IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v25y2017i2d10.1007_s10100-017-0466-y.html
   My bibliography  Save this article

One-dimensional stock cutting: optimization of usable leftovers in consecutive orders

Author

Listed:
  • Luka Tomat

    (University of Ljubljana)

  • Mirko Gradišar

    (University of Ljubljana)

Abstract

This paper deals with usable leftovers (UL) in one-dimensional stock cutting in consecutive orders. UL are leftovers longer than a certain threshold and are returned to stock in order to be used in future orders. Shorter leftovers are treated as trim-loss. If UL are being used at a slower pace, than they are being generated for a longer period of time, excessive growth of UL in stock can appear. This is not acceptable due to higher costs of manipulations and warehousing. However, a certain amount of UL in stock is desirable because it contributes to greater variety of stock lengths, which in general results in lower trim-loss. The method solves the problem of how to calculate the near optimal amount of UL in stock and how to control the stock. The proposed method is tested by using a computer simulation in which UL from previous orders are used in the next ones instead of being randomly generated. The computational results indicate that trim-loss in consecutive orders is reduced, and excessive growth of UL in stock is prevented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:cejnor:v:25:y:2017:i:2:d:10.1007_s10100-017-0466-y
    DOI: 10.1007/s10100-017-0466-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10100-017-0466-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10100-017-0466-y?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. 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.
    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. 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.
    4. 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.
    5. L. V. Kantorovich, 1960. "Mathematical Methods of Organizing and Planning Production," Management Science, INFORMS, vol. 6(4), pages 366-422, July.
    6. Claudio Arbib & Fabrizio Marinelli & Fabrizio Rossi & Francesco Di Iorio, 2002. "Cutting and Reuse: An Application from Automobile Component Manufacturing," Operations Research, INFORMS, vol. 50(6), pages 923-934, December.
    7. 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.
    8. Gau, T. & Wascher, G., 1995. "CUTGEN1: A problem generator for the standard one-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 84(3), pages 572-579, August.
    9. Diegel, Adolf & Montocchio, Edouard & Walters, Edward & van Schalkwyk, Sias & Naidoo, Spurs, 1996. "Setup minimising conditions in the trim loss problem," European Journal of Operational Research, Elsevier, vol. 95(3), pages 631-640, December.
    10. 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.
    11. 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.
    12. Nikolaus Furian & Siegfried Vössner, 2014. "A hybrid algorithm for constrained order packing," 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(1), pages 157-186, March.
    13. Leão, Aline A.S. & Santos, Maristela O. & Hoto, Robinson & Arenales, Marcos N., 2011. "The constrained compartmentalized knapsack problem: mathematical models and solution methods," European Journal of Operational Research, Elsevier, vol. 212(3), pages 455-463, August.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    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. Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2017. "Editorial," 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(3), pages 521-523, September.
    7. 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.
    8. 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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Aktin, Tülin & Özdemir, RIfat Gürcan, 2009. "An integrated approach to the one-dimensional cutting stock problem in coronary stent manufacturing," European Journal of Operational Research, Elsevier, vol. 196(2), pages 737-743, July.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Hajizadeh, Iman & Lee, Chi-Guhn, 2007. "Alternative configurations for cutting machines in a tube cutting mill," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1385-1396, 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:spr:cejnor:v:25:y:2017:i:2:d:10.1007_s10100-017-0466-y. 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.