IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v249y2016i3p1092-1101.html
   My bibliography  Save this article

A branch-and-cut algorithm for the profitable windy rural postman problem

Author

Listed:
  • Ávila, Thais
  • Corberán, Ángel
  • Plana, Isaac
  • Sanchis, José M.

Abstract

In this paper we study the profitable windy rural postman problem. This is an arc routing problem with profits defined on a windy graph in which there is a profit associated with some of the edges of the graph, consisting of finding a route maximizing the difference between the total profit collected and the total cost. This problem generalizes the rural postman problem and other well-known arc routing problems and has real-life applications, mainly in snow removal operations. We propose here a formulation for the problem and study its associated polyhedron. Several families of facet-inducing inequalities are described and used in the design of a branch-and-cut procedure. The algorithm has been tested on a large set of benchmark instances and compared with other existing algorithms. The results obtained show that the branch-and-cut algorithm is able to solve large-sized instances optimally in reasonable computing times.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:249:y:2016:i:3:p:1092-1101
    DOI: 10.1016/j.ejor.2015.10.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715009236
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.10.016?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. Gianfranco Guastaroba & Renata Mansini & M Grazia Speranza, 2009. "Modeling the Pre Auction Stage The Truckload Case," Lecture Notes in Economics and Mathematical Systems, in: Jo A.E.E. Nunen & M. Grazia Speranza & Luca Bertazzi (ed.), Innovations in Distribution Logistics, chapter 11, pages 219-233, Springer.
    2. Malandraki, Chryssi & Daskin, Mark S., 1993. "The maximum benefit Chinese postman problem and the maximum benefit traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 65(2), pages 218-234, March.
    3. Benjamin Dussault & Bruce Golden & Edward Wasil, 2014. "The downhill plow problem with multiple plows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(10), pages 1465-1474, October.
    4. 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.
    5. 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.
    6. 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.
    7. Enrique Benavent & Ángel Corberán & Luís Gouveia & Maria Mourão & Leonor Pinto, 2015. "Profitable mixed capacitated arc routing and related problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 244-274, April.
    8. J Euchi & H Chabchoub, 2011. "Hybrid metaheuristics for the profitable arc tour problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(11), pages 2013-2022, November.
    9. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    10. Dominique Feillet & Pierre Dejax & Michel Gendreau, 2005. "Traveling Salesman Problems with Profits," Transportation Science, INFORMS, vol. 39(2), pages 188-205, May.
    11. 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.
    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. Vansteenwegen, Pieter & Souffriau, Wouter & Oudheusden, Dirk Van, 2011. "The orienteering problem: A survey," European Journal of Operational Research, Elsevier, vol. 209(1), pages 1-10, February.
    14. 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.
    15. J Euchi & H Chabchoub, 2011. "Hybrid metaheuristics for the profitable arc tour problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(11), pages 2013-2022, November.
    16. 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.
    17. Tunchan Cura, 2013. "An artificial bee colony approach for the undirected capacitated arc routing problem with profits," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 17(4), pages 483-508.
    18. Pearn, W. L. & Wang, K. H., 2003. "On the Maximum Benefit Chinese Postman Problem," Omega, Elsevier, vol. 31(4), pages 269-273, August.
    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. Mostafa Khorramizadeh & Roghayeh Javvi, 2024. "A branch-and-cut algorithm for the windy profitable location rural postman problem," Annals of Operations Research, Springer, vol. 341(2), pages 993-1022, October.
    2. 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.
    3. 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. 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.
    2. Enrique Benavent & Ángel Corberán & Luís Gouveia & Maria Mourão & Leonor Pinto, 2015. "Profitable mixed capacitated arc routing and related problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 244-274, April.
    3. 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.
    4. 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.
    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. 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.
    7. 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.
    8. 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.
    9. 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.
    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. Summerfield, Nichalin S. & Dror, Moshe & Cohen, Morris A., 2015. "City streets parking enforcement inspection decisions: The Chinese postman’s perspective," European Journal of Operational Research, Elsevier, vol. 242(1), pages 149-160.
    12. Kobeaga, Gorka & Rojas-Delgado, Jairo & Merino, María & Lozano, Jose A., 2024. "A revisited branch-and-cut algorithm for large-scale orienteering problems," European Journal of Operational Research, Elsevier, vol. 313(1), pages 44-68.
    13. 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.
    14. 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.
    15. Gunawan, Aldy & Lau, Hoong Chuin & Vansteenwegen, Pieter, 2016. "Orienteering Problem: A survey of recent variants, solution approaches and applications," European Journal of Operational Research, Elsevier, vol. 255(2), pages 315-332.
    16. Orlis, Christos & Laganá, Demetrio & Dullaert, Wout & Vigo, Daniele, 2020. "Distribution with Quality of Service Considerations: The Capacitated Routing Problem with Profits and Service Level Requirements," Omega, Elsevier, vol. 93(C).
    17. Oruc, Buse Eylul & Kara, Bahar Yetis, 2018. "Post-disaster assessment routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 116(C), pages 76-102.
    18. Riera-Ledesma, Jorge & Salazar-González, Juan José, 2017. "Solving the Team Orienteering Arc Routing Problem with a column generation approach," European Journal of Operational Research, Elsevier, vol. 262(1), pages 14-27.
    19. 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.
    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:eee:ejores:v:249:y:2016:i:3:p:1092-1101. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.