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A simple and effective recursive procedure for the manufacturer's pallet loading problem

Author

Listed:
  • R Morabito

    (Universidade Federal de São Carlos)

  • S Morales

    (Universidade Federal de São Carlos)

Abstract

In this paper we present a simple and effective heuristic to solve the problem of packing the maximum number of rectangles of sizes (l,w) and (w,l) into a larger rectangle (L,W) without overlapping. This problem appears in the loading of identical boxes on pallets, namely the manufacturer's pallet loading (MPL), as well as in package design and truck or rail car loading. Although apparently easy to be optimally solved, the MPL is claimed to be NP-complete and several authors have proposed approximate methods to deal with it. The procedure described in the present paper can be seen as a refinement of Bischoff and Dowsland's heuristic and can easily be implemented on a microcomputer. Using moderate computational resources, the procedure was able to find the optimal solution of 99.9% of more than 20 000 examples analysed.

Suggested Citation

  • R Morabito & S Morales, 1998. "A simple and effective recursive procedure for the manufacturer's pallet loading problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 49(8), pages 819-828, August.
    • Handle: RePEc:pal:jorsoc:v:49:y:1998:i:8:d:10.1057_palgrave.jors.2600588
    DOI: 10.1057/palgrave.jors.2600588
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    Citations

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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. 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.
    3. 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.
    4. Adamos Daios & Nikolaos Kladovasilakis & Ioannis Kostavelis, 2024. "Mixed Palletizing for Smart Warehouse Environments: Sustainability Review of Existing Methods," Sustainability, MDPI, vol. 16(3), pages 1-15, February.
    5. 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.
    6. Lorenzo Brunetta & Philippe Grégoire, 2005. "A General Purpose Algorithm for Three-Dimensional Packing," INFORMS Journal on Computing, INFORMS, vol. 17(3), pages 328-338, August.
    7. M. T. Alonso & R. Alvarez-Valdes & F. Parreño, 2020. "A GRASP algorithm for multi container loading problems with practical constraints," 4OR, Springer, vol. 18(1), pages 49-72, March.
    8. Hugo Barros & Teresa Pereira & António G. Ramos & Fernanda A. Ferreira, 2021. "Complexity Constraint in the Distributor’s Pallet Loading Problem," Mathematics, MDPI, vol. 9(15), pages 1-20, July.
    9. Linda S. Moonen & Frits C. R. Spieksma, 2006. "Exact Algorithms for a Loading Problem with Bounded Clique Width," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 455-465, November.
    10. Naiara P. V. Sebbe & Francisco J. G. Silva & Alcinda M. S. Barreiras & Isabel M. Pinto & Rita C. M. Sales-Contini & Luis P. Ferreira & Ana B. M. Machado, 2024. "Pallet Loading Problem: A Case Study in the Automotive Industry Applying a Simplified Mathematical Model," Mathematics, MDPI, vol. 12(7), pages 1-17, March.
    11. 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.

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