IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v196y2009i3p897-908.html
   My bibliography  Save this article

The one-dimensional cutting stock problem with usable leftover - A heuristic approach

Author

Listed:
  • Cherri, Adriana Cristina
  • Arenales, Marcos Nereu
  • Yanasse, Horacio Hideki

Abstract

In this work we consider a one-dimensional cutting stock problem in which the non-used material in the cutting patterns may be used in the future, if large enough. This feature introduces difficulties in comparing solutions of the cutting problem, for example, up to what extent a minimum leftover solution is the most interesting one when the leftover may be used. Some desirable characteristics of good solutions are defined and classical heuristic methods are modified, so that cutting patterns with undesirable leftover (not large enough to be used, nor too small to be acceptable waste) are redesigned. The performance of the modified heuristics is observed by solving instances from the literature, practical instances and randomly generated instances.

Suggested Citation

  • Cherri, Adriana Cristina & Arenales, Marcos Nereu & Yanasse, Horacio Hideki, 2009. "The one-dimensional cutting stock problem with usable leftover - A heuristic approach," European Journal of Operational Research, Elsevier, vol. 196(3), pages 897-908, August.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:3:p:897-908
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00399-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Hinxman, A. I., 1980. "The trim-loss and assortment problems: A survey," European Journal of Operational Research, Elsevier, vol. 5(1), pages 8-18, July.
    2. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    3. Stadtler, Hartmut, 1990. "A one-dimensional cutting stock problem in the aluminium industry and its solution," European Journal of Operational Research, Elsevier, vol. 44(2), pages 209-223, January.
    4. P. C. Gilmore & R. E. Gomory, 1963. "A Linear Programming Approach to the Cutting Stock Problem---Part II," Operations Research, INFORMS, vol. 11(6), pages 863-888, December.
    5. Gradisar, Miro & Resinovic, Gortan & Kljajic, Miroljub, 1999. "A hybrid approach for optimization of one-dimensional cutting," European Journal of Operational Research, Elsevier, vol. 119(3), pages 719-728, December.
    6. Gradisar, Miro & Kljajic, Miroljub & Resinovic, Gortan & Jesenko, Joze, 1999. "A sequential heuristic procedure for one-dimensional cutting," European Journal of Operational Research, Elsevier, vol. 114(3), pages 557-568, May.
    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 & 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. Santiago V. Ravelo & Cláudio N. Meneses & Maristela O. Santos, 2020. "Meta-heuristics for the one-dimensional cutting stock problem with usable leftover," Journal of Heuristics, Springer, vol. 26(4), pages 585-618, August.
    3. Cherri, Adriana Cristina & Cherri, Luiz Henrique & Oliveira, Beatriz Brito & Oliveira, José Fernando & Carravilla, Maria Antónia, 2023. "A stochastic programming approach to the cutting stock problem with usable leftovers," European Journal of Operational Research, Elsevier, vol. 308(1), pages 38-53.
    4. Cui, Yaodong & Yang, Yuli, 2010. "A heuristic for the one-dimensional cutting stock problem with usable leftover," European Journal of Operational Research, Elsevier, vol. 204(2), pages 245-250, July.
    5. 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.
    6. Kelly Poldi & Silvio Araujo, 2016. "Mathematical models and a heuristic method for the multiperiod one-dimensional cutting stock problem," Annals of Operations Research, Springer, vol. 238(1), pages 497-520, March.
    7. Yaodong Cui & Xiang Song & Yan Chen & Yi-Ping Cui, 2017. "New model and heuristic solution approach for one-dimensional cutting stock problem with usable leftovers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(3), pages 269-280, March.
    8. 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.
    9. Dongho Lee & Seunghyun Son & Doyeong Kim & Sunkuk Kim, 2020. "Special-Length-Priority Algorithm to Minimize Reinforcing Bar-Cutting Waste for Sustainable Construction," Sustainability, MDPI, vol. 12(15), pages 1-15, July.
    10. D. N. Nascimento & S. A. Araujo & A. C. Cherri, 2022. "Integrated lot-sizing and one-dimensional cutting stock problem with usable leftovers," Annals of Operations Research, Springer, vol. 316(2), pages 785-803, September.
    11. Keehoon Kwon & Doyeong Kim & Sunkuk Kim, 2021. "Cutting Waste Minimization of Rebar for Sustainable Structural Work: A Systematic Literature Review," Sustainability, MDPI, vol. 13(11), pages 1-21, May.
    12. Luka Tomat & Mirko Gradišar, 2017. "One-dimensional stock cutting: optimization of usable leftovers in consecutive orders," 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. 25(2), pages 473-489, June.
    13. Gonçalo R. L. Cerqueira & Sérgio S. Aguiar & Marlos Marques, 2021. "Modified Greedy Heuristic for the one-dimensional cutting stock problem," Journal of Combinatorial Optimization, Springer, vol. 42(3), pages 657-674, October.

