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Preemptive Scheduling of Two Uniform Machines to Minimize the Number of Late Jobs

Author

Listed:
  • E. L. Lawler

    (University of California, Berkeley, California)

  • C. U. Martel

    (University of California, Davis, California)

Abstract

Suppose that n jobs, each with a specified processing requirement and due date, are to be preemptively scheduled for processing by a number of parallel machines, with the objective of maximizing the number of jobs that are completed by their due dates. It is known that this scheduling problem is NP-hard, even for identical machines, if the number of machines is variable, that is, specified as part of the problem instance. However, if the machine environment consists of a fixed set of uniform machines, the problem can be solved in polynomial time. An O ( n 3 ) algorithm is presented for the special case of two uniform machines. The running time of this algorithm becomes O ( Wn 2 ), where W is the sum of the job weights, for the more general problem in which it is desired to minimize the weighted number of late jobs. A fully polynomial approximation scheme is also presented for the weighted case.

Suggested Citation

  • E. L. Lawler & C. U. Martel, 1989. "Preemptive Scheduling of Two Uniform Machines to Minimize the Number of Late Jobs," Operations Research, INFORMS, vol. 37(2), pages 314-318, April.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:2:p:314-318
    DOI: 10.1287/opre.37.2.314
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    Citations

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    Cited by:

    1. Siwate Rojanasoonthon & Jonathan Bard, 2005. "A GRASP for Parallel Machine Scheduling with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 32-51, February.
    2. Gupta, Jatinder N. D. & Ho, Johnny C., 1996. "Scheduling with two job classes and setup times to minimize the number of tardy jobs," International Journal of Production Economics, Elsevier, vol. 42(3), pages 205-216, April.
    3. Ho, Johnny C. & Chang, Yih-Long, 1995. "Minimizing the number of tardy jobs for m parallel machines," European Journal of Operational Research, Elsevier, vol. 84(2), pages 343-355, July.
    4. Hui-Chih Hung & Bertrand M. T. Lin & Marc E. Posner & Jun-Min Wei, 2019. "Preemptive parallel-machine scheduling problem of maximizing the number of on-time jobs," Journal of Scheduling, Springer, vol. 22(4), pages 413-431, August.
    5. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    6. Timkovsky, Vadim G., 2003. "Identical parallel machines vs. unit-time shops and preemptions vs. chains in scheduling complexity," European Journal of Operational Research, Elsevier, vol. 149(2), pages 355-376, September.
    7. Joseph Y.-T. Leung & Michael Pinedo & Guohua Wan, 2010. "Competitive Two-Agent Scheduling and Its Applications," Operations Research, INFORMS, vol. 58(2), pages 458-469, April.
    8. S. Knust & N. V. Shakhlevich & S. Waldherr & C. Weiß, 2019. "Shop scheduling problems with pliable jobs," Journal of Scheduling, Springer, vol. 22(6), pages 635-661, December.
    9. Lushchakova, Irina N., 2012. "Preemptive scheduling of two uniform parallel machines to minimize total tardiness," European Journal of Operational Research, Elsevier, vol. 219(1), pages 27-33.
    10. Detienne, Boris, 2014. "A mixed integer linear programming approach to minimize the number of late jobs with and without machine availability constraints," European Journal of Operational Research, Elsevier, vol. 235(3), pages 540-552.
    11. Bahram Alidaee & Haibo Wang & R. Bryan Kethley & Frank Landram, 2019. "A unified view of parallel machine scheduling with interdependent processing rates," Journal of Scheduling, Springer, vol. 22(5), pages 499-515, October.
    12. Bornstein, Claudio Thomas & Alcoforado, Luciane Ferreira & Maculan, Nelson, 2005. "A graph-oriented approach for the minimization of the number of late jobs for the parallel machines scheduling problem," European Journal of Operational Research, Elsevier, vol. 165(3), pages 649-656, September.

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