IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v45y2011i3p317-334.html
   My bibliography  Save this article

The Windy Clustered Prize-Collecting Arc-Routing Problem

Author

Listed:
  • Ángel Corberán

    (Statistics and Operations Research Department, University of Valencia, 46100 Burjassot, Spain)

  • Elena Fernández

    (Statistics and Operations Research Department, Technical University of Catalonia, 08034 Barcelona, Spain)

  • Carles Franquesa

    (Statistics and Operations Research Department, Technical University of Catalonia, 08034 Barcelona, Spain)

  • José María Sanchis

    (Applied Mathematics Department, Technical University of Valencia, 46022 Valencia, Spain)

Abstract

This paper introduces the windy clustered prize-collecting arc-routing problem. It is an arc-routing problem where each demand edge is associated with a profit that is collected once if the edge is serviced, independent of the number of times the edge is traversed. It is further required that if a demand edge is serviced, then all the demand edges of its component are also serviced. A mathematical programming formulation is given and some polyhedral results including several facet-defining and valid inequalities are presented. The separation problem for the different families of inequalities is studied. Numerical results from computational experiments are analyzed.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:45:y:2011:i:3:p:317-334
    DOI: 10.1287/trsc.1110.0370
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.1110.0370
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.1110.0370?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
    ---><---

    References listed on IDEAS

    as
    1. Alain Hertz & Gilbert Laporte & Pierrette Nanchen Hugo, 1999. "Improvement Procedures for the Undirected Rural Postman Problem," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 53-62, February.
    2. Julián Aráoz & Elena Fernández & Carles Franquesa, 2009. "The Clustered Prize-Collecting Arc Routing Problem," Transportation Science, INFORMS, vol. 43(3), pages 287-300, August.
    3. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    4. Aráoz, Julián & Fernández, Elena & Meza, Oscar, 2009. "Solving the Prize-collecting Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 196(3), pages 886-896, August.
    5. Dominique Feillet & Pierre Dejax & Michel Gendreau, 2005. "The Profitable Arc Tour Problem: Solution with a Branch-and-Price Algorithm," Transportation Science, INFORMS, vol. 39(4), pages 539-552, November.
    6. 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.
    7. Corberan, A. & Sanchis, J. M., 1994. "A polyhedral approach to the rural postman problem," European Journal of Operational Research, Elsevier, vol. 79(1), pages 95-114, November.
    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. Fernández, Elena & Roca-Riu, Mireia & Speranza, M. Grazia, 2018. "The Shared Customer Collaboration Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1078-1093.
    2. Kasaei, Maziar & Salman, F. Sibel, 2016. "Arc routing problems to restore connectivity of a road network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 95(C), pages 177-206.
    3. Colombi, Marco & Mansini, Renata, 2014. "New results for the Directed Profitable Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 238(3), pages 760-773.
    4. Elena Fernández & Jessica Rodríguez-Pereira, 2017. "Multi-depot rural postman problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 340-372, July.
    5. Archetti, Claudia & Bertazzi, Luca & Laganà, Demetrio & Vocaturo, Francesca, 2017. "The Undirected Capacitated General Routing Problem with Profits," European Journal of Operational Research, Elsevier, vol. 257(3), pages 822-833.
    6. Claudia Archetti & M. Grazia Speranza & Ángel Corberán & José M. Sanchis & Isaac Plana, 2014. "The Team Orienteering Arc Routing Problem," Transportation Science, INFORMS, vol. 48(3), pages 442-457, August.
    7. Elena Fernández & Gilbert Laporte & Jessica Rodríguez-Pereira, 2018. "A Branch-and-Cut Algorithm for the Multidepot Rural Postman Problem," Transportation Science, INFORMS, vol. 52(2), pages 353-369, March.
    8. Colombi, Marco & Corberán, Ángel & Mansini, Renata & Plana, Isaac & Sanchis, José M., 2017. "The directed profitable rural postman problem with incompatibility constraints," European Journal of Operational Research, Elsevier, vol. 261(2), pages 549-562.

