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A heuristic for solving large bin packing problems in two and three dimensions

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  • Daniel Mack
  • Andreas Bortfeldt

Abstract

The more-dimensional bin packing problem (BPP) considered here requires packing a set of rectangular-shaped items into a minimum number of identical rectangular-shaped bins. All items may be rotated and the guillotine cut constraint has to be respected. A straightforward heuristic is presented that is based on a method for the container loading problem following a wall-building approach and on a method for the one-dimensional BPP. 1,800 new benchmark instances are introduced for the two-dimensional and three-dimensional BPP. The instances include more than 1,500 items on average. Applied to these very large instances, the heuristic generates solutions of acceptable quality in short computation times. Moreover, the influence of different instance parameters on the solution quality is investigated by an extended computational study. Copyright Springer-Verlag 2012

Suggested Citation

  • Daniel Mack & Andreas Bortfeldt, 2012. "A heuristic for solving large bin packing problems in two and three dimensions," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(2), pages 337-354, June.
    • Handle: RePEc:spr:cejnor:v:20:y:2012:i:2:p:337-354
    DOI: 10.1007/s10100-010-0184-1
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    References listed on IDEAS

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    Cited by:

    1. Igor Kierkosz & Maciej Luczak, 2014. "A hybrid evolutionary algorithm for the two-dimensional packing problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(4), pages 729-753, December.
    2. Gonçalves, José Fernando & Resende, Mauricio G.C., 2013. "A biased random key genetic algorithm for 2D and 3D bin packing problems," International Journal of Production Economics, Elsevier, vol. 145(2), pages 500-510.
    3. Cui, Yi-Ping & Cui, Yaodong & Tang, Tianbing, 2015. "Sequential heuristic for the two-dimensional bin-packing problem," European Journal of Operational Research, Elsevier, vol. 240(1), pages 43-53.
    4. Pedro Rochavetz Lara Andrade & Silvio Alexandre Araujo & Adriana Cristina Cherri & Felipe Kesrouani Lemos, 2023. "The cutting stock problem applied to the hardening process in an automotive spring factory," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(2), pages 637-664, June.
    5. Nikolaus Furian & Siegfried Vössner, 2014. "A hybrid algorithm for constrained order packing," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(1), pages 157-186, March.
    6. Carlos A. Vega-Mejía & Jairo R. Montoya-Torres & Sardar M. N. Islam, 2019. "Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review," Annals of Operations Research, Springer, vol. 273(1), pages 311-375, February.

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