Skip to main content
SpringerLink
Log in

Preemptive parallel-machine scheduling problem of maximizing the number of on-time jobs

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

This paper investigates the classical preemptive parallel-machine scheduling problem of maximizing number of on-time jobs. While the problem is known to be NP-hard, no theoretical analysis of approximation algorithms exists in the literature. As part of the analysis, a new non-standard mixed integer formulation is developed. We propose heuristics based on different design strategies. These heuristics have asymptotically tight relative errors of 1/2. Experimental tests evaluate the computational performance of the procedures.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Amazon.com (2017). Amazon Web Services. Accessed January 16, 2017 from https://aws.amazon.com/?nc1=h_ls.

  • Błażewicz, J., Ecker, K. H., Pesch, E., Schmidt, G., & Wȩglarz, J. (2007). Handbook on scheduling: From theory to applications. Berlin: Springer.

    Google Scholar 

  • Chen, B., Potts, C. N., & Woeginger, G. J. (1998). A review of machine scheduling: Complexity, algorithms and approximability. In Handbook of combinatorial optimization (pp. 1493–1641). New York: Springer.

  • Cheng, T. C. E., & Sin, C. C. (1990). A state-of-the-art review of parallel-machine scheduling research. European Journal of Operational Research, 47(3), 271–292.

    Article  Google Scholar 

  • Galvin, P. B., Gagne, G., & Silberschatz, A. (2013). Operating system concepts. New York: Wiley.

    Google Scholar 

  • Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnoy Kan, A. H. G. (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics, 5, 287–326.

    Article  Google Scholar 

  • Garey, M. R., & Johnson, D. S. (1978). “Strong” NP-completeness results: motivation, examples, and implications. Journal of the Association of Computing Machinery, 25(3), 499–508.

    Article  Google Scholar 

  • Ibarra, O. H., & Kim, C. E. (1978). Approximation algorithms for certain scheduling problems. Mathematics of Operations Research, 3(3), 197–204.

    Article  Google Scholar 

  • Lawler, E. L. (1979). Preemptive scheduling of uniform parallel machines to minimize the weighted number of late jobs. Report BW 105, Centre for Mathematics and Computer Science, Amsterdam.

  • Lawler, E. L. (1983). Recent results in the theory of machine scheduling. In A. Bachem, M. Groetschel, & B. Korte (Eds.), Mathematical programming: The State of the Art (Bonn, 1982) (pp. 202–234). Berlin: Springer.

    Chapter  Google Scholar 

  • Lawler, E. L., & Martel, C. U. (1989). Preemptive scheduling of two uniform machines to minimize the number of late jobs. Operations Research, 37(2), 314–318.

    Article  Google Scholar 

  • Lee, K., Leung, J. Y. T., Jia, Z. H., Li, W., Pinedo, M. L., & Lin, B. M. T. (2014). Fast approximation algorithms for bi-criteria scheduling with machine assignment costs. European Journal of Operational Research, 238(1), 54–64.

    Article  Google Scholar 

  • Leung, J. Y. (Ed.). (2004). Handbook of scheduling: Algorithms, models, and performance analysis. Boca Raton, FL: CRC Press.

  • McNaughton, R. (1959). Scheduling with deadlines and loss functions. Management Science, 6(1), 1–12.

    Article  Google Scholar 

  • Mokotoff, E. (2001). Parallel machine scheduling problems: A survey. Asia-Pacific Journal of Operational Research, 18, 193–242.

    Google Scholar 

  • Moore, J. M. (1968). An \(n\) job, one machine sequencing algorithm for minimizing the number of late jobs. Management Science, 15(1), 102–109.

    Article  Google Scholar 

  • Pinedo, M. L. (2015). Scheduling: Theory, algorithms, and systems. New York: Springer.

    Google Scholar 

  • Prot, D., Bellenguez-Morineau, O., & Lahlou, C. (2013). New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria. European Journal of Operational Research, 231(3), 282–287.

    Article  Google Scholar 

  • Sahni, S., & Cho, Y. (1980). Scheduling independent tasks with due time on a uniform processor system. Journal of the Association for Computing Machinery, 27(3), 550–563.

    Article  Google Scholar 

  • Singh, S., & Chana, J. (2016). A survey on resource scheduling in cloud computing: Issues and challenges. Journal of Grid Computing, 14(2), 217–264.

    Article  Google Scholar 

  • Sturm, L. B. J. M. (1970). A simple optimality proof of Moore’s sequencing algorithm. Management Science, 17(1), 116–118.

    Article  Google Scholar 

  • Tanenbaum, A. S., & Bos, H. (2014). Modern Operating Systems. New Jersey: Prentice Hall Press.

    Google Scholar 

  • Tucker, A., & Gupta, A. (1989). Process control and scheduling issues for multiprogrammed shared-memory multiprocessors. ACM SIGOPS Operating Systems Review, 23(5), 159–166.

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported in part by the Ministry of Science and Technology of Taiwan under the grants NSC104-2912-I-009-513 and MOST107-2912-I-009-514.

Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Management, National Chiao Tung University, 1001 University Rd., Hsinchu, Taiwan

    Hui-Chih Hung & Jun-Min Wei

  2. Institute of Information Management, National Chiao Tung University, 1001 University Rd., Hsinchu, Taiwan

    Bertrand M. T. Lin

  3. Department of Integrated Systems Engineering, The Ohio State University, 1971 Neil Avenue, Columbus, OH, 43210, USA

    Marc E. Posner

Authors
  1. Hui-Chih Hung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bertrand M. T. Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marc E. Posner
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jun-Min Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bertrand M. T. Lin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hung, HC., Lin, B.M.T., Posner, M.E. et al. Preemptive parallel-machine scheduling problem of maximizing the number of on-time jobs. J Sched 22, 413–431 (2019). https://doi.org/10.1007/s10951-018-0584-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-018-0584-y

Keywords

Search

Navigation