sub-network is a path visiting two or more nodes. The lower level sub-network is a forest connecting the remaining nodes to the path. We optimally solve the problem using an ad hoc branch and cut procedure. Relaxed versions of a base model are solved using an optimization package and, if binary variables have fractional values or if some of the relaxed constraints are violated in the solution, cutting planes are added. Once no more cuts can be added, branch and bound is used. The method for finding valid cutting planes is presented. Finally, we use different available test instances to compare the procedure with the best known published optimal procedure, with good results. In none of the instances we needed to apply branch and bound, but only the cutting planes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:1:p:28-35
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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. 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.
    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. 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.
    8. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    9. John R. Current, 1988. "The Design of a Hierarchical Transportation Network with Transshipment Facilities," Transportation Science, INFORMS, vol. 22(4), pages 270-277, November.
    10. Osman Alp & Erhan Erkut & Zvi Drezner, 2003. "An Efficient Genetic Algorithm for the p-Median Problem," Annals of Operations Research, Springer, vol. 122(1), pages 21-42, September.
    11. 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.
    12. Prakash Mirchandani, 1996. "The Multi-Tier Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 8(3), pages 202-218, August.
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