IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v326y2025i2p207-219.html

Two-dimensional cutting stock problem with flexible length and usable leftovers in the steel industry

Author

Listed:
  • Ma, Yunfeng
  • Zhang, Jiayi
  • Yang, Xijie
  • Li, Jihao
  • Su, Xiaoxin
  • Chen, Haoxun

Abstract

In this work, we introduce a two-dimensional cutting stock problem with flexible length and usable leftovers, in which multiple objectives, including minimizing the waste area of material, the exceeding area of orders and the number of slitter adjustments, are considered simultaneously. This problem is inspired by a real-world made-to-order manufacturer of special steel plates. We propose a non-linear mathematical programming model for this problem. This model is then linearized and reinforced by symmetry-breaking inequalities and other valid inequalities. To solve this model, we propose an iterated local search algorithm, which is able to tackle large instances of the problem. Numerical results demonstrate the validity of the proposed model and the effectiveness of the iterated local search algorithm. Besides, sensitive experiments are conducted to assess the impact of different parameter settings on the objective function.

Suggested Citation

  • Ma, Yunfeng & Zhang, Jiayi & Yang, Xijie & Li, Jihao & Su, Xiaoxin & Chen, Haoxun, 2025. "Two-dimensional cutting stock problem with flexible length and usable leftovers in the steel industry," European Journal of Operational Research, Elsevier, vol. 326(2), pages 207-219.
    • Handle: RePEc:eee:ejores:v:326:y:2025:i:2:p:207-219
    DOI: 10.1016/j.ejor.2025.04.036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221725003212
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2025.04.036?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

    for a different version of it.

