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Modified Greedy Heuristic for the one-dimensional cutting stock problem

Author

Listed:
  • Gonçalo R. L. Cerqueira

    (State University of Southwest Bahia)

  • Sérgio S. Aguiar

    (State University of Southwest Bahia)

  • Marlos Marques

    (State University of Southwest Bahia)

Abstract

One can get an integer solution for the one-dimensional cutting stock problem by means of the constructive or residual heuristic. In this work we propose a change in the Constructive Greedy Heuristic that consists in building a cutting pattern by sorting in descending order the items of pair or odd length, priority being given to those which appear more frequently in the problem, cut from objects in stock with pair or odd length respectively, with the aim of minimizing the quantity of cut objects. Computing tests that were carried out showed the efficiency of the proposed heuristic when compared with other methods in the literature that generate an integer solution for the problem and will be presented at the end of this work.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:42:y:2021:i:3:d:10.1007_s10878-021-00695-4
    DOI: 10.1007/s10878-021-00695-4
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    References listed on IDEAS

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    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. Farley, Alan A., 1990. "The cutting stock problem in the canvas industry," European Journal of Operational Research, Elsevier, vol. 44(2), pages 247-255, January.
    6. 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.
    7. Wascher, Gerhard, 1990. "An LP-based approach to cutting stock problems with multiple objectives," European Journal of Operational Research, Elsevier, vol. 44(2), pages 175-184, January.
    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. Scheithauer, Guntram & Terno, Johannes, 1995. "The modified integer round-up property of the one-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 84(3), pages 562-571, August.
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    Cited by:

    1. 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.
    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.

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