IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v320y2025i3p505-515.html
   My bibliography  Save this article

Quadratic horizontally elastic not-first/not-last filtering algorithm for cumulative constraint

Author

Listed:
  • Kameugne, Roger
  • Betmbe, Sévérine Fetgo
  • Noulamo, Thierry

Abstract

The not-first/not-last rule is a pendant of the edge finding rule, generally embedded in the cumulative constraint during constraint-based scheduling. It is combined with other filtering rules for more pruning of the tree search. In this paper, the Profile data structure in which tasks are scheduled in a horizontally elastic way is used to strengthen the classic not-first/not-last rule. Potential not-first task intervals are selected using criteria (specified later in the paper), and the Profile data structure is applied to selected task intervals. We prove that this new rule subsumes the classic not-first rule. A quadratic filtering algorithm is proposed for the new rule, thus improving the complexity of the horizontally elastic not-first/not-last algorithm from O(n3) to O(n2). The fixed part of external tasks that overlap with the selected task intervals is considered during the computation of the earliest completion time of task intervals. This improvement increases the filtering power of the algorithm while remaining quadratic. Experimental results, on a well-known suite of benchmark instances of Resource-Constrained Project Scheduling Problems (RCPSPs), show that the propounded algorithms are competitive with the state-of-the-art not-first algorithms in terms of tree search and running time reduction.

Suggested Citation

  • Kameugne, Roger & Betmbe, Sévérine Fetgo & Noulamo, Thierry, 2025. "Quadratic horizontally elastic not-first/not-last filtering algorithm for cumulative constraint," European Journal of Operational Research, Elsevier, vol. 320(3), pages 505-515.
    • Handle: RePEc:eee:ejores:v:320:y:2025:i:3:p:505-515
    DOI: 10.1016/j.ejor.2024.09.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221724006945
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2024.09.003?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. Jacques Carlier & Abderrahim Sahli & Antoine Jouglet & Eric Pinson, 2022. "A faster checker of the energetic reasoning for the cumulative scheduling problem," International Journal of Production Research, Taylor & Francis Journals, vol. 60(11), pages 3419-3434, June.
    2. Carlier, J. & Neron, E., 2003. "On linear lower bounds for the resource constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 149(2), pages 314-324, September.
    3. Carlier, J. & Pinson, E. & Sahli, A. & Jouglet, A., 2020. "An O(n2) algorithm for time-bound adjustments for the cumulative scheduling problem," European Journal of Operational Research, Elsevier, vol. 286(2), pages 468-476.
    4. Luc Mercier & Pascal Van Hentenryck, 2008. "Edge Finding for Cumulative Scheduling," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 143-153, February.
    5. Roger Kameugne & Laure Pauline Fotso, 2013. "A cumulative not-first/not-last filtering algorithm in O(n 2log(n))," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(1), pages 95-115, February.
    Full references (including those not matched with items on IDEAS)

    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. Sévérine Fetgo Betmbe & Clémentin Tayou Djamegni, 2022. "Horizontally Elastic Edge-Finder Algorithm for Cumulative Resource Constraint Revisited," SN Operations Research Forum, Springer, vol. 3(4), pages 1-32, December.
    2. Moukrim, Aziz & Quilliot, Alain & Toussaint, Hélène, 2015. "An effective branch-and-price algorithm for the Preemptive Resource Constrained Project Scheduling Problem based on minimal Interval Order Enumeration," European Journal of Operational Research, Elsevier, vol. 244(2), pages 360-368.
    3. Hamed Fahimi & Claude-Guy Quimper, 2023. "Overload-Checking and Edge-Finding for Robust Cumulative Scheduling," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1419-1438, November.
    4. Jacques Carlier & Claire Hanen, 2024. "Measuring the slack between lower bounds for scheduling on parallel machines," Annals of Operations Research, Springer, vol. 338(1), pages 347-377, July.
    5. Arkhipov, Dmitry & Battaïa, Olga & Lazarev, Alexander, 2019. "An efficient pseudo-polynomial algorithm for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem," European Journal of Operational Research, Elsevier, vol. 275(1), pages 35-44.
    6. Carlier, Jacques & Neron, Emmanuel, 2007. "Computing redundant resources for the resource constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1452-1463, February.
    7. Christian Artigues & Emmanuel Hébrard & Alain Quilliot & Hélène Toussaint, 2024. "The Continuous Time-Resource Trade-off Scheduling Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1676-1695, December.
    8. Mostafa Khatami & Amir Salehipour, 2021. "A binary search algorithm for the general coupled task scheduling problem," 4OR, Springer, vol. 19(4), pages 593-611, December.
    9. Nicolas Beldiceanu & Mats Carlsson & Sophie Demassey & Emmanuel Poder, 2011. "New filtering for the cumulative constraint in the context of non-overlapping rectangles," Annals of Operations Research, Springer, vol. 184(1), pages 27-50, April.
    10. Thierry Petit & Emmanuel Poder, 2011. "Global propagation of side constraints for solving over-constrained problems," Annals of Operations Research, Springer, vol. 184(1), pages 295-314, April.
    11. Coughlan, Eamonn T. & Lübbecke, Marco E. & Schulz, Jens, 2015. "A branch-price-and-cut algorithm for multi-mode resource leveling," European Journal of Operational Research, Elsevier, vol. 245(1), pages 70-80.
    12. Evgeny Gafarov & Alexander Lazarev & Frank Werner, 2014. "Approximability results for the resource-constrained project scheduling problem with a single type of resources," Annals of Operations Research, Springer, vol. 213(1), pages 115-130, February.
    13. Alexander Tesch, 2020. "A polyhedral study of event-based models for the resource-constrained project scheduling problem," Journal of Scheduling, Springer, vol. 23(2), pages 233-251, April.
    14. Roger Kameugne & Laure Pauline Fotso, 2013. "A cumulative not-first/not-last filtering algorithm in O(n 2log(n))," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(1), pages 95-115, February.
    15. François Clautiaux & Cláudio Alves & José Valério de Carvalho, 2010. "A survey of dual-feasible and superadditive functions," Annals of Operations Research, Springer, vol. 179(1), pages 317-342, September.

    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:320:y:2025:i:3:p:505-515. 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.