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Generating unconstrained two-dimensional non-guillotine cutting patterns by a Recursive Partitioning Algorithm

Author

Listed:
  • E G Birgin

    (University of São Paulo, São Paulo, Brazil)

  • R D Lobato

    (University of São Paulo, São Paulo, Brazil)

  • R Morabito

    (Federal University of São Carlos, São Carlos, Brazil)

Abstract

In this study, a dynamic programming approach to deal with the unconstrained two-dimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer's pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. The method is able to find the optimal cutting pattern of a large number of pro blem instances of moderate sizes known in the literature and a counterexample for which the approach fails to find known optimal solutions was not found. For the instances that the required computer runtime is excessive, the approach is combined with simple heuristics to reduce its running time. Detailed numerical experiments show the reliability of the method.

Suggested Citation

  • E G Birgin & R D Lobato & R Morabito, 2012. "Generating unconstrained two-dimensional non-guillotine cutting patterns by a Recursive Partitioning Algorithm," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(2), pages 183-200, February.
    • Handle: RePEc:pal:jorsoc:v:63:y:2012:i:2:p:183-200
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    Cited by:

    1. Wei, Lijun & Hu, Qian & Lim, Andrew & Liu, Qiang, 2018. "A best-fit branch-and-bound heuristic for the unconstrained two-dimensional non-guillotine cutting problem," European Journal of Operational Research, Elsevier, vol. 270(2), pages 448-474.
    2. 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.
    3. Jéssica Gabriela Almeida Cunha & Vinícius Loti de Lima & Thiago Alves Queiroz, 2020. "Grids for cutting and packing problems: a study in the 2D knapsack problem," 4OR, Springer, vol. 18(3), pages 293-339, September.

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