IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v184y2011i1p27-5010.1007-s10479-010-0731-0.html
   My bibliography  Save this article

New filtering for the cumulative constraint in the context of non-overlapping rectangles

Author

Listed:
  • Nicolas Beldiceanu
  • Mats Carlsson
  • Sophie Demassey
  • Emmanuel Poder

Abstract

This article describes new filtering methods for the cumulative constraint. The first method introduces the so called longest closed hole and longest open hole problems. For these two problems it first provides bounds and exact methods and then shows how to use them in the context of the non-overlapping constraint. The second method introduces balancing knapsack constraints which relate the total height of the tasks that end at a specific time-point with the total height of the tasks that start at the same time-point. Experiments on tight rectangle packing problems show that these methods drastically reduce both the time and the number of backtracks for finding all solutions as well as for finding the first solution. For example, we found without backtracking all solutions to 65 perfect square instances of order 22–25 and sizes ranging from 192×192 to 661×661. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:184:y:2011:i:1:p:27-50:10.1007/s10479-010-0731-0
    DOI: 10.1007/s10479-010-0731-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-010-0731-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-010-0731-0?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. Michael Trick, 2003. "A Dynamic Programming Approach for Consistency and Propagation for Knapsack Constraints," Annals of Operations Research, Springer, vol. 118(1), pages 73-84, February.
    2. Clautiaux, Francois & Carlier, Jacques & Moukrim, Aziz, 2007. "A new exact method for the two-dimensional orthogonal packing problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1196-1211, December.
    3. Luc Mercier & Pascal Van Hentenryck, 2008. "Edge Finding for Cumulative Scheduling," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 143-153, 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. Gleb Belov & Heide Rohling, 2013. "LP Bounds in an Interval-Graph Algorithm for Orthogonal-Packing Feasibility," Operations Research, INFORMS, vol. 61(2), pages 483-497, April.

    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. Gregory S. Taylor & Yupo Chan & Ghulam Rasool, 2017. "A three-dimensional bin-packing model: exact multicriteria solution and computational complexity," Annals of Operations Research, Springer, vol. 251(1), pages 397-427, April.
    2. Igor Kierkosz & Maciej Luczak, 2014. "A hybrid evolutionary algorithm for the two-dimensional packing problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(4), pages 729-753, December.
    3. 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.
    4. Wei, Lijun & Oon, Wee-Chong & Zhu, Wenbin & Lim, Andrew, 2011. "A skyline heuristic for the 2D rectangular packing and strip packing problems," European Journal of Operational Research, Elsevier, vol. 215(2), pages 337-346, December.
    5. Krzysztof Fleszar, 2016. "An Exact Algorithm for the Two-Dimensional Stage-Unrestricted Guillotine Cutting/Packing Decision Problem," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 703-720, November.
    6. de Armas, Jesica & Miranda, Gara & León, Coromoto, 2012. "Improving the efficiency of a best-first bottom-up approach for the Constrained 2D Cutting Problem," European Journal of Operational Research, Elsevier, vol. 219(2), pages 201-213.
    7. 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.
    8. 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.
    9. François Clautiaux & Antoine Jouglet & Aziz Moukrim, 2013. "A New Graph-Theoretical Model for the Guillotine-Cutting Problem," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 72-86, February.
    10. Jean-François Côté & Michel Gendreau & Jean-Yves Potvin, 2020. "The Vehicle Routing Problem with Stochastic Two-Dimensional Items," Transportation Science, INFORMS, vol. 54(2), pages 453-469, March.
    11. Khanafer, Ali & Clautiaux, François & Talbi, El-Ghazali, 2010. "New lower bounds for bin packing problems with conflicts," European Journal of Operational Research, Elsevier, vol. 206(2), pages 281-288, October.
    12. Fabio Furini & Enrico Malaguti & Dimitri Thomopulos, 2016. "Modeling Two-Dimensional Guillotine Cutting Problems via Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 736-751, November.
    13. Gilles Pesant, 2015. "Achieving Domain Consistency and Counting Solutions for Dispersion Constraints," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 690-703, November.
    14. 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.
    15. Iori, Manuel & de Lima, Vinícius L. & Martello, Silvano & Miyazawa, Flávio K. & Monaci, Michele, 2021. "Exact solution techniques for two-dimensional cutting and packing," European Journal of Operational Research, Elsevier, vol. 289(2), pages 399-415.
    16. Felix Prause & Kai Hoppmann-Baum & Boris Defourny & Thorsten Koch, 2021. "The maximum diversity assortment selection problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 521-554, June.
    17. Igor Kierkosz & Maciej Łuczak, 2019. "A one-pass heuristic for nesting problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(1), pages 37-60.
    18. Stéphane Grandcolas & Cyril Pain-Barre, 2022. "A hybrid metaheuristic for the two-dimensional strip packing problem," Annals of Operations Research, Springer, vol. 309(1), pages 79-102, February.
    19. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    20. Côté, J.F. & Guastaroba, G. & Speranza, M.G., 2017. "The value of integrating loading and routing," European Journal of Operational Research, Elsevier, vol. 257(1), pages 89-105.

    More about this item

    Statistics

    Access and download statistics

    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:spr:annopr:v:184:y:2011:i:1:p:27-50:10.1007/s10479-010-0731-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.