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International Conference on Computer Aided Systems Theory

EUROCAST 2015: Computer Aided Systems Theory – EUROCAST 2015 pp 384–392Cite as

A Scalable Approach for the K-Staged Two-Dimensional Cutting Stock Problem with Variable Sheet Size

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9520))

Abstract

We present a new scalable approach for the K-staged two-dimensional cutting stock problem with variable sheet size, particularly aiming to solve large-scale instances from industry. A construction heuristic exploiting the congruency of subpatterns efficiently computes sheet patterns of high quality. This heuristic is embedded in a beam-search framework to allow for a meaningful selection from the available sheet types. Computational experiments on benchmark instances show the effectiveness of our approach and demonstrate its scalability.

We thank LodeStar Technology for their support and collaboration in this project.

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References

  1. Berkey, J.O., Wang, P.Y.: Two-dimensional finite bin-packing algorithms. J. Oper. Res. Soc. 38(5), 423–429 (1987)

    Article  MATH  Google Scholar 

  2. Cintra, G., Miyazawa, F., Wakabayashi, Y., Xavier, E.: Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation. Eur. J. Oper. Res. 191(1), 61–85 (2008)

    Article  MATH  Google Scholar 

  3. Fleszar, K.: Three insertion heuristics and a justification improvement heuristic for two-dimensional bin packing with guillotine cuts. Comput. Oper. Res. 40(1), 463–474 (2013)

    Article  Google Scholar 

  4. Gilmore, P.C., Gomory, R.E.: Multistage cutting stock problems of two and more dimensions. Oper. Res. 13(1), 94–120 (1965)

    Article  MATH  Google Scholar 

  5. Hong, S., Zhang, D., Lau, H.C., Zeng, X., Si, Y.: A hybrid heuristic algorithm for the 2D variable-sized bin packing problem. Eur. J. Oper. Res. 238(1), 95–103 (2014)

    Article  MathSciNet  Google Scholar 

  6. Hopper, E., Turton, B.C.H.: An empirical study of meta-heuristics applied to 2D rectangular bin packing - Part I. Stud. Informatica Univers. 2(1), 77–92 (2002)

    Google Scholar 

  7. Lodi, A., Martello, S., Monaci, M.: Two-dimensional packing problems: a survey. Eur. J. Oper. Res. 141(2), 241–252 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lodi, A., Martello, S., Vigo, D.: Recent advances on two-dimensional bin packing problems. Discrete Appl. Math. 123(13), 379–396 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lowerre, B.T.: The harpy speech recognition system. Ph.D. thesis, Carnegie Mellon University, Pittsburgh, PA, USA (1976)

    Google Scholar 

  10. Martello, S., Vigo, D.: Exact solution of the two-dimensional finite bin packing problem. Manage. Sci. 44(3), 388–399 (1998)

    Article  MATH  Google Scholar 

  11. Pisinger, D., Sigurd, M.: The two-dimensional bin packing problem with variable bin sizes and costs. Discrete Optim. 2(2), 154–167 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computer Graphics and Algorithms, TU Wien, Vienna, Austria

    Frederico Dusberger & Günther R. Raidl

Authors
  1. Frederico Dusberger
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  2. Günther R. Raidl
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Corresponding author

Correspondence to Frederico Dusberger .

Editor information

Editors and Affiliations

  1. de Gran Canaria, Universidad de las Palmas de Gran Canari, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Johannes Kepler University Linz, Linz, Austria

    Franz Pichler

  3. de Gran Canaria, Universidad de las Palmas de Gran Canari, Las Palmas de Gran Canaria, Spain

    Alexis Quesada-Arencibia

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© 2015 Springer International Publishing Switzerland

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Dusberger, F., Raidl, G.R. (2015). A Scalable Approach for the K-Staged Two-Dimensional Cutting Stock Problem with Variable Sheet Size. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2015. EUROCAST 2015. Lecture Notes in Computer Science(), vol 9520. Springer, Cham. https://doi.org/10.1007/978-3-319-27340-2_48

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  • DOI: https://doi.org/10.1007/978-3-319-27340-2_48

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27339-6

  • Online ISBN: 978-3-319-27340-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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