    References listed on IDEAS

    as
    1. François Clautiaux & Ruslan Sadykov & François Vanderbeck & Quentin Viaud, 2019. "Pattern-based diving heuristics for a two-dimensional guillotine cutting-stock problem with leftovers," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 265-297, September.
    2. 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.
    3. Ricardo Andrade & Ernesto G Birgin & Reinaldo Morabito & Débora P Ronconi, 2014. "MIP models for two-dimensional non-guillotine cutting problems with usable leftovers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(11), pages 1649-1663, November.
    4. 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.
    5. 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.
    6. Paula Terán-Viadero & Antonio Alonso-Ayuso & F. Javier Martín-Campo, 2024. "A 2-dimensional guillotine cutting stock problem with variable-sized stock for the honeycomb cardboard industry," International Journal of Production Research, Taylor & Francis Journals, vol. 62(1-2), pages 483-500, January.
    7. Supphakorn Sumetthapiwat & Boonyarit Intiyot & Chawalit Jeenanunta, 2020. "A column generation on two-dimensional cutting stock problem with fixed-size usable leftover and multiple stock sizes," International Journal of Logistics Systems and Management, Inderscience Enterprises Ltd, vol. 35(2), pages 273-288.
    8. 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.
    9. Sierra-Paradinas, María & Soto-Sánchez, Óscar & Alonso-Ayuso, Antonio & Martín-Campo, F. Javier & Gallego, Micael, 2021. "An exact model for a slitting problem in the steel industry," European Journal of Operational Research, Elsevier, vol. 295(1), pages 336-347.
    10. Parreño, F. & Alvarez-Valdes, R., 2021. "Mathematical models for a cutting problem in the glass manufacturing industry," Omega, Elsevier, vol. 103(C).
    11. Terán-Viadero, Paula & Alonso-Ayuso, Antonio & Martín-Campo, F. Javier, 2024. "Mathematical optimisation in the honeycomb cardboard industry: A model for the two-dimensional variable-sized cutting stock problem," European Journal of Operational Research, Elsevier, vol. 319(1), pages 303-315.
    12. Anantaram Balakrishnan & Joseph Geunes, 2003. "Production Planning with Flexible Product Specifications: An Application to Specialty Steel Manufacturing," Operations Research, INFORMS, vol. 51(1), pages 94-112, February.
    13. P. Y. Wang, 1983. "Two Algorithms for Constrained Two-Dimensional Cutting Stock Problems," Operations Research, INFORMS, vol. 31(3), pages 573-586, June.
    14. Helena Ramalhinho Lourenço & Olivier C. Martin & Thomas Stützle, 2019. "Iterated Local Search: Framework and Applications," International Series in Operations Research & Management Science, in: Michel Gendreau & Jean-Yves Potvin (ed.), Handbook of Metaheuristics, edition 3, chapter 0, pages 129-168, Springer.
    15. 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.
    16. Palhazi Cuervo, Daniel & Goos, Peter & Sörensen, Kenneth & Arráiz, Emely, 2014. "An iterated local search algorithm for the vehicle routing problem with backhauls," European Journal of Operational Research, Elsevier, vol. 237(2), pages 454-464.
    17. Jongsung Lee & Byung-in kim & Andrew Johnson, 2013. "A two-dimensional bin packing problem with size changeable items for the production of wind turbine flanges in the open die forging industry," IISE Transactions, Taylor & Francis Journals, vol. 45(12), pages 1332-1344.
    18. 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.
    19. Libralesso, Luc & Fontan, Florian, 2021. "An anytime tree search algorithm for the 2018 ROADEF/EURO challenge glass cutting problem," European Journal of Operational Research, Elsevier, vol. 291(3), pages 883-893.
    20. Malaguti, Enrico & Medina Durán, Rosa & Toth, Paolo, 2014. "Approaches to real world two-dimensional cutting problems," Omega, Elsevier, vol. 47(C), pages 99-115.
    21. 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.
    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. 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.
    2. 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.
    3. Terán-Viadero, Paula & Alonso-Ayuso, Antonio & Martín-Campo, F. Javier, 2024. "Mathematical optimisation in the honeycomb cardboard industry: A model for the two-dimensional variable-sized cutting stock problem," European Journal of Operational Research, Elsevier, vol. 319(1), pages 303-315.
    4. 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).
    5. 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.
    6. Rapine, Christophe & Pedroso, Joao Pedro & Akbalik, Ayse, 2022. "The two-dimensional knapsack problem with splittable items in stacks," Omega, Elsevier, vol. 112(C).
    7. Alyne Toscano & Socorro Rangel & Horacio Hideki Yanasse, 2017. "A heuristic approach to minimize the number of saw cycles in small-scale furniture factories," Annals of Operations Research, Springer, vol. 258(2), pages 719-746, November.
    8. Óscar Soto-Sánchez & María Sierra-Paradinas & Micael Gallego & Antonio Alonso-Ayuso & Francisco Gortázar, 2025. "A heuristic algorithm to improving the coil slitting process in the steel industry," Journal of Heuristics, Springer, vol. 31(1), pages 1-38, March.
    9. 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.
    10. 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.
    11. Parreño, F. & Alvarez-Valdes, R., 2021. "Mathematical models for a cutting problem in the glass manufacturing industry," Omega, Elsevier, vol. 103(C).
    12. 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.
    13. Elisama Araújo Silva Oliveira & Elizabeth Wanner & Elisangela Martins Sá & Sérgio Ricardo Souza, 2025. "A local branching-based solution for the multi-period cutting stock problem with tardiness, earliness, and setup costs," Journal of Heuristics, Springer, vol. 31(1), pages 1-57, March.
    14. 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.
    15. Paredes-Belmar, Germán & Montero, Elizabeth & Lüer-Villagra, Armin & Marianov, Vladimir & Araya-Sassi, Claudio, 2022. "Vehicle routing for milk collection with gradual blending: A case arising in Chile," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1403-1416.
    16. 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.
    17. 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.
    18. Mateus Martin & Horacio Hideki Yanasse & Luiz Leduíno Salles-Neto, 2022. "Pattern-based ILP models for the one-dimensional cutting stock problem with setup cost," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 557-582, August.
    19. Wuttke, David A. & Heese, H. Sebastian, 2018. "Two-dimensional cutting stock problem with sequence dependent setup times," European Journal of Operational Research, Elsevier, vol. 265(1), pages 303-315.
    20. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:eee:ejores:v:326:y:2025:i:2:p:207-219. 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.