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Formulations and exact algorithms for the distance-constrained generalized directed rural postman problem

Author

Listed:
  • Thais Ávila

    (Universitat de València)

  • Ángel Corberán

    (Universitat de València)

  • Isaac Plana

    (Universitat de València)

  • José M. Sanchis

    (Universidad Politécnica de Valencia)

Abstract

The generalized directed rural postman problem is an arc routing problem with many interesting real-life applications, such as routing for meter reading. In this application, a vehicle with a receiver travels through a series of neighborhoods. If the vehicle gets closer than a certain distance to a meter, the receiver is able to record the gas, water, or electricity consumption. Therefore, the vehicle does not need to traverse every street, but only a few, to get close enough to each meter. We study an extension of this problem in which a fleet of vehicles is available. Given the characteristics of the mentioned application, the vehicles have no capacities but there is a maximum distance (or time) constraint all of them have to satisfy. We introduce four formulations for this problem, propose some families of valid inequalities, and present four branch-and-cut algorithms for its solution. The formulations and the algorithms are compared on a large set of instances.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurjco:v:5:y:2017:i:3:d:10.1007_s13675-015-0053-8
    DOI: 10.1007/s13675-015-0053-8
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    References listed on IDEAS

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    1. Michael Drexl, 2014. "On the generalized directed rural postman problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(8), pages 1143-1154, August.
    2. Benavent, Enrique & Carrotta, Alessandro & Corberan, Angel & Sanchis, Jose M. & Vigo, Daniele, 2007. "Lower bounds and heuristics for the Windy Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 176(2), pages 855-869, January.
    3. Michel Gendreau & Gilbert Laporte & Frédéric Semet, 1997. "The Covering Tour Problem," Operations Research, INFORMS, vol. 45(4), pages 568-576, August.
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    Cited by:

    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.
    2. Glock, Katharina & Meyer, Anne, 2023. "Spatial coverage in routing and path planning problems," European Journal of Operational Research, Elsevier, vol. 305(1), pages 1-20.
    3. 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.
    4. 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.

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