    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. 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.
    2. 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.
    3. B. S. C. Campello & C. T. L. S. Ghidini & A. O. C. Ayres & W. A. Oliveira, 2022. "A residual recombination heuristic for one-dimensional cutting stock problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 194-220, April.
    4. 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.
    5. Holthaus, Oliver, 2002. "Decomposition approaches for solving the integer one-dimensional cutting stock problem with different types of standard lengths," European Journal of Operational Research, Elsevier, vol. 141(2), pages 295-312, September.
    6. 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.
    7. Yanasse, Horacio Hideki & Pinto Lamosa, Maria Jose, 2007. "An integrated cutting stock and sequencing problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1353-1370, December.
    8. Gonçalo R. L. Cerqueira & Sérgio S. Aguiar & Marlos Marques, 2021. "Modified Greedy Heuristic for the one-dimensional cutting stock problem," Journal of Combinatorial Optimization, Springer, vol. 42(3), pages 657-674, October.
    9. Hoto, Robinson & Arenales, Marcos & Maculan, Nelson, 2007. "The one dimensional Compartmentalised Knapsack Problem: A case study," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1183-1195, December.
    10. Trkman, Peter & Gradisar, Miro, 2007. "One-dimensional cutting stock optimization in consecutive time periods," European Journal of Operational Research, Elsevier, vol. 179(2), pages 291-301, June.
    11. 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.
    12. Alfieri, Arianna & van de Velde, Steef & Woeginger, Gerhard J., 2007. "Roll cutting in the curtain industry, or: A well-solvable allocation problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1397-1404, December.
    13. Krzysztof C. Kiwiel, 2010. "An Inexact Bundle Approach to Cutting-Stock Problems," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 131-143, February.
    14. Morabito, Reinaldo & Belluzzo, Luciano, 2007. "Optimising the cutting of wood fibre plates in the hardboard industry," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1405-1420, December.
    15. Pedro Rochavetz Lara Andrade & Silvio Alexandre Araujo & Adriana Cristina Cherri & Felipe Kesrouani Lemos, 2023. "The cutting stock problem applied to the hardening process in an automotive spring factory," 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. 31(2), pages 637-664, June.
    16. Gradisar, Miro & Resinovic, Gortan & Kljajic, Miroljub, 1999. "A hybrid approach for optimization of one-dimensional cutting," European Journal of Operational Research, Elsevier, vol. 119(3), pages 719-728, December.
    17. Keehoon Kwon & Doyeong Kim & Sunkuk Kim, 2021. "Cutting Waste Minimization of Rebar for Sustainable Structural Work: A Systematic Literature Review," Sustainability, MDPI, vol. 13(11), pages 1-21, May.
    18. Morgan, Leslie O. & Morton, Alysse R. & Daniels, Richard L., 2006. "Simultaneously determining the mix of space launch vehicles and the assignment of satellites to rockets," European Journal of Operational Research, Elsevier, vol. 172(3), pages 747-760, August.
    19. Valerio de Carvalho, J. M., 2002. "LP models for bin packing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 141(2), pages 253-273, September.
    20. 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.

    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:196:y:2009:i:3:p:897-908. 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.