Skip to main content
Log in

Solution of The Liu–Layland Problem Via Bottleneck Just-In-Time Sequencing

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

This paper proposes a new approach to the well-known Liu–Layland periodic scheduling problem. This approach proves that any just-in-time sequence with maximum absolute deviation being less than one is in fact a periodic schedule. Consequently, periodic schedules can be obtained by any algorithm capable of generating just-in-time sequences with maximum absolute deviation being less than one, for instance, any algorithm minimizing maximum deviation or the quota methods of apportionment.

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

  • Balinski, M. and H. P. Young, “The quota method of apportionment,” American Mathematics Monthly, 82, 701–730 (1975).

    Google Scholar 

  • Blazewicz, J., K. Ecker, E. Pesch, G. Schmidt, and J. Weglarz, Scheduling Computer and Manufacturing Processes, 2nd edition, Springer, Berlin, 1996.

    Google Scholar 

  • Bratley, P., M. Florian, and P. Robillard, “Scheduling with earliest start and due date constraints,” Naval Research Logistics Quarterly, 18, 511–517 (1971).

    Google Scholar 

  • Brauner, N. and Y. Crama, “The maximum deviation just-in-time scheduling problem,” Discrete Applied Mathematics, 134, 25–50 (2004).

    Google Scholar 

  • Brauner, N., V. Jost, and W. Kubiak, “On symmetric Fraenkel’s and small deviations conjectures,” Les cahiers du Laboratoire Leibniz-IMAG, no 54, Grenoble, France, 2002.

  • Buttazzo, G. C., Predictable Scheduling Algorithms and Applications, Hard Real-Time Computing Systems, Kluwer Academic Publishers, Dordrecht, 1997.

    Google Scholar 

  • Dertouzos, M., “Control Robotics: The procedural control of physical processes,” in Proceedings of IFIP Congress, 1974, pp. 807–813.

  • Devillers, R. and J. Goossens, “Liu and Layland’s schedulability test revisited,” Information Processing Letters, 73, 157–161 (2000).

    Google Scholar 

  • Glover, F., “Maximum matching in a convex bipartite graph,” Naval Research Logistics Quarterly, 4, 313–316 (1967).

    Google Scholar 

  • Kubiak, W., “On small deviations conjecture,” Bulletin of the Polish Academy of Sciences, 51, 189–203 (2003).

    Google Scholar 

  • Kubiak, W. and S. P. Sethi, “A Note on ‘Level schedules for mixed-model assembly lines in just-in-time production systems,” Management Science, 37, 121–122 (1991).

    Google Scholar 

  • Kubiak, W. and S. P. Sethi “Optimal just-in-time schedules for flexible transfer lines,” The International Journal of Flexible Manufacturing Systems, 6, 137–154 (1994).

    Google Scholar 

  • Lawler, E., Combinatorial Optimization. Networks and Matroids, Holt, Rinehart & Winston, New York, 1976.

    Google Scholar 

  • Liu, C. L. and J. W. Layland, “Scheduling algorithm for multiprogramming in a hard real-time environment,” Journal of ACM, 20, 46–61 (1973).

    Google Scholar 

  • Monden, Y., Toyota Production Systems, Industrial Engineering and Management Press, Norcross, GA, 1983.

    Google Scholar 

  • Still J. W., “A class of new methods for congressional apportionment,” SIAM Journal of Applied Mathematics, 37, 401–418 1979.

    Google Scholar 

  • Steiner, G. and S. Yeomans, “Level schedules for mixed-model, just-in-time production processes,” Management Science, 39, 401–418 (1993).

    Google Scholar 

  • Tijdeman, R., “The chairman assignment problem,” Discrete Mathematics, 32, 323–330 (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wieslaw Kubiak.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kubiak, W. Solution of The Liu–Layland Problem Via Bottleneck Just-In-Time Sequencing. J Sched 8, 295–302 (2005). https://doi.org/10.1007/s10951-005-1638-5

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-005-1638-5

Key Words

Navigation