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The Team Orienteering Problem: Formulations and Branch-Cut and Price

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Abstract

The Team Orienteering Problem is a routing problem on a graph with durations associated to the arcs and profits assigned to visiting the vertices. A fixed number of identical vehicles, with a limited total duration for their routes, is given. The total profit gathered by all routes is to be maximized. We devise an extended formulation where edges are indexed by the time they are placed in the route. A new class of inequalities, min cut, and the triangle clique cuts of Pessoa et. al., 2007 are added. The resulting formulation is solved by column generation. Branching is done following the work of Boussier et al. 2007, to which the branch-cut-and-price algorithm here proposed is compared. A few new upper bounds were obtained. Overall the presented approach has shown to be very competitive.

BibTeX - Entry

@InProceedings{poggi_et_al:OASIcs:2010:2756,
  author =	{Marcus Poggi and Henrique Viana and Eduardo Uchoa},
  title =	{{The Team Orienteering Problem: Formulations and Branch-Cut and Price}},
  booktitle =	{10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10)},
  pages =	{142--155},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-20-0},
  ISSN =	{2190-6807},
  year =	{2010},
  volume =	{14},
  editor =	{Thomas Erlebach and Marco L{\"u}bbecke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2756},
  URN =		{urn:nbn:de:0030-drops-27561},
  doi =		{http://dx.doi.org/10.4230/OASIcs.ATMOS.2010.142},
  annote =	{Keywords: Branch-Cut and Price, Team Orienteering Problem, Column Generation}
}

Keywords: Branch-Cut and Price, Team Orienteering Problem, Column Generation
Seminar: 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10)
Issue date: 2010
Date of publication: 2010


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