IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v229y2013i3p595-598.html
   My bibliography  Save this article

A note on the separation of subtour elimination constraints in elementary shortest path problems

Author

Listed:
  • Drexl, Michael

Abstract

This note proposes an alternative procedure for identifying violated subtour elimination constraints (SECs) in branch-and-cut algorithms for elementary shortest path problems. The procedure is also applicable to other routing problems, such as variants of travelling salesman or shortest Hamiltonian path problems, on directed graphs. The proposed procedure is based on computing the strong components of the support graph. The procedure possesses a better worst-case time complexity than the standard way of separating SECs, which uses maximum flow algorithms, and is easier to implement.

Suggested Citation

  • Drexl, Michael, 2013. "A note on the separation of subtour elimination constraints in elementary shortest path problems," European Journal of Operational Research, Elsevier, vol. 229(3), pages 595-598.
  • Handle: RePEc:eee:ejores:v:229:y:2013:i:3:p:595-598
    DOI: 10.1016/j.ejor.2013.03.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713002178
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2013.03.009?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. Matteo Fischetti & Paolo Toth, 1997. "A Polyhedral Approach to the Asymmetric Traveling Salesman Problem," Management Science, INFORMS, vol. 43(11), pages 1520-1536, November.
    2. 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.
    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. Skålnes, Jørgen & Andersson, Henrik & Desaulniers, Guy & Stålhane, Magnus, 2022. "An improved formulation for the inventory routing problem with time-varying demands," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1189-1201.
    2. Taccari, Leonardo, 2016. "Integer programming formulations for the elementary shortest path problem," European Journal of Operational Research, Elsevier, vol. 252(1), pages 122-130.
    3. Lera-Romero, Gonzalo & Miranda-Bront, Juan José, 2021. "A branch and cut algorithm for the time-dependent profitable tour problem with resource constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 879-896.
    4. Tamke, Felix & Buscher, Udo, 2021. "A branch-and-cut algorithm for the vehicle routing problem with drones," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 174-203.
    5. Rafael Castro Andrade & Rommel Dias Saraiva, 2020. "MTZ-primal-dual model, cutting-plane, and combinatorial branch-and-bound for shortest paths avoiding negative cycles," Annals of Operations Research, Springer, vol. 286(1), pages 147-172, March.

    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. Michael Drexl, 2012. "A Note on the Separation of Subtour Elimination Constraints in Asymmetric Routing Problems," Working Papers 1205, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    2. Filippo Focacci & Andrea Lodi & Michela Milano, 2002. "A Hybrid Exact Algorithm for the TSPTW," INFORMS Journal on Computing, INFORMS, vol. 14(4), pages 403-417, November.
    3. Dang, Duc-Cuong & Guibadj, Rym Nesrine & Moukrim, Aziz, 2013. "An effective PSO-inspired algorithm for the team orienteering problem," European Journal of Operational Research, Elsevier, vol. 229(2), pages 332-344.
    4. Ido Orenstein & Tal Raviv & Elad Sadan, 2019. "Flexible parcel delivery to automated parcel lockers: models, solution methods and analysis," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 683-711, December.
    5. Morteza Keshtkaran & Koorush Ziarati & Andrea Bettinelli & Daniele Vigo, 2016. "Enhanced exact solution methods for the Team Orienteering Problem," International Journal of Production Research, Taylor & Francis Journals, vol. 54(2), pages 591-601, January.
    6. Furini, Fabio & Persiani, Carlo Alfredo & Toth, Paolo, 2016. "The Time Dependent Traveling Salesman Planning Problem in Controlled Airspace," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 38-55.
    7. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2019. "Interdiction Games and Monotonicity, with Application to Knapsack Problems," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 390-410, April.
    8. Stacy A. Voccia & Ann Melissa Campbell & Barrett W. Thomas, 2019. "The Same-Day Delivery Problem for Online Purchases," Service Science, INFORMS, vol. 53(1), pages 167-184, February.
    9. 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.
    10. Racha El-Hajj & Rym Nesrine Guibadj & Aziz Moukrim & Mehdi Serairi, 2020. "A PSO based algorithm with an efficient optimal split procedure for the multiperiod vehicle routing problem with profit," Annals of Operations Research, Springer, vol. 291(1), pages 281-316, August.
    11. Jonathan F. Bard & George Kontoravdis & Gang Yu, 2002. "A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 36(2), pages 250-269, May.
    12. Jorge Riera-Ledesma & Juan-José Salazar-González, 2006. "Solving the asymmetric traveling purchaser problem," Annals of Operations Research, Springer, vol. 144(1), pages 83-97, April.
    13. Maximilian Schiffer & Michael Schneider & Grit Walther & Gilbert Laporte, 2019. "Vehicle Routing and Location Routing with Intermediate Stops: A Review," Transportation Science, INFORMS, vol. 53(2), pages 319-343, March.
    14. Dikas, G. & Minis, I., 2014. "Scheduled paratransit transport systems," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 18-34.
    15. Shu Zhang & Jeffrey W. Ohlmann & Barrett W. Thomas, 2018. "Dynamic Orienteering on a Network of Queues," Transportation Science, INFORMS, vol. 52(3), pages 691-706, June.
    16. Zhang, Shu & Ohlmann, Jeffrey W. & Thomas, Barrett W., 2014. "A priori orienteering with time windows and stochastic wait times at customers," European Journal of Operational Research, Elsevier, vol. 239(1), pages 70-79.
    17. Dewil, R. & Vansteenwegen, P. & Cattrysse, D. & Van Oudheusden, D., 2015. "A minimum cost network flow model for the maximum covering and patrol routing problem," European Journal of Operational Research, Elsevier, vol. 247(1), pages 27-36.
    18. Michiel A. J. uit het Broek & Albert H. Schrotenboer & Bolor Jargalsaikhan & Kees Jan Roodbergen & Leandro C. Coelho, 2021. "Asymmetric Multidepot Vehicle Routing Problems: Valid Inequalities and a Branch-and-Cut Algorithm," Operations Research, INFORMS, vol. 69(2), pages 380-409, March.
    19. Dumez, Dorian & Lehuédé, Fabien & Péton, Olivier, 2021. "A large neighborhood search approach to the vehicle routing problem with delivery options," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 103-132.
    20. Shima Azizi & Özge Aygül & Brenton Faber & Sharon Johnson & Renata Konrad & Andrew C. Trapp, 2023. "Select, route and schedule: optimizing community paramedicine service delivery with mandatory visits and patient prioritization," Health Care Management Science, Springer, vol. 26(4), pages 719-746, December.

    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:229:y:2013:i:3:p:595-598. 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.