    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. Ávila, Thais & Corberán, Ángel & Plana, Isaac & Sanchis, José M., 2016. "A branch-and-cut algorithm for the profitable windy rural postman problem," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1092-1101.
    2. Arbib, Claudio & Servilio, Mara & Archetti, Claudia & Speranza, M. Grazia, 2014. "The directed profitable location Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 811-819.
    3. 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.
    4. Elena Fernández & Jessica Rodríguez-Pereira, 2017. "Multi-depot rural postman problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 340-372, July.
    5. Aráoz, Julián & Fernández, Elena & Meza, Oscar, 2009. "Solving the Prize-collecting Rural Postman Problem," European Journal of Operational Research, Elsevier, vol. 196(3), pages 886-896, August.
    6. Kasaei, Maziar & Salman, F. Sibel, 2016. "Arc routing problems to restore connectivity of a road network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 95(C), pages 177-206.
    7. Colombi, Marco & Corberán, Ángel & Mansini, Renata & Plana, Isaac & Sanchis, José M., 2017. "The directed profitable rural postman problem with incompatibility constraints," European Journal of Operational Research, Elsevier, vol. 261(2), pages 549-562.
    8. Luc Muyldermans & Patrick Beullens & Dirk Cattrysse & Dirk Van Oudheusden, 2005. "Exploring Variants of 2-Opt and 3-Opt for the General Routing Problem," Operations Research, INFORMS, vol. 53(6), pages 982-995, December.
    9. Archetti, Claudia & Bertazzi, Luca & Laganà, Demetrio & Vocaturo, Francesca, 2017. "The Undirected Capacitated General Routing Problem with Profits," European Journal of Operational Research, Elsevier, vol. 257(3), pages 822-833.
    10. Julián Aráoz & Elena Fernández & Carles Franquesa, 2009. "The Clustered Prize-Collecting Arc Routing Problem," Transportation Science, INFORMS, vol. 43(3), pages 287-300, August.
    11. Elena Fernández & Gilbert Laporte & Jessica Rodríguez-Pereira, 2018. "A Branch-and-Cut Algorithm for the Multidepot Rural Postman Problem," Transportation Science, INFORMS, vol. 52(2), pages 353-369, March.
    12. Claudia Archetti & M. Grazia Speranza & Ángel Corberán & José M. Sanchis & Isaac Plana, 2014. "The Team Orienteering Arc Routing Problem," Transportation Science, INFORMS, vol. 48(3), pages 442-457, August.
    13. Barbara De Rosa & Gennaro Improta & Gianpaolo Ghiani & Roberto Musmanno, 2002. "The Arc Routing and Scheduling Problem with Transshipment," Transportation Science, INFORMS, vol. 36(3), pages 301-313, August.
    14. Cabral, Edgar Alberto & Gendreau, Michel & Ghiani, Gianpaolo & Laporte, Gilbert, 2004. "Solving the hierarchical Chinese postman problem as a rural postman problem," European Journal of Operational Research, Elsevier, vol. 155(1), pages 44-50, May.
    15. Elena Fernández & Gilbert Laporte & Jessica Rodríguez-Pereira, 2019. "Exact Solution of Several Families of Location-Arc Routing Problems," Transportation Science, INFORMS, vol. 53(5), pages 1313-1333, September.
    16. Angel Corberán & Gustavo Mejía & José M. Sanchis, 2005. "New Results on the Mixed General Routing Problem," Operations Research, INFORMS, vol. 53(2), pages 363-376, April.
    17. Archetti, Claudia & Corberán, Ángel & Plana, Isaac & Sanchis, José Maria & Speranza, M. Grazia, 2015. "A matheuristic for the Team Orienteering Arc Routing Problem," European Journal of Operational Research, Elsevier, vol. 245(2), pages 392-401.
    18. Fung, Richard Y.K. & Liu, Ran & Jiang, Zhibin, 2013. "A memetic algorithm for the open capacitated arc routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 50(C), pages 53-67.
    19. Jessica Rodríguez-Pereira & Gilbert Laporte, 2022. "The target visitation arc routing problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 60-76, April.
    20. Zachariadis, E.E. & Kiranoudis, C.T., 2011. "Local search for the undirected capacitated arc routing problem with profits," European Journal of Operational Research, Elsevier, vol. 210(2), pages 358-367, April.

    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:inm:ortrsc:v:45:y:2011:i:3:p:317-334. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.