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On the Distance-Constrained Close Enough Arc Routing Problem

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  • Corberán, Ángel
  • Plana, Isaac
  • Reula, Miguel
  • Sanchis, José M.

Abstract

Arc routing problems consist basically of finding one or several routes traversing a given set of arcs and/or edges that must be serviced. The Close-Enough Arc Routing Problem, or Generalized Directed Rural Postman Problem, does not assume that customers are located at specific arcs, but can be serviced by traversing any arc of a given subset. Real-life applications include routing for meter reading, in which a vehicle equipped with a receiver travels a street network. If the vehicle gets within a certain distance of a meter, the receiver collects its data. Therefore, only a few streets which are close enough to the meters need to be traversed. In this paper we study the generalization of this problem to the case in which a fleet of vehicles is available. This problem, the Distance-Constrained Close Enough Arc Routing Problem, consists of finding a set of routes with minimum total cost such that their length does not exceed a maximum distance.

Suggested Citation

  • Corberán, Ángel & Plana, Isaac & Reula, Miguel & Sanchis, José M., 2021. "On the Distance-Constrained Close Enough Arc Routing Problem," European Journal of Operational Research, Elsevier, vol. 291(1), pages 32-51.
    • Handle: RePEc:eee:ejores:v:291:y:2021:i:1:p:32-51
    DOI: 10.1016/j.ejor.2020.09.012
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    References listed on IDEAS

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    1. Thais Ávila & Ángel Corberán & Isaac Plana & José M. Sanchis, 2016. "A New Branch-and-Cut Algorithm for the Generalized Directed Rural Postman Problem," Transportation Science, INFORMS, vol. 50(2), pages 750-761, May.
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    4. Thais Ávila & Ángel Corberán & Isaac Plana & José M. Sanchis, 2017. "Formulations and exact algorithms for the distance-constrained generalized directed rural postman problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 339-365, September.
    5. Julián Aráoz & Elena Fernández & Carles Franquesa, 2017. "The Generalized Arc Routing Problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 497-525, October.
    6. Michel Gendreau & Gilbert Laporte & Frédéric Semet, 1997. "The Covering Tour Problem," Operations Research, INFORMS, vol. 45(4), pages 568-576, August.
    7. Ángel Corberán & Isaac Plana & Miguel Reula & José M. Sanchis, 2019. "A matheuristic for the Distance-Constrained Close-Enough Arc Routing Problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 312-326, July.
    8. Walton Pereira Coutinho & Roberto Quirino do Nascimento & Artur Alves Pessoa & Anand Subramanian, 2016. "A Branch-and-Bound Algorithm for the Close-Enough Traveling Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 752-765, November.
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    1. Bianchessi, Nicola & Corberán, Ángel & Plana, Isaac & Reula, Miguel & Sanchis, José M., 2022. "The min-max close-enough arc routing problem," European Journal of Operational Research, Elsevier, vol. 300(3), pages 837-851.

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