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Relations between capacity utilization, minimal bin size and bin number

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  • Torsten Buchwald
  • Kirsten Hoffmann
  • Guntram Scheithauer

Abstract

We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer $${k} \ge 3$$ k ≥ 3 that at most $${k}-1$$ k - 1 bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed $${k}/4$$ k / 4 -times the bin area. Moreover, this bound is tight. Furthermore, we show that only two bins are necessary to pack all items if the total area of items is not larger than the bin area, and if the height of each item is not larger than a third of the bin height and the width of every item does not exceed half of the bin width. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Torsten Buchwald & Kirsten Hoffmann & Guntram Scheithauer, 2014. "Relations between capacity utilization, minimal bin size and bin number," Annals of Operations Research, Springer, vol. 217(1), pages 55-76, June.
    • Handle: RePEc:spr:annopr:v:217:y:2014:i:1:p:55-76:10.1007/s10479-014-1572-z
    DOI: 10.1007/s10479-014-1572-z
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    References listed on IDEAS

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    1. Sándor P. Fekete & Jörg Schepers, 2004. "A General Framework for Bounds for Higher-Dimensional Orthogonal Packing Problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 311-329, October.
    2. Lodi, Andrea & Martello, Silvano & Monaci, Michele, 2002. "Two-dimensional packing problems: A survey," European Journal of Operational Research, Elsevier, vol. 141(2), pages 241-252, September.
    3. Silvano Martello & Daniele Vigo, 1998. "Exact Solution of the Two-Dimensional Finite Bin Packing Problem," Management Science, INFORMS, vol. 44(3), pages 388-399, March.
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