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Exact solutions for the 2d-strip packing problem using the positions-and-covering methodology

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  • Nestor M Cid-Garcia
  • Yasmin A Rios-Solis

Abstract

We use the Positions and Covering methodology to obtain exact solutions for the two-dimensional, non-guillotine restricted, strip packing problem. In this classical NP-hard problem, a given set of rectangular items has to be packed into a strip of fixed weight and infinite height. The objective consists in determining the minimum height of the strip. The Positions and Covering methodology is based on a two-stage procedure. First, it is generated, in a pseudo-polynomial way, a set of valid positions in which an item can be packed into the strip. Then, by using a set-covering formulation, the best configuration of items into the strip is selected. Based on the literature benchmark, experimental results validate the quality of the solutions and method’s effectiveness for small and medium-size instances. To the best of our knowledge, this is the first approach that generates optimal solutions for some literature instances for which the optimal solution was unknown before this study.

Suggested Citation

  • Nestor M Cid-Garcia & Yasmin A Rios-Solis, 2021. "Exact solutions for the 2d-strip packing problem using the positions-and-covering methodology," PLOS ONE, Public Library of Science, vol. 16(1), pages 1-20, January.
    • Handle: RePEc:plo:pone00:0245267
    DOI: 10.1371/journal.pone.0245267
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    References listed on IDEAS

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    1. Jakobs, Stefan, 1996. "On genetic algorithms for the packing of polygons," European Journal of Operational Research, Elsevier, vol. 88(1), pages 165-181, January.
    2. Silvano Martello & Michele Monaci & Daniele Vigo, 2003. "An Exact Approach to the Strip-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 310-319, August.
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