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Journal of Global Optimization

, Volume 74, Issue 3, pp 467–476 | Cite as

Large proper gaps in bin packing and dual bin packing problems

  • Vadim M. Kartak
  • Artem V. RipattiEmail author
Article

Abstract

We consider the one-dimensional skiving stock problem, also known as the dual bin packing problem, with the aim of maximizing the best known dual and proper dual gaps. We apply the methods of computational search of large gaps initially developed for the one-dimensional cutting stock problem, which is related to the bin packing problem. The best known dual gap is raised from 1.0476 to 1.1795. The proper dual gap is improved to 1.1319. We also apply a number of new heuristics developed for the skiving stock problem back to the cutting stock problem, raising the largest known proper gap from 1.0625 to 1.1.

Keywords

Skiving stock problem Cutting stock problem Bin packing problem Dual bin packing problem Integer round-up property Equivalence of classes Proper gap 

Notes

Acknowledgements

The authors would like to thank Dresden Technical University for providing computing power and Damir Akhmetzyanov, who helped to improve English in this paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Bashkir State Pedagogical University named after M. AkmullahUfaRussia
  2. 2.Ufa State Aviation Technical UniversityUfaRussia

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