IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v144y2013i2p432-439.html
   My bibliography  Save this article

Sequential grouping heuristic for the two-dimensional cutting stock problem with pattern reduction

Author

Listed:
  • Cui, Yaodong
  • Yang, Liu
  • Zhao, Zhigang
  • Tang, Tianbing
  • Yin, Mengxiao

Abstract

A sequential grouping heuristic (SGH) that supports parallel computing is presented for solving the two-dimensional cutting stock problem with pattern reduction, where a set of rectangular items with given demand are cut from rectangular stock plates of the same size, considering both input-minimization (main objective) and pattern reduction (auxiliary objective). It is based on the sequential heuristic procedure that generates each next pattern to fulfill some portion of the remaining items and repeats until all items are fulfilled. The SGH uses a grouping technique to select the items that can be used to generate the next pattern, and adjusts the item values according to the sequential value correction method after the next pattern is generated. Each next pattern is generated using a dynamic programming recursion. The computational results indicate that the SGH is powerful in both input-minimization and pattern reduction, and the parallel computing is useful to reduce computation time.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:proeco:v:144:y:2013:i:2:p:432-439
    DOI: 10.1016/j.ijpe.2013.03.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925527313001278
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijpe.2013.03.011?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. 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.
    2. Erjavec, J. & Gradisar, M. & Trkman, P., 2012. "Assessment of stock size to minimize cutting stock production costs," International Journal of Production Economics, Elsevier, vol. 135(1), pages 170-176.
    3. 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.
    4. 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.
    5. Mhand Hifi & Rym M'Hallah & Toufik Saadi, 2008. "Algorithms for the Constrained Two-Staged Two-Dimensional Cutting Problem," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 212-221, May.
    6. Mhand Hifi & Catherine Roucairol, 2001. "Approximate and Exact Algorithms for Constrained (Un) Weighted Two-dimensional Two-staged Cutting Stock Problems," Journal of Combinatorial Optimization, Springer, vol. 5(4), pages 465-494, December.
    7. Umetani, Shunji & Yagiura, Mutsunori & Ibaraki, Toshihide, 2003. "One-dimensional cutting stock problem to minimize the number of different patterns," European Journal of Operational Research, Elsevier, vol. 146(2), pages 388-402, April.
    8. P. Y. Wang, 1983. "Two Algorithms for Constrained Two-Dimensional Cutting Stock Problems," Operations Research, INFORMS, vol. 31(3), pages 573-586, June.
    9. Mhand Hifi & Rym M'Hallah, 2005. "An Exact Algorithm for Constrained Two-Dimensional Two-Staged Cutting Problems," Operations Research, INFORMS, vol. 53(1), pages 140-150, February.
    10. Gleb Belov & Guntram Scheithauer, 2007. "Setup and Open-Stacks Minimization in One-Dimensional Stock Cutting," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 27-35, February.
    11. Haessler, Robert W. & Sweeney, Paul E., 1991. "Cutting stock problems and solution procedures," European Journal of Operational Research, Elsevier, vol. 54(2), pages 141-150, September.
    12. Song, X. & Chu, C.B. & Nie, Y.Y. & Bennell, J.A., 2006. "An iterative sequential heuristic procedure to a real-life 1.5-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1870-1889, December.
    13. Belov, G. & Scheithauer, G., 2006. "A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting," European Journal of Operational Research, Elsevier, vol. 171(1), pages 85-106, May.
    14. Arbib, Claudio & Marinelli, Fabrizio & Pezzella, Ferdinando, 2012. "An LP-based tabu search for batch scheduling in a cutting process with finite buffers," International Journal of Production Economics, Elsevier, vol. 136(2), pages 287-296.
    15. Suliman, S.M.A., 2006. "A sequential heuristic procedure for the two-dimensional cutting-stock problem," International Journal of Production Economics, Elsevier, vol. 99(1-2), pages 177-185, February.
    16. Parada Daza, Victor & Gomes de Alvarenga, Arlindo & de Diego, Jose, 1995. "Exact solutions for constrained two-dimensional cutting problems," European Journal of Operational Research, Elsevier, vol. 84(3), pages 633-644, August.
    17. Mhand Hifi & Toufik Saadi, 2012. "A parallel algorithm for two-staged two-dimensional fixed-orientation cutting problems," Computational Optimization and Applications, Springer, vol. 51(2), pages 783-807, March.
    18. Cintra, G.F. & Miyazawa, F.K. & Wakabayashi, Y. & Xavier, E.C., 2008. "Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation," European Journal of Operational Research, Elsevier, vol. 191(1), pages 61-85, November.
    19. François Vanderbeck, 2000. "Exact Algorithm for Minimising the Number of Setups in the One-Dimensional Cutting Stock Problem," Operations Research, INFORMS, vol. 48(6), pages 915-926, December.
    20. Hifi, Mhand & M'Hallah, Rym, 2006. "Strip generation algorithms for constrained two-dimensional two-staged cutting problems," European Journal of Operational Research, Elsevier, vol. 172(2), pages 515-527, July.
    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. Cui, Yaodong & Zhong, Cheng & Yao, Yi, 2015. "Pattern-set generation algorithm for the one-dimensional cutting stock problem with setup cost," European Journal of Operational Research, Elsevier, vol. 243(2), pages 540-546.
    2. Silva, Eduardo M. & Melega, Gislaine M. & Akartunalı, Kerem & de Araujo, Silvio A., 2023. "Formulations and theoretical analysis of the one-dimensional multi-period cutting stock problem with setup cost," European Journal of Operational Research, Elsevier, vol. 304(2), pages 443-460.
    3. 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.

