IDEAS home Printed from https://ideas.repec.org/a/spr/eurjco/v5y2017i3d10.1007_s13675-015-0053-8.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13675-015-0053-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13675-015-0053-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Michel Gendreau & Gilbert Laporte & Frédéric Semet, 1997. "The Covering Tour Problem," Operations Research, INFORMS, vol. 45(4), pages 568-576, August.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. Veenstra, Marjolein & Roodbergen, Kees Jan & Coelho, Leandro C. & Zhu, Stuart X., 2018. "A simultaneous facility location and vehicle routing problem arising in health care logistics in the Netherlands," European Journal of Operational Research, Elsevier, vol. 268(2), pages 703-715.
    4. R Baldacci & E Bartolini & G Laporte, 2010. "Some applications of the generalized vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(7), pages 1072-1077, July.
    5. 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.
    6. 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.
    7. Liwei Zeng & Sunil Chopra & Karen Smilowitz, 2019. "The Covering Path Problem on a Grid," Transportation Science, INFORMS, vol. 53(6), pages 1656-1672, November.
    8. Xiaoguang Bao & Xinhao Ni, 2024. "Approximation algorithms for two clustered arc routing problems," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-12, July.
    9. Ivan Contreras & Moayad Tanash & Navneet Vidyarthi, 2017. "Exact and heuristic approaches for the cycle hub location problem," Annals of Operations Research, Springer, vol. 258(2), pages 655-677, November.
    10. Rahma Lahyani & Leandro C. Coelho & Jacques Renaud, 2018. "Alternative formulations and improved bounds for the multi-depot fleet size and mix vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 125-157, January.
    11. Glize, Estèle & Roberti, Roberto & Jozefowiez, Nicolas & Ngueveu, Sandra Ulrich, 2020. "Exact methods for mono-objective and Bi-Objective Multi-Vehicle Covering Tour Problems," European Journal of Operational Research, Elsevier, vol. 283(3), pages 812-824.
    12. J Renaud & F F Boctor & G Laporte, 2004. "Efficient heuristics for Median Cycle Problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(2), pages 179-186, February.
    13. Ángel Corberán & Elena Fernández & Carles Franquesa & José María Sanchis, 2011. "The Windy Clustered Prize-Collecting Arc-Routing Problem," Transportation Science, INFORMS, vol. 45(3), pages 317-334, August.
    14. Pop, Petrică C. & Cosma, Ovidiu & Sabo, Cosmin & Sitar, Corina Pop, 2024. "A comprehensive survey on the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 314(3), pages 819-835.
    15. Dominique Feillet & Pierre Dejax & Michel Gendreau, 2005. "Traveling Salesman Problems with Profits," Transportation Science, INFORMS, vol. 39(2), pages 188-205, May.
    16. Fischer, Vera & Pacheco Paneque, Meritxell & Legrain, Antoine & Bürgy, Reinhard, 2024. "A capacitated multi-vehicle covering tour problem on a road network and its application to waste collection," European Journal of Operational Research, Elsevier, vol. 315(1), pages 338-353.
    17. Coelho, Leandro C. & Laporte, Gilbert, 2014. "Improved solutions for inventory-routing problems through valid inequalities and input ordering," International Journal of Production Economics, Elsevier, vol. 155(C), pages 391-397.
    18. Christian Artigues & Nicolas Jozefowiez & Boadu M. Sarpong, 2018. "Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(2), pages 117-142, June.
    19. Keisuke Murakami, 2018. "Iterative Column Generation Algorithm for Generalized Multi-Vehicle Covering Tour Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(04), pages 1-22, August.
    20. Leticia Vargas & Nicolas Jozefowiez & Sandra Ulrich Ngueveu, 2017. "A dynamic programming operator for tour location problems applied to the covering tour problem," Journal of Heuristics, Springer, vol. 23(1), pages 53-80, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:eurjco:v:5:y:2017:i:3:d:10.1007_s13675-015-0053-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.