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Cut-First Branch-and-Price Second for the Capacitated Arc-Routing Problem

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Operations Research Proceedings 2014

Part of the book series: Operations Research Proceedings ((ORP))

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Abstract

The basic multiple-vehicle arc-routing problem is called capacitated arc-routing problem (CARP) and was introduced by Golden and Wong (Networks 11:305–315, 1981 [9]). This paper presents a full-fledged branch-and-price (bap) algorithm for the CARP. In the first phase, the one-index formulation of the CARP is solved in order to produce strong cuts and an excellent lower bound. In the second phase, the master program is initialized with the strong cuts, CARP tours are iteratively generated by a pricing procedure, and branching is required to produce integer solutions. Furthermore, different pricing problem relaxations are analyzed and the construction of new labeling algorithms for their solution is presented. The cut-first branch-and-price second algorithm provides a powerful approach to solve knowingly hard instances of the CARP to proven optimality.

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Notes

  1. 1.

    All instances can be downloaded from http://logistik.bwl.uni-mainz.de/benchmarks.php.

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Author information

Authors and Affiliations

  1. Chair of Logistics Management, Johannes Gutenberg University Mainz, Jakob-Welder-Weg 9, 55128, Mainz, Germany

    Claudia Schlebusch & Stefan Irnich

Authors
  1. Claudia Schlebusch
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  2. Stefan Irnich
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Corresponding authors

Correspondence to Claudia Schlebusch or Stefan Irnich .

Editor information

Editors and Affiliations

  1. Operations Research, RWTH Aachen University, Aachen, Germany

    Marco Lübbecke

  2. Lehrstuhl II für Mathematik, RWTH Aachen University, Aachen, Germany

    Arie Koster

  3. RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Peter Letmathe

  4. E.ON Energy Research Center, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Reinhard Madlener

  5. Management Science, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Britta Peis

  6. Chair of Operations Management, RWTH Aachen University, Aachen, Germany

    Grit Walther

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© 2016 Springer International Publishing Switzerland

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Schlebusch, C., Irnich, S. (2016). Cut-First Branch-and-Price Second for the Capacitated Arc-Routing Problem. In: Lübbecke, M., Koster, A., Letmathe, P., Madlener, R., Peis, B., Walther, G. (eds) Operations Research Proceedings 2014. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-28697-6_70

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