Skip to main content
Log in

Models and Complexity of Multibin Packing Problems

  • Published:
Journal of Mathematical Modelling and Algorithms

Abstract

This paper extends the previous work on multibin packing problems and gives a deeper insight into these models and their complexity, so as to provide a strong framework for future application-oriented studies. In a multibin problem, an object requires several bins to be packed. New models are represented, including the maximum cardinality multibin packing. Their complexity is studied and several pseudo-polynomial time algorithms are described, together with a fully polynomial time approximation scheme (FPTAS) for a fixed number of bins.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abouelaoualim, A.: Heuristiques avec performances pour les problèmes de rangements multiboîtes.' Master's thesis, INPG, Grenoble, France, 2003.

  2. Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A. and Protasi, M.: Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties, Springer, Berlin, 1999.

    MATH  Google Scholar 

  3. Baker, B. S. and Coffman Jr, E. G.: Mutual exclusion scheduling, Theor. Comp. Sci. 162(2) (1996) 225–243.

    Article  MathSciNet  MATH  Google Scholar 

  4. Błażewicz, J., Drabowski, M. and Węglarz, J.: Scheduling multiprocessor tasks to minimize schedule length. IEEE Trans. Comput. C-35 (1986) 389–393.

    Article  Google Scholar 

  5. Błażewicz, J., Drozdowski, M. and Ecker, K.: Management of resources in parallel systems, in J. Błażewicz, K. Ecker, B. Plateau and D. Trystram (eds.), Handbook on Parallel and Distributed Processing, Springer, Heidelberg, 1999, pp. 216–293.

    Google Scholar 

  6. Błażewicz, J., Drozdowski, M. and Węglarz, J.: Scheduling multiprocessor tasks – a survey, Int. J. Microcomput. Appl. 13(2) (1994) 89–97.

    Google Scholar 

  7. Błażewicz, J., Ecker, K. H., Pesch, E., Schmidt, G. and Węglarz, J.: Scheduling Computer and Manufacturing Processes, Springer-Verlag, 1996.

  8. Bodlaender, H. L., Jansen, K. and Woeginger, G.: Scheduling with incompatible jobs, Discrete Appl. Math. 55(3) (1994) 219–232.

    Article  MathSciNet  MATH  Google Scholar 

  9. Chen, B., Potts, C. N. and Woeginger, G. J.: A review of machine scheduling: Complexity, algorithms and approximability, in D.-Z. Du and P. Pardalos (eds.), Handbook of Combinatorial Optimization, Kluwer Academic Publishers, Dordrecht, 1998, pp. 21–169.

    Google Scholar 

  10. Coffman Jr, E. G., Garey, M. R. and Johnson, D. S.: Approximation algorithms for bin-packing: a survey (Chap. 2), in D. S. Hochbaum (ed.), Approximation Algorithms for NP-hard Problems, PWS Publishing Company, Boston, 1997, pp. 46–93.

    Google Scholar 

  11. Drozdowski, M.: Scheduling multiprocessor tasks – An overview, Eur. J. Oper. Res. 94 (1996) 215–230.

    Article  MATH  Google Scholar 

  12. Du, J. and Leung, J. Y.-T.: Complexity of scheduling parallel task systems, SIAM J. Discrete Math. 2(4) (1989) 473–487.

    Article  MathSciNet  MATH  Google Scholar 

  13. Garey, M. R. and Johnson, D. S.: Computers and Intractability (A Guide to the Theory of NP-Completeness), Freeman, San Francisco, CA, 1979.

    MATH  Google Scholar 

  14. Irani, S. and Leung, V. J.: Scheduling with conflicts, and applications to traffic signal control, in SODA: ACM-SIAM Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms), 1996, pp. 85–94.

  15. Jansen, K.: An approximation scheme for bin packing with conflicts, J. Comb. Optim. 3 (1999) 363–377.

    Article  MathSciNet  MATH  Google Scholar 

  16. Khanna, S.: A polynomial time approximation scheme for the SONET ring loading problem, Bell Lab. Tech. J., 1997, pp. 36–41.

  17. Labbé, M., Laporte, G. and Martello, S.: An exact algorithm for the dual bin packing problem, Oper. Res. Lett. 17(1) (1995) 9–18.

    Article  MathSciNet  MATH  Google Scholar 

  18. Labbé, M., Laporte, G. and Martello, S.: Upper bounds and algorithms for the maximum cardinality bin packing problem, Eur. J. Oper. Res. 149(3) (2003) 490–498.

    Article  MATH  Google Scholar 

  19. Lemaire, P.: Rangements d'objets multiboîtes : modèles et algorithmes,' Ph.D. thesis, Université Joseph Fourier (Grenoble 1), Grenoble, France, 2004.

  20. Lemaire, P., Finke, G. and Brauner, N.: Packing of Multibin Objects, Technical Report 69, Les Cahiers du Laboratoire Leibniz-IMAG, http://wwwleibniz.IMAG.fr/LesCahiers, 2002.

  21. Lemaire, P., Finke, G. and Brauner, N.: Packing of multibin objects, in IEPM'03, International Conference on Industrial Engineering and Production Management, Vol. 1. Porto, Portugal, 2003, pp. 422–431. available update (http://www-leibniz.imag.fr/~lemaire).

  22. Lemaire, P., Finke, G. and Brauner, N.: The best-fit rule for multibin packing: An extension of Graham's list algorithms, in G. Kendall, E. Burke, S. Petrovic and M. Gendreau (eds.), Multidisciplinary Scheduling; Theory and Applications, Springer, Heidelberg, 2005, pp. 269–286.

    Chapter  Google Scholar 

  23. Lovász, L. and Plummer, M. D.: Matching Theory, Akadémiai Kiadó, Budapest, 1986.

    MATH  Google Scholar 

  24. McNaughton, R.: Scheduling with deadlines and loss functions, Manage. Sci. 6 (1959) 1–12.

    Article  MathSciNet  MATH  Google Scholar 

  25. Myung, Y.-S.: An efficient algorithm for the ring loading problem with integer demand splitting, SIAM J. Discrete Math. 14(3) (2001) 291–298.

    Article  MathSciNet  MATH  Google Scholar 

  26. Schrijver, A., Seymour, P. and Winkler, P.: The ring loading problem, SIAM J. Discrete Math. 11(1) (1998) 1–14.

    Article  MathSciNet  MATH  Google Scholar 

  27. SONET, The SONET Home Page, http://www.sonet.com.

  28. Wu, T.-H.: Fiber Network Service Survivability, Artech House, Norway, MA, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. Lemaire.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lemaire, P., Finke, G. & Brauner, N. Models and Complexity of Multibin Packing Problems. J Math Model Algor 5, 353–370 (2006). https://doi.org/10.1007/s10852-005-9025-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10852-005-9025-y

Mathematics Subject Classifications (2000):

Key words

Navigation