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The Three-Dimensional Bin Packing Problem

Author

Listed:
  • Silvano Martello

    (DEIS, University of Bologna, Viale Risorgimento 2, Bologna, Italy)

  • David Pisinger

    (DIKU, University of Copenhagen, University Parken 1, Copenhagen, Denmark)

  • Daniele Vigo

    (DEIS, University of Bologna, Viale Risorgimento 2, Bologna, Italy)

Abstract

The problem addressed in this paper is that of orthogonally packing a given set of rectangular-shaped items into the minimum number of three-dimensional rectangular bins. The problem is strongly NP-hard and extremely difficult to solve in practice. Lower bounds are discussed, and it is proved that the asymptotic worst-case performance ratio of the continuous lower bound is 1/8. An exact algorithm for filling a single bin is developed, leading to the definition of an exact branch-and-bound algorithm for the three-dimensional bin packing problem, which also incorporates original approximation algorithms. Extensive computational results, involving instances with up to 90 items, are presented: It is shown that many instances can be solved to optimality within a reasonable time limit.

Suggested Citation

  • Silvano Martello & David Pisinger & Daniele Vigo, 2000. "The Three-Dimensional Bin Packing Problem," Operations Research, INFORMS, vol. 48(2), pages 256-267, April.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:2:p:256-267
    DOI: 10.1287/opre.48.2.256.12386
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    References listed on IDEAS

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