Skip to main content
SpringerLink
Log in

Efficient Lower Bounds for Packing Problems in Heterogeneous Bins with Conflicts Constraint

  • Conference paper
  • First Online:
Intelligent Mathematics II: Applied Mathematics and Approximation Theory

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 441))

  • 902 Accesses

Abstract

In this paper we discuss a version of the classical one dimensional bin-packing problem, where the objective is to minimize the total cost of heterogeneous bins needed to store given items, each with some space requirements. In this version, some of the items are incompatible with each other, and cannot be packed together. This problem with various real world applications generalizes both the Variable Sized Bin Packing Problem and the Vertex Coloring Problem. We propose two lower bounds for this problem based on both the relaxation of the integrity constraints and the computation of the large clique in the conflicts graph.

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

Access this chapter

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

Institutional subscriptions

References

  1. Zhang, G.: A new version of on-line variable-sized bin packing. Discrete Appl. Math. 72(3), 193–197 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Epstein, L., Favrholdt, L.L.M., Levin, A.: Online variable-sized bin packing with conflicts. Discrete Optim. 8, 333–343 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Kang, J., Park, S.: Algorithms for the variable sized bin-packing problem. Eur. J. Oper. Res. 147, 365–372 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Haouari, M., Serairi, M.: Heuristics for the variable sized bin-packing problem. Comput. Oper. Res. 36(10), 2877–2884 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Haouari, M., Serairi, M.: Relaxations and exact solution of the variable sized bin packing problem. Comput. Optim. Appl. 48, 345–368 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci. 9, 256–278 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gendreau, M., Laporte, G., Semet, F.: Heuristics and lower bounds for the bin packing problem with conflicts. Comput. Oper. Res. 31, 347–358 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Muritiba, A.E.F., Iori, M., Malaguti, E., Toth, P.: Algorithms for the bin packing problem with conflicts. INFORMS J. Comput. 22, 401–415 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Mathématiques Appliquées-Ecole Militaire Polytechnique, Bordj El Bahri-Alger, Algiers, Algeria

    Mohamed Maiza

  2. Laboratoire de Modélisation et Optimisation des Systémes, Université de Béjaia, Béjaia, Algeria

    Mohammed Said Radjef

  3. Centre de Recherche en Informatique de Lens CNRS-UMR8188, Université d’Artois, F-62300, Lens, France

    Lakhdar Sais

Authors
  1. Mohamed Maiza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammed Said Radjef
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lakhdar Sais
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed Maiza .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee, USA

    George A. Anastassiou

  2. Department of Mathematics, TOBB Economics and Technology University, Ankara, Turkey

    Oktay Duman

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Maiza, M., Said Radjef, M., Sais, L. (2016). Efficient Lower Bounds for Packing Problems in Heterogeneous Bins with Conflicts Constraint. In: Anastassiou, G., Duman, O. (eds) Intelligent Mathematics II: Applied Mathematics and Approximation Theory. Advances in Intelligent Systems and Computing, vol 441. Springer, Cham. https://doi.org/10.1007/978-3-319-30322-2_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-30322-2_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30320-8

  • Online ISBN: 978-3-319-30322-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation