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Controlling Cutting Pattern Changes in One-Dimensional Trim Problems

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  • Robert W. Haessler

    (Wright State University, Dayton, Ohio)

Abstract

This paper develops a formulation of the one-dimensional trim problem when there is a fixed charge associated with using a cutting pattern. The purpose of the fixed charge is to limit the number of pattern changes that must be made. Because of the large number of possible cutting patterns, the resulting problem is a combinatorial program that is far beyond the capability of existing algorithms. As a result, we develop a heuristic procedure that can be experimentally tuned to balance the potentially conflicting objectives of minimizing both trim loss and pattern changes. The heuristic procedure is organized around a sequential search that relies on descriptors of the unscheduled orders to set goals on factors such as trim loss and pattern usage for the next pattern to enter the solution. A sample problem is presented along with a discussion of the scope of the application of the heuristic procedure.

Suggested Citation

  • Robert W. Haessler, 1975. "Controlling Cutting Pattern Changes in One-Dimensional Trim Problems," Operations Research, INFORMS, vol. 23(3), pages 483-493, June.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:3:p:483-493
    DOI: 10.1287/opre.23.3.483
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    Cited by:

    1. 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.
    2. Maimon, Oded & Dayagi, Arie, 1995. "Nesting planning based on production priorities and technological efficiency," European Journal of Operational Research, Elsevier, vol. 80(1), pages 121-129, January.
    3. 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.
    4. Malaguti, Enrico & Medina Durán, Rosa & Toth, Paolo, 2014. "Approaches to real world two-dimensional cutting problems," Omega, Elsevier, vol. 47(C), pages 99-115.
    5. 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.
    6. Gramani, Maria Cristina N. & Franca, Paulo M., 2006. "The combined cutting stock and lot-sizing problem in industrial processes," European Journal of Operational Research, Elsevier, vol. 174(1), pages 509-521, October.
    7. Suliman, Saad M. A., 2001. "Pattern generating procedure for the cutting stock problem," International Journal of Production Economics, Elsevier, vol. 74(1-3), pages 293-301, December.
    8. 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.
    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. 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.
    11. 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.
    12. Tao Wu & Kerem Akartunal? & Raf Jans & Zhe Liang, 2017. "Progressive Selection Method for the Coupled Lot-Sizing and Cutting-Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 523-543, August.
    13. Jie Fang & Yunqing Rao & Qiang Luo & Jiatai Xu, 2023. "Solving One-Dimensional Cutting Stock Problems with the Deep Reinforcement Learning," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    14. 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.
    15. Wagner, Bret J., 1999. "A genetic algorithm solution for one-dimensional bundled stock cutting," European Journal of Operational Research, Elsevier, vol. 117(2), pages 368-381, September.
    16. 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.
    17. 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.
    18. 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.
    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. 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.
    21. Degraeve, Zeger & Gochet, Willy & Jans, Raf, 2002. "Alternative formulations for a layout problem in the fashion industry," European Journal of Operational Research, Elsevier, vol. 143(1), pages 80-93, November.
    22. 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.
    23. Vahrenkamp, Richard, 1996. "Random search in the one-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 95(1), pages 191-200, November.

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