IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v53y2005i2p363-376.html
   My bibliography  Save this article

New Results on the Mixed General Routing Problem

Author

Listed:
  • Angel Corberán

    (Departament d’Estadística i Investigació Operativa, Universitat de València, València, Spain)

  • Gustavo Mejía

    (Departamento de Ciencias Básicas, Universidad EAFIT, Medellín, Colombia)

  • José M. Sanchis

    (Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Valencia, Spain)

Abstract

In this paper, we deal with the polyhedral description and the resolution of the Mixed General Routing Problem. This problem, in which the service activity occurs both at some of the nodes and at some of the arcs and edges of a mixed graph, contains a large number of important arc and node routing problems as special cases. Here, a large family of facet-defining inequalities, the Honeycomb inequalities, is described. Furthermore, a cutting-plane algorithm for this problem that incorporates new separation procedures for the K-C, Regular Path-Bridge, and Honeycomb inequalities is presented. Branch and bound is invoked when the final solution of the cutting-plane procedure is fractional. Extensive computational experiments over different sets of instances are included.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:2:p:363-376
    DOI: 10.1287/opre.1040.0168
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1040.0168
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1040.0168?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. Fleischmann, Bernhard, 1985. "A cutting plane procedure for the travelling salesman problem on road networks," European Journal of Operational Research, Elsevier, vol. 21(3), pages 307-317, September.
    2. H. A. Eiselt & Michel Gendreau & Gilbert Laporte, 1995. "Arc Routing Problems, Part II: The Rural Postman Problem," Operations Research, INFORMS, vol. 43(3), pages 399-414, June.
    3. Letchford, Adam N., 1999. "The general routing polyhedron: A unifying framework," European Journal of Operational Research, Elsevier, vol. 112(1), pages 122-133, January.
    4. Corberan, A. & Sanchis, J. M., 1998. "The general routing problem polyhedron: Facets from the RPP and GTSP polyhedra," European Journal of Operational Research, Elsevier, vol. 108(3), pages 538-550, August.
    5. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    6. Elena Fernández & Oscar Meza & Robert Garfinkel & Maruja Ortega, 2003. "On the Undirected Rural Postman Problem: Tight Bounds Based on a New Formulation," Operations Research, INFORMS, vol. 51(2), pages 281-291, April.
    7. Letchford, Adam N., 1997. "New inequalities for the General Routing Problem," European Journal of Operational Research, Elsevier, vol. 96(2), pages 317-322, January.
    8. 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.
    9. H. A. Eiselt & Michel Gendreau & Gilbert Laporte, 1995. "Arc Routing Problems, Part I: The Chinese Postman Problem," Operations Research, INFORMS, vol. 43(2), pages 231-242, April.
    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. 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.
    2. Jinghao Sun & Yakun Meng & Guozhen Tan, 2015. "An integer programming approach for the Chinese postman problem with time-dependent travel time," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 565-588, April.
    3. D Soler & E Martínez & J C Micó, 2008. "A transformation for the mixed general routing problem with turn penalties," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(4), pages 540-547, April.
    4. Benavent, Enrique & Corberán, Ángel & Laganà, Demetrio & Vocaturo, Francesca, 2023. "A two-phase hybrid algorithm for the periodic rural postman problem with irregular services on mixed graphs," European Journal of Operational Research, Elsevier, vol. 307(1), pages 64-81.

    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. 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.
    2. 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.
    3. Letchford, Adam N., 1999. "The general routing polyhedron: A unifying framework," European Journal of Operational Research, Elsevier, vol. 112(1), pages 122-133, January.
    4. Elena Fernández & Oscar Meza & Robert Garfinkel & Maruja Ortega, 2003. "On the Undirected Rural Postman Problem: Tight Bounds Based on a New Formulation," Operations Research, INFORMS, vol. 51(2), pages 281-291, April.
    5. Corberan, A. & Sanchis, J. M., 1998. "The general routing problem polyhedron: Facets from the RPP and GTSP polyhedra," European Journal of Operational Research, Elsevier, vol. 108(3), pages 538-550, August.
    6. Rodríguez-Pereira, Jessica & Fernández, Elena & Laporte, Gilbert & Benavent, Enrique & Martínez-Sykora, Antonio, 2019. "The Steiner Traveling Salesman Problem and its extensions," European Journal of Operational Research, Elsevier, vol. 278(2), pages 615-628.
    7. 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.
    8. Letchford, A.N. & Eglese, R.W., 1998. "The rural postman problem with deadline classes," European Journal of Operational Research, Elsevier, vol. 105(3), pages 390-400, March.
    9. 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.
    10. 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.
    11. 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.
    12. Irnich, Stefan & Laganà, Demetrio & Schlebusch, Claudia & Vocaturo, Francesca, 2015. "Two-phase branch-and-cut for the mixed capacitated general routing problem," European Journal of Operational Research, Elsevier, vol. 243(1), pages 17-29.
    13. 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.
    14. Gilbert Laporte & Roberto Musmanno & Francesca Vocaturo, 2010. "An Adaptive Large Neighbourhood Search Heuristic for the Capacitated Arc-Routing Problem with Stochastic Demands," Transportation Science, INFORMS, vol. 44(1), pages 125-135, February.
    15. 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.
    16. 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.
    17. Beullens, Patrick & Muyldermans, Luc & Cattrysse, Dirk & Van Oudheusden, Dirk, 2003. "A guided local search heuristic for the capacitated arc routing problem," European Journal of Operational Research, Elsevier, vol. 147(3), pages 629-643, June.
    18. Corberan, A. & Marti, R. & Sanchis, J. M., 2002. "A GRASP heuristic for the mixed Chinese postman problem," European Journal of Operational Research, Elsevier, vol. 142(1), pages 70-80, October.
    19. Letchford, Adam N., 1997. "New inequalities for the General Routing Problem," European Journal of Operational Research, Elsevier, vol. 96(2), pages 317-322, January.
    20. John Sniezek & Lawrence Bodin, 2006. "Using mixed integer programming for solving the capacitated arc routing problem with vehicle/site dependencies with an application to the routing of residential sanitation collection vehicles," Annals of Operations Research, Springer, vol. 144(1), pages 33-58, 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:oropre:v:53:y:2005:i:2:p:363-376. 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.