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Pattern-set generation algorithm for the one-dimensional cutting stock problem with setup cost

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  • Cui, Yaodong
  • Zhong, Cheng
  • Yao, Yi

Abstract

The primary objective in the one-dimensional cutting stock problem is to minimize material cost. In real applications it is often necessary to consider auxiliary objectives, one of which is to reduce the number of different cutting patterns (setups). This paper first presents an integer linear programming model to minimize the sum of material and setup costs over a given pattern set, and then describes a sequential grouping procedure to generate the patterns in the set. Two sets of benchmark instances are used in the computational test. The results indicate that the approach is efficient in improving the solution quality.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:2:p:540-546
    DOI: 10.1016/j.ejor.2014.12.015
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    References listed on IDEAS

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    1. 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.
    2. Robert W. Haessler, 1975. "Controlling Cutting Pattern Changes in One-Dimensional Trim Problems," Operations Research, INFORMS, vol. 23(3), pages 483-493, June.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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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    Cited by:

    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. 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.
    3. 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.
    4. 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.
    5. Lin Liu & Xinbao Liu & Jun Pei & Wenjuan Fan & Panos M. Pardalos, 2017. "A study on decision making of cutting stock with frustum of cone bars," Operational Research, Springer, vol. 17(1), pages 187-204, April.
    6. 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.

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