    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 & Zhao, Zhigang, 2013. "Heuristic for the rectangular two-dimensional single stock size cutting stock problem with two-staged patterns," European Journal of Operational Research, Elsevier, vol. 231(2), pages 288-298.
    2. 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.
    3. Silva, Elsa & Oliveira, José Fernando & Silveira, Tiago & Mundim, Leandro & Carravilla, Maria Antónia, 2023. "The Floating-Cuts model: a general and flexible mixed-integer programming model for non-guillotine and guillotine rectangular cutting problems," Omega, Elsevier, vol. 114(C).
    4. Song, X. & Chu, C.B. & Lewis, R. & Nie, Y.Y. & Thompson, J., 2010. "A worst case analysis of a dynamic programming-based heuristic algorithm for 2D unconstrained guillotine cutting," European Journal of Operational Research, Elsevier, vol. 202(2), pages 368-378, April.
    5. 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.
    6. Mhand Hifi & Toufik Saadi, 2012. "A parallel algorithm for two-staged two-dimensional fixed-orientation cutting problems," Computational Optimization and Applications, Springer, vol. 51(2), pages 783-807, March.
    7. 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.
    8. Ramiro Varela & Camino Vela & Jorge Puente & María Sierra & Inés González-Rodríguez, 2009. "An effective solution for a real cutting stock problem in manufacturing plastic rolls," Annals of Operations Research, Springer, vol. 166(1), pages 125-146, February.
    9. 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.
    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. Mhand Hifi & Rym M'Hallah & Toufik Saadi, 2008. "Algorithms for the Constrained Two-Staged Two-Dimensional Cutting Problem," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 212-221, May.
    12. 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.
    13. Malaguti, Enrico & Medina Durán, Rosa & Toth, Paolo, 2014. "Approaches to real world two-dimensional cutting problems," Omega, Elsevier, vol. 47(C), pages 99-115.
    14. 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.
    15. 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.
    16. Douglas Nogueira Nascimento & Adriana Cristina Cherri & José Fernando Oliveira, 2022. "The two-dimensional cutting stock problem with usable leftovers: mathematical modelling and heuristic approaches," Operational Research, Springer, vol. 22(5), pages 5363-5403, November.
    17. M. Hifi & R. M’Hallah & T. Saadi, 2009. "Approximate and exact algorithms for the double-constrained two-dimensional guillotine cutting stock problem," Computational Optimization and Applications, Springer, vol. 42(2), pages 303-326, March.
    18. Wang, Danni & Xiao, Fan & Zhou, Lei & Liang, Zhe, 2020. "Two-dimensional skiving and cutting stock problem with setup cost based on column-and-row generation," European Journal of Operational Research, Elsevier, vol. 286(2), pages 547-563.
    19. 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.
    20. Parreño, F. & Alvarez-Valdes, R., 2021. "Mathematical models for a cutting problem in the glass manufacturing industry," Omega, Elsevier, vol. 103(C).

    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:proeco:v:144:y:2013:i:2:p:432-439. 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/ijpe .

    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.