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, Volume 23, Issue 1, pp 244–274 | Cite as

Profitable mixed capacitated arc routing and related problems

  • Enrique Benavent
  • Ángel Corberán
  • Luís Gouveia
  • Maria Cândida Mourão
  • Leonor Santiago Pinto
Original Paper

Abstract

Mixed capacitated arc routing problems aim to identify a set of vehicle tours that, starting and ending at a depot node, serve a given number of links at minimum cost, while satisfying the vehicles capacity. If both profits and costs on arcs are considered, we may define the profitable mixed capacitated arc routing problem (PMCARP). In this paper we present compact flow-based models for the PMCARP, where two types of services are tackled, mandatory and optional. Adaptations of the models to fit into some other related problems are also proposed. The models are evaluated, according to their bounds quality as well as to the CPU times, over large sets of test instances. New instances have been created for some variants that have been introduced here for the first time. Results show the new models performance within CPLEX and compare, whenever available, the proposed models against other resolution methods.

Keywords

Routing Arc routing problems Profits Flow-based models 

Mathematics Subject Classification

90B10 

Notes

Acknowledgments

Authors want to thank two anonymous referees for their comments and suggestions that have contributed to improve the content and readability of the paper. E. Benavent and Á. Corberán wish to thank the Ministerio of Economía y Competitividad (project MTM2012-36163-C06-02) of Spain and the Generalitat Valenciana (project GVPROMETEO2013-049) for their support. L. Gouveia, M.C. Mourão and L.S. Pinto wish to thank the Fundação para a Ciência e Tecnologia (projects PEsT-OE/EGE/UI0491; PEsT-OE/MAT/UI0152; PTDC/EGE-GES/121406) for their support. Project MTM2012-36163-C06-02 is funded in cooperation with the European Community Fund FEDER.

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2014

Authors and Affiliations

  • Enrique Benavent
    • 1
  • Ángel Corberán
    • 1
  • Luís Gouveia
    • 2
    • 4
  • Maria Cândida Mourão
    • 3
    • 4
  • Leonor Santiago Pinto
    • 3
    • 5
    • 6
  1. 1.Dep. Estadística e Investigación OperativaUniv. ValenciaValenciaSpain
  2. 2.DEIO, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal
  3. 3.Instituto Superior de Economia e GestãoUniversidade de LisboaLisbonPortugal
  4. 4.Centro de Investigação OperacionalLisbonPortugal
  5. 5.CEMAPRE, Centro de Matemática Aplicada à Previsão e Decisão EconómicaLisbonPortugal
  6. 6.ISEG-ULisboaLisbonPortugal

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