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Positions and covering: A two-stage methodology to obtain optimal solutions for the 2d-bin packing problem

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

Abstract

We present a two-stage methodology called Positions and Covering (P&C) to solve the two-dimensional bin packing problem (2D-BPP). The objective of this classical combinatorial NP-hard problem is to pack a set of items (small rectangles) in the minimum number of bins (larger rectangles). The first stage is the key-point of the Positions and Covering, where for each item, it is generated in a pseudo-polynomial way a set of valid positions that indicate the possible ways of packing the item into the bin. In the second stage, a new set-covering formulation, strengthen with three sets of valid inequalities, is used to select the optimal non-overlapping configuration of items for each bin. Experimental results for the P&C method are presented and compared with some of the best algorithms in the literature for small and medium size instances. Furthermore, we are considering both cases of the 2D-BPP, with and without rotations of the items by 90°. To the best of our knowledge, this is one of the first exact approaches to obtain optimal solutions for the rotation case.

Suggested Citation

  • Nestor M Cid-Garcia & Yasmin A Rios-Solis, 2020. "Positions and covering: A two-stage methodology to obtain optimal solutions for the 2d-bin packing problem," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-22, April.
    • Handle: RePEc:plo:pone00:0229358
    DOI: 10.1371/journal.pone.0229358
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    1. Thanh-Hung Nguyen & Xuan-Thuan Nguyen, 2023. "Space Splitting and Merging Technique for Online 3-D Bin Packing," Mathematics, MDPI, vol. 11(8), pages 1-16, April.

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