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An effective recursive partitioning approach for the packing of identical rectangles in a rectangle

Author

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  • E G Birgin

    (University of São Paulo)

  • R D Lobato

    (University of São Paulo)

  • R Morabito

    (Federal University of São Paulo)

Abstract

In this work, we deal with the problem of packing (orthogonally and without overlapping) identical rectangles in a rectangle. This problem appears in different logistics settings, such as the loading of boxes on pallets, the arrangements of pallets in trucks and the stowing of cargo in ships. We present a recursive partitioning approach combining improved versions of a recursive five-block heuristic and an L-approach for packing rectangles into larger rectangles and L-shaped pieces. The combined approach is able to rapidly find the optimal solutions of all instances of the pallet loading problem sets Cover I and II (more than 50 000 instances). It is also effective for solving the instances of problem set Cover III (almost 100 000 instances) and practical examples of a woodpulp stowage problem, if compared to other methods from the literature. Some theoretical results are also discussed and, based on them, efficient computer implementations are introduced. The computer implementation and the data sets are available for benchmarking purposes.

Suggested Citation

  • E G Birgin & R D Lobato & R Morabito, 2010. "An effective recursive partitioning approach for the packing of identical rectangles in a rectangle," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(2), pages 306-320, February.
    • Handle: RePEc:pal:jorsoc:v:61:y:2010:i:2:d:10.1057_jors.2008.141
    DOI: 10.1057/jors.2008.141
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    References listed on IDEAS

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    12. L Lins & S Lins & R Morabito, 2003. "An L-approach for packing (ℓ, w)-rectangles into rectangular and L-shaped pieces," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(7), pages 777-789, July.
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    14. E G Birgin & R Morabito & F H Nishihara, 2005. "A note on an L-approach for solving the manufacturer's pallet loading problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(12), pages 1448-1451, December.
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    Cited by:

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    2. Bayón-Cueli, C. & Barbón, A. & Bayón, L. & Barbón, N., 2020. "A cost-energy based methodology for small-scale linear Fresnel reflectors on flat roofs of urban buildings," Renewable Energy, Elsevier, vol. 146(C), pages 944-959.
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    4. Michele Monaci & André Gustavo Santos, 2018. "Minimum tiling of a rectangle by squares," Annals of Operations Research, Springer, vol. 271(2), pages 831-851, December.

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