Skip to main content
SpringerLink
Log in
Book cover

International Conference on Industrial Engineering

ICIE 2018: Proceedings of the 4th International Conference on Industrial Engineering pp 1875–1883Cite as

Packing Compaction Algorithm for Rectangular Cutting and Orthogonal Packing Problems

  • Conference paper
  • First Online:

  • 97 Accesses

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

The rectangular cutting and orthogonal packing problems which have many practical applications in industry and engineering are considered. Increasing the density of placement schemes leads to reducing the material usage in solving the rectangular cutting problems and reducing the unused resources at solving the orthogonal packing problems. This article contains the description of the developed packing compaction algorithm and its investigation. This algorithm uses six object selection rules, which select objects from a container for deleting and subsequent reallocation of them into freed spaces of the container. The packing compaction algorithm iteratively applies a one-pass heuristic algorithm which finds the best placement of the deleted objects in order to increase the density of the result packing. The effectiveness of the application of the proposed algorithm is investigated on the standard two-dimensional strip packing problems which are the rectangular cutting problems with only one container of a fixed width and an infinite length. Based on the test results, the effective sequence of application of the proposed rules used as the part of the packing algorithm was determined. The packing compaction algorithm is implemented in a general form which makes it possible for application in the rectangular cutting and orthogonal packing problems of arbitrary dimension.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Wascher G, Haubner H, Schumann H (2007) An improved typology of cutting and packing problems. EJOR 183(3):1109–1130

    Article  Google Scholar 

  2. Johnson DS (2012) A brief history of NP-completeness, 1954–2012. Doc Math Extra Volume ISMP 359–376

    Google Scholar 

  3. Chekanin VA, Chekanin AV (2014) Development of the multimethod genetic algorithm for the strip packing problem. Appl Mech Mater 598:377–381

    Article  Google Scholar 

  4. Goncalves JF, Resende MGC (2013) A biased random key genetic algorithm for 2D and 3D bin packing problems. Int J Prod Econ 145(2):500–510

    Article  Google Scholar 

  5. Kierkosz I, Luczak M (2014) A hybrid evolutionary algorithm for the two-dimensional packing problem. Cent Eur J Oper Res 22(4):729–753

    Article  MathSciNet  Google Scholar 

  6. Leung SCH, Zhang DF, Zhou CL, Wu T (2012) A hybrid simulated annealing metaheuristic algorithm for the two-dimensional knapsack packing problem. Comput Oper Res 39(1):64–73

    Article  Google Scholar 

  7. Bortfeldt A, Wascher G (2013) Constraints in container loading—a state-of-the-art review. EJOR 229(1):1–20

    Article  MathSciNet  Google Scholar 

  8. Fekete SP, Schepers J, van der Veen JC (2007) An exact algorithm for higher-dimensional orthogonal packing. Oper Res 55(3):569–587

    Article  MathSciNet  Google Scholar 

  9. Lins L, Lins S, Morabito R (2002) An n-tet graph approach for non-guillotine packings of n-dimensional boxes into an n-container. EJOR 141(2):421–439

    Article  MathSciNet  Google Scholar 

  10. Westerlund J, Papageorgiou LG, Westerlund T (2007) A MILP model for N-dimensional allocation. Comput Chem Eng 31(12):1702–1714

    Article  Google Scholar 

  11. Chekanin VA, Chekanin AV (2015) An efficient model for the orthogonal packing problem. Adv Mech Eng 22:33–38

    MATH  Google Scholar 

  12. Chekanin VA, Chekanin AV (2016) Implementation of packing methods for the orthogonal packing problems. J Theor Appl Inf Technol 88(3):421–430

    MATH  Google Scholar 

  13. Chekanin AV, Chekanin VA (2014) Effective data structure for the multidimensional orthogonal bin packing problems. Adv Mater Res 962–965:2868–2871

    Article  Google Scholar 

  14. Chekanin VA, Chekanin AV (2014) Improved data structure for the orthogonal packing problem. Adv Mater Res 945–949:3143–3146

    Article  Google Scholar 

  15. Chekanin VA, Chekanin AV (2017) Algorithms and methods in multidimensional orthogonal packing problems. Int J Appl Eng Res 12(6):1009–1019

    MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  18. Chekanin VA, Chekanin AV (2015) Development of optimization software to solve practical packing and cutting problems. Adv Intell Syst Res 123:379–382

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University of Technology “STANKIN”, 3a, Vadkovsky Lane, Moscow, 127055, Russia

    V. A. Chekanin & A. V. Chekanin

Authors
  1. V. A. Chekanin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Chekanin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. A. Chekanin .

Editor information

Editors and Affiliations

  1. South Ural State University, Chelyabinsk, Russia

    Andrey A. Radionov

  2. Platov South-Russian State Polytechnic University, Novocherkassk, Russia

    Oleg A. Kravchenko

  3. South Ural State University, Chelyabinsk, Russia

    Victor I. Guzeev

  4. South Ural State University, Chelyabinsk, Russia

    Yurij V. Rozhdestvenskiy

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Chekanin, V.A., Chekanin, A.V. (2019). Packing Compaction Algorithm for Rectangular Cutting and Orthogonal Packing Problems. In: Radionov, A., Kravchenko, O., Guzeev, V., Rozhdestvenskiy, Y. (eds) Proceedings of the 4th International Conference on Industrial Engineering. ICIE 2018. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-95630-5_201

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-95630-5_201

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-95629-9

  • Online ISBN: 978-3-319-95630-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation