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A hybrid placement strategy for the three-dimensional strip packing problem

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  • Allen, S.D.
  • Burke, E.K.
  • Kendall, G.

Abstract

This paper presents a hybrid placement strategy for the three-dimensional strip packing problem which involves packing a set of cuboids ('boxes') into a three-dimensional bin (parallelepiped) of fixed width and height but unconstrained length (the 'container'). The goal is to pack all of the boxes into the container, minimising its resulting length. This problem has potential industry application in stock cutting (wood, polystyrene, etc. - minimising wastage) and also cargo loading, as well as other applications in areas such as multi-dimensional resource scheduling. In addition to the proposed strategy a number of test results on available literature benchmark problems are presented and analysed. The results of empirical testing of the algorithm show that it out-performs other methods from the literature, consistently in terms of speed and solution quality-producing 28 best known results from 35 test cases.

Suggested Citation

  • Allen, S.D. & Burke, E.K. & Kendall, G., 2011. "A hybrid placement strategy for the three-dimensional strip packing problem," European Journal of Operational Research, Elsevier, vol. 209(3), pages 219-227, March.
    • Handle: RePEc:eee:ejores:v:209:y:2011:i:3:p:219-227
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    References listed on IDEAS

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    1. Bischoff, E. E. & Ratcliff, M. S. W., 1995. "Issues in the development of approaches to container loading," Omega, Elsevier, vol. 23(4), pages 377-390, August.
    2. Faina, Loris, 1999. "An application of simulated annealing to the cutting stock problem," European Journal of Operational Research, Elsevier, vol. 114(3), pages 542-556, May.
    3. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    4. E. K. Burke & G. Kendall & G. Whitwell, 2004. "A New Placement Heuristic for the Orthogonal Stock-Cutting Problem," Operations Research, INFORMS, vol. 52(4), pages 655-671, August.
    5. Edmund K. Burke & Graham Kendall & Glenn Whitwell, 2009. "A Simulated Annealing Enhancement of the Best-Fit Heuristic for the Orthogonal Stock-Cutting Problem," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 505-516, August.
    6. Hopper, E. & Turton, B. C. H., 2001. "An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem," European Journal of Operational Research, Elsevier, vol. 128(1), pages 34-57, January.
    7. Teodor Gabriel Crainic & Guido Perboli & Roberto Tadei, 2008. "Extreme Point-Based Heuristics for Three-Dimensional Bin Packing," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 368-384, August.
    8. Bortfeldt, Andreas & Mack, Daniel, 2007. "A heuristic for the three-dimensional strip packing problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1267-1279, December.
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    Citations

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    Cited by:

    1. Wei, Lijun & Oon, Wee-Chong & Zhu, Wenbin & Lim, Andrew, 2012. "A reference length approach for the 3D strip packing problem," European Journal of Operational Research, Elsevier, vol. 220(1), pages 37-47.
    2. Bortfeldt, Andreas, 2013. "A reduction approach for solving the rectangle packing area minimization problem," European Journal of Operational Research, Elsevier, vol. 224(3), pages 486-496.
    3. Andreas Bortfeldt & Sabine Jungmann, 2012. "A tree search algorithm for solving the multi-dimensional strip packing problem with guillotine cutting constraint," Annals of Operations Research, Springer, vol. 196(1), pages 53-71, July.
    4. Kurpel, Deidson Vitorio & Scarpin, Cassius Tadeu & Pécora Junior, José Eduardo & Schenekemberg, Cleder Marcos & Coelho, Leandro C., 2020. "The exact solutions of several types of container loading problems," European Journal of Operational Research, Elsevier, vol. 284(1), pages 87-107.
    5. Sam D. Allen & Edmund K. Burke, 2012. "Data Structures for Higher-Dimensional Rectilinear Packing," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 457-470, August.
    6. Eunice López-Camacho & Gabriela Ochoa & Hugo Terashima-Marín & Edmund Burke, 2013. "An effective heuristic for the two-dimensional irregular bin packing problem," Annals of Operations Research, Springer, vol. 206(1), pages 241-264, July.
    7. 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.
    8. Thiago Queiroz & Flávio Miyazawa, 2014. "Order and static stability into the strip packing problem," Annals of Operations Research, Springer, vol. 223(1), pages 137-154, December.
    9. Bortfeldt, Andreas & Wäscher, Gerhard, 2013. "Constraints in container loading – A state-of-the-art review," European Journal of Operational Research, Elsevier, vol. 229(1), pages 1-20.

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