IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v179y2010i1p15-3310.1007-s10479-008-0458-3.html
   My bibliography  Save this article

Bun splitting: a practical cutting stock problem

Author

Listed:
  • Celia Glass
  • Jeroen Oostrum

Abstract

We describe a new hierarchical 2D-guillotine Cutting Stock Problem. In contrast to the classic cutting stock problem, waste is not an issue. The problem relates to the removal of a defective part and assembly of the remaining parts into homogeneous size blocks. The context is the packing stages of cake manufacturing. The company’s primary objective is to minimise total processing time at the subsequent, packing stage. This objective reduces to one of minimising the number of parts produced when cutting the tray load of buns. We offer a closed form optimization approach to this class of problems for certain cases, without recourse to mathematical programming or heuristics. The methodology is demonstrated through a case study in which the number of parts is reduced by almost a fifth, and the manufacturer’s subsidiary requirement to reduce isolated single bun parts and hence customer complaints is also satisfied. Copyright The Author(s) 2010

Suggested Citation

  • Celia Glass & Jeroen Oostrum, 2010. "Bun splitting: a practical cutting stock problem," Annals of Operations Research, Springer, vol. 179(1), pages 15-33, September.
    • Handle: RePEc:spr:annopr:v:179:y:2010:i:1:p:15-33:10.1007/s10479-008-0458-3
    DOI: 10.1007/s10479-008-0458-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0458-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0458-3?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. Nicos Christofides & Charles Whitlock, 1977. "An Algorithm for Two-Dimensional Cutting Problems," Operations Research, INFORMS, vol. 25(1), pages 30-44, February.
    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. P. C. Gilmore & R. E. Gomory, 1966. "The Theory and Computation of Knapsack Functions," Operations Research, INFORMS, vol. 14(6), pages 1045-1074, December.
    4. Ronny Aboudi & Paulo Barcia, 1998. "Determining cutting stock patternswhen defects are present," Annals of Operations Research, Springer, vol. 82(0), pages 343-354, August.
    5. 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.
    6. Ronnqvist, Mikael & Astrand, Erik, 1998. "Integrated defect detection and optimization for cross cutting of wooden boards," European Journal of Operational Research, Elsevier, vol. 108(3), pages 490-508, August.
    7. Sweeney, Paul E. & Haessler, Robert W., 1990. "One-dimensional cutting stock decisions for rolls with multiple quality grades," European Journal of Operational Research, Elsevier, vol. 44(2), pages 224-231, January.
    8. Susan G. Hahn, 1968. "On the Optimal Cutting of Defective Sheets," Operations Research, INFORMS, vol. 16(6), pages 1100-1114, December.
    9. Ronnqvist, Mikael, 1995. "A method for the cutting stock problem with different qualities," European Journal of Operational Research, Elsevier, vol. 83(1), pages 57-68, May.
    10. Dyckhoff, Harald, 1990. "A typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 145-159, January.
    11. Christofides, Nicos & Hadjiconstantinou, Eleni, 1995. "An exact algorithm for orthogonal 2-D cutting problems using guillotine cuts," European Journal of Operational Research, Elsevier, vol. 83(1), pages 21-38, May.
    12. P. C. Gilmore & R. E. Gomory, 1965. "Multistage Cutting Stock Problems of Two and More Dimensions," Operations Research, INFORMS, vol. 13(1), pages 94-120, February.
    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. 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.

    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. 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).
    2. Vera Neidlein & Andrèa C. G. Vianna & Marcos N. Arenales & Gerhard Wäscher, 2008. "The Two-Dimensional, Rectangular, Guillotineable-Layout Cutting Problem with a Single Defect," FEMM Working Papers 08035, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    3. 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.
    4. 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.
    5. Felix Prause & Kai Hoppmann-Baum & Boris Defourny & Thorsten Koch, 2021. "The maximum diversity assortment selection problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 521-554, June.
    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. Mhand Hifi, 2004. "Dynamic Programming and Hill-Climbing Techniques for Constrained Two-Dimensional Cutting Stock Problems," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 65-84, March.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. de Armas, Jesica & Miranda, Gara & León, Coromoto, 2012. "Improving the efficiency of a best-first bottom-up approach for the Constrained 2D Cutting Problem," European Journal of Operational Research, Elsevier, vol. 219(2), pages 201-213.
    13. 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.
    14. Hadjiconstantinou, Eleni & Iori, Manuel, 2007. "A hybrid genetic algorithm for the two-dimensional single large object placement problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1150-1166, December.
    15. Chen, C. S. & Lee, S. M. & Shen, Q. S., 1995. "An analytical model for the container loading problem," European Journal of Operational Research, Elsevier, vol. 80(1), pages 68-76, January.
    16. Rapine, Christophe & Pedroso, Joao Pedro & Akbalik, Ayse, 2022. "The two-dimensional knapsack problem with splittable items in stacks," Omega, Elsevier, vol. 112(C).
    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. 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.
    19. Claudio Arbib & Fabrizio Marinelli & Mustafa Ç. Pınar & Andrea Pizzuti, 2022. "Robust stock assortment and cutting under defects in automotive glass production," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 4154-4172, November.
    20. Wei, Lijun & Lim, Andrew, 2015. "A bidirectional building approach for the 2D constrained guillotine knapsack packing problem," European Journal of Operational Research, Elsevier, vol. 242(1), pages 63-71.

    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:annopr:v:179:y:2010:i:1:p:15-33:10.1007/s10479-008-0458-3. 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.