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An algorithm for the three-dimensional packing problem with asymptotic performance analysis

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Abstract

The three-dimensional packing problem can be stated as follows. Given a list of boxes, each with a given length, width, and height, the problem is to pack these boxes into a rectangular box of fixed-size bottom and unbounded height, so that the height of this packing is minimized. The boxes have to be packed orthogonally and oriented in all three dimensions. We present an approximation algorithm for this problem and show that its asymptotic performance bound is between 2.5 and 2.67. This result answers a question raised by Li and Cheng [5] about the existence of an algorithm for this problem with an asymptotic performance bound less than 2.89.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05315-970, São Paulo, SP, Brazil

    F. K. Miyazawa & Y. Wakabayashi

Authors
  1. F. K. Miyazawa
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  2. Y. Wakabayashi
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Additional information

Communicated by M. X. Goemans.

This research was partially supported by FAPESP (proc. 93/0603-1) and by CNPq/ProTeM-CC, project ProComb (proc. 680065/94-6).

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Miyazawa, F.K., Wakabayashi, Y. An algorithm for the three-dimensional packing problem with asymptotic performance analysis. Algorithmica 18, 122–144 (1997). https://doi.org/10.1007/BF02523692

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  • DOI: https://doi.org/10.1007/BF02523692

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