IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v55y2013i2p349-357.html
   My bibliography  Save this article

A new dynamic programming procedure for three-staged cutting patterns

Author

Listed:
  • Yaodong Cui

Abstract

Three-staged patterns are often used to solve the 2D cutting stock problem of rectangular items. They can be divided into items in three stages: Vertical cuts divide the plate into segments; then horizontal cuts divide the segments into strips, and finally vertical cuts divide the strips into items. An algorithm for unconstrained three-staged patterns is presented, where a set of rectangular item types are packed into the plate so as to maximize the pattern value, and there is no constraint on the frequencies of each item type. It can be used jointly with the linear programming approach to solve the cutting stock problem. The algorithm solves three large knapsack problems to obtain the optimal pattern: One for the item layout on the widest strip, one for the strip layout on the longest segment, and the third for the segment layout on the plate. The computational results indicate that the algorithm is efficient. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Yaodong Cui, 2013. "A new dynamic programming procedure for three-staged cutting patterns," Journal of Global Optimization, Springer, vol. 55(2), pages 349-357, February.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:2:p:349-357
    DOI: 10.1007/s10898-012-9930-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-9930-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-9930-3?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. François Vanderbeck, 2001. "A Nested Decomposition Approach to a Three-Stage, Two-Dimensional Cutting-Stock Problem," Management Science, INFORMS, vol. 47(6), pages 864-879, June.
    2. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    3. Oliveira, Jose Fernando & Wascher, Gerhard, 2007. "Cutting and Packing," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1106-1108, December.
    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. Jianyu Long & Zhong Zheng & Xiaoqiang Gao & Panos M. Pardalos & Wanzhe Hu, 2020. "An effective heuristic based on column generation for the two-dimensional three-stage steel plate cutting problem," Annals of Operations Research, Springer, vol. 289(2), pages 291-311, June.
    2. Russo, Mauro & Sforza, Antonio & Sterle, Claudio, 2013. "An improvement of the knapsack function based algorithm of Gilmore and Gomory for the unconstrained two-dimensional guillotine cutting problem," International Journal of Production Economics, Elsevier, vol. 145(2), pages 451-462.

    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. Cui, Yaodong & Huang, Baixiong, 2012. "Reducing the number of cuts in generating three-staged cutting patterns," European Journal of Operational Research, Elsevier, vol. 218(2), pages 358-365.
    2. 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.
    3. Jean-François Côté & Manuel Iori, 2018. "The Meet-in-the-Middle Principle for Cutting and Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 646-661, November.
    4. 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.
    5. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    6. Reinaldo Morabito & Vitória Pureza, 2010. "A heuristic approach based on dynamic programming and and/or-graph search for the constrained two-dimensional guillotine cutting problem," Annals of Operations Research, Springer, vol. 179(1), pages 297-315, September.
    7. Castro, Pedro M. & Oliveira, José F., 2011. "Scheduling inspired models for two-dimensional packing problems," European Journal of Operational Research, Elsevier, vol. 215(1), pages 45-56, November.
    8. Setzer, Thomas & Bichler, Martin, 2013. "Using matrix approximation for high-dimensional discrete optimization problems: Server consolidation based on cyclic time-series data," European Journal of Operational Research, Elsevier, vol. 227(1), pages 62-75.
    9. Alexander Abuabara & Reinaldo Morabito, 2009. "Cutting optimization of structural tubes to build agricultural light aircrafts," Annals of Operations Research, Springer, vol. 169(1), pages 149-165, July.
    10. Kallrath, Julia & Rebennack, Steffen & Kallrath, Josef & Kusche, Rüdiger, 2014. "Solving real-world cutting stock-problems in the paper industry: Mathematical approaches, experience and challenges," European Journal of Operational Research, Elsevier, vol. 238(1), pages 374-389.
    11. Chiranjit Changdar & Rajat Kumar Pal & Ghanshaym Singha Mahapatra & Abhinandan Khan, 2020. "A genetic algorithm based approach to solve multi-resource multi-objective knapsack problem for vegetable wholesalers in fuzzy environment," Operational Research, Springer, vol. 20(3), pages 1321-1352, September.
    12. Cui, Yaodong & Yang, Liu & Zhao, Zhigang & Tang, Tianbing & Yin, Mengxiao, 2013. "Sequential grouping heuristic for the two-dimensional cutting stock problem with pattern reduction," International Journal of Production Economics, Elsevier, vol. 144(2), pages 432-439.
    13. Silva, Elsa & Alvelos, Filipe & Valério de Carvalho, J.M., 2010. "An integer programming model for two- and three-stage two-dimensional cutting stock problems," European Journal of Operational Research, Elsevier, vol. 205(3), pages 699-708, September.
    14. Muter, İbrahim & Sezer, Zeynep, 2018. "Algorithms for the one-dimensional two-stage cutting stock problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 20-32.
    15. Huang, Wenqi & He, Kun, 2009. "A caving degree approach for the single container loading problem," European Journal of Operational Research, Elsevier, vol. 196(1), pages 93-101, July.
    16. 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.
    17. 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.
    18. Cui, Yaodong & Gu, Tianlong & Hu, Wei, 2009. "A cutting-and-inventory control problem in the manufacturing industry of stainless steel wares," Omega, Elsevier, vol. 37(4), pages 864-875, August.
    19. Cherri, Adriana Cristina & Arenales, Marcos Nereu & Yanasse, Horacio Hideki & Poldi, Kelly Cristina & Gonçalves Vianna, Andréa Carla, 2014. "The one-dimensional cutting stock problem with usable leftovers – A survey," European Journal of Operational Research, Elsevier, vol. 236(2), pages 395-402.
    20. Hadj Salem, Khadija & Silva, Elsa & Oliveira, José Fernando & Carravilla, Maria Antónia, 2023. "Mathematical models for the two-dimensional variable-sized cutting stock problem in the home textile industry," European Journal of Operational Research, Elsevier, vol. 306(2), pages 549-566.

    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:jglopt:v:55:y:2013:i:2:p:349-357. 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.