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An L-approach for packing (ℓ, w)-rectangles into rectangular and L-shaped pieces

Author

Listed:
  • L Lins

    (Universidade Federal de Pernambuco)

  • S Lins

    (Universidade Federal de Pernambuco)

  • R Morabito

    (Universidade Federal de São Carlos)

Abstract

This paper presents an approach using a recursive algorithm for packing (ℓ, w)-rectangles into larger rectangular and L-shaped pieces. Such a problem has actual applications for non-guillotine cutting and pallet/container loading. Our motivation for developing the L-approach is based on the fact that it can solve difficult pallet loading instances. Indeed, it is able to solve all testing problems (more than 20 000 representatives of infinite equivalence classes of the literature), including the 18 hard instances unresolved by other heuristics. We conjecture that the L-approach always finds optimum packings of (ℓ, w)-rectangles into rectangular pieces. Moreover, the approach may also be useful when dealing with cutting and packing problems involving L-shaped pieces.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:54:y:2003:i:7:d:10.1057_palgrave.jors.2601553
    DOI: 10.1057/palgrave.jors.2601553
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. E G Birgin & J M Martínez & W F Mascarenhas & D P Ronconi, 2006. "Method of sentinels for packing items within arbitrary convex regions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 735-746, June.
    3. Martins, Gustavo H.A. & Dell, Robert F., 2007. "The minimum size instance of a Pallet Loading Problem equivalence class," European Journal of Operational Research, Elsevier, vol. 179(1), pages 17-26, May.
    4. 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.
    5. 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.
    6. 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.
    7. Martins, Gustavo H.A. & Dell, Robert F., 2008. "Solving the pallet loading problem," European Journal of Operational Research, Elsevier, vol. 184(2), pages 429-440, January.
    8. Lu, Yiping & Cha, Jianzhong, 2014. "A fast algorithm for identifying minimum size instances of the equivalence classes of the Pallet Loading Problem," European Journal of Operational Research, Elsevier, vol. 237(3), pages 794-801.
    9. G M Ribeiro & L A N Lorena, 2008. "Optimizing the woodpulp stowage using Lagrangean relaxation with clusters," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(5), pages 600-606, May.

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