A branch and cut algorithm for the hierarchical network design problem

Carlos Obreque, Macarena Donoso, Gabriel Gutiérrez, Vladimir Marianov

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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.

Original languageEnglish
Pages (from-to)28-35
Number of pages8
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - 1 Jan 2010
Externally publishedYes


  • Branch and cut
  • Cutting planes
  • Extensive facility location
  • Hierarchical networks


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