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Benders, metric and cutset inequalities for multicommodity capacitated network design

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Abstract

Solving multicommodity capacitated network design problems is a hard task that requires the use of several strategies like relaxing some constraints and strengthening the model with valid inequalities. In this paper, we compare three sets of inequalities that have been widely used in this context: Benders, metric and cutset inequalities. We show that Benders inequalities associated to extreme rays are metric inequalities. We also show how to strengthen Benders inequalities associated to non-extreme rays to obtain metric inequalities. We show that cutset inequalities are Benders inequalities, but not necessarily metric inequalities. We give a necessary and sufficient condition for a cutset inequality to be a metric inequality. Computational experiments show the effectiveness of strengthening Benders and cutset inequalities to obtain metric inequalities.

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Authors and Affiliations

  1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, CP 668, São Carlos, 13560-970, São Paulo, Brazil

    Alysson M. Costa

  2. Chaire de recherche du Canada en distributique and Centre de recherche sur les transports, HEC Montréal, 3000 chemin de la Côte-Sainte-Catherine, Montréal, Canada, H3T 2A7

    Jean-François Cordeau

  3. Département d’informatique et de recherche opérationnelle, and Centre de recherche sur les transports, Université de Montréal, C.P. 6128, succ. Centre-ville, Montréal, Canada, H3C 3J7

    Bernard Gendron

Authors
  1. Alysson M. Costa
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  2. Jean-François Cordeau
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  3. Bernard Gendron
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Correspondence to Jean-François Cordeau.

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Costa, A.M., Cordeau, JF. & Gendron, B. Benders, metric and cutset inequalities for multicommodity capacitated network design. Comput Optim Appl 42, 371–392 (2009). https://doi.org/10.1007/s10589-007-9122-0

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  • DOI: https://doi.org/10.1007/s10589-007-9122-0

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