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On Scheduling Independent Tasks with Restricted Execution Times

Author

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  • Joseph Y.-T. Leung

    (Northwestern University, Evanston, Illinois)

Abstract

We consider the problem of nonpreemptively scheduling n independent tasks on m identical and parallel machines with the objective of minimizing the overall finishing time. The problem has been shown to be NP-complete in the strong sense and hence there probably will not be any pseudopolynomial time algorithm for solving this problem. We show, however, that if the execution times are restricted to a fixed number, say k , of different values, then it can be solved in polynomial time. Our algorithm can be implemented to run in time 0(log 2 p * log 2 m * n 2( k −1) ) and space 0(log 2 m * n k −1 ) in the worst case, where p is the largest execution time.

Suggested Citation

  • Joseph Y.-T. Leung, 1982. "On Scheduling Independent Tasks with Restricted Execution Times," Operations Research, INFORMS, vol. 30(1), pages 163-171, February.
    • Handle: RePEc:inm:oropre:v:30:y:1982:i:1:p:163-171
    DOI: 10.1287/opre.30.1.163
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    Citations

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    Cited by:

    1. Choi, Byung-Cheon & Briskorn, Dirk & Lee, Kangbok & Leung, Joseph & Pinedo, Michael, 2008. "Allocating containers to ships with fixed departure times," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 641, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    2. Bampis, Evripidis & Giannakos, Aristotelis & Konig, Jean-Claude, 1996. "On the complexity of scheduling with large communication delays," European Journal of Operational Research, Elsevier, vol. 94(2), pages 252-260, October.
    3. Jinwen Ou & Joseph Y.‐T. Leung & Chung‐Lun Li, 2008. "Scheduling parallel machines with inclusive processing set restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 328-338, June.
    4. A. Agnetis & S. Smriglio, 2000. "Optimal assignment of high multiplicity flight plans to dispatchers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(5), pages 359-376, August.
    5. Brucker, Peter & Kramer, Andreas, 1996. "Polynomial algorithms for resource-constrained and multiprocessor task scheduling problems," European Journal of Operational Research, Elsevier, vol. 90(2), pages 214-226, April.
    6. S. Thomas McCormick & Scott R. Smallwood & Frits C. R. Spieksma, 2001. "A Polynomial Algorithm for Multiprocessor Scheduling with Two Job Lengths," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 31-49, February.

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