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The complexity of mean flow time scheduling problems with release times

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Abstract

We study the problem of preemptive scheduling of n} jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. In this paper, show that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming. Our algorithm can also be applied to the open-shop problem with release times and unit processing times. For the general case (when processing times are arbitrary), we show that the problem is unary NP-hard.

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References

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Author information

Authors and Affiliations

  1. CNRS LIX, Ecole Polytechnique, 91128, Palaiseau, France

    Philippe Baptiste & Christoph Dürr

  2. Universität Osnabrück, Fachbereich Mathematik/Informatik, 49069, Osnabrück, Germany

    Philippe Baptiste & Peter Brucker

  3. Department of Computer Science, University of California, Riverside, CA, 92521, USA

    Marek Chrobak

  4. United Institute of Informatics Problems, Surganova St. 6, 220012, Minsk, Belarus

    Svetlana A. Kravchenko

  5. CNRS LIP6, Université Pierre et Marie Curie, Place de Jussieu, 75005, Paris, France

    Francis Sourd

Authors
  1. Philippe Baptiste
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  2. Peter Brucker
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  3. Marek Chrobak
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  4. Christoph Dürr
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  5. Svetlana A. Kravchenko
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  6. Francis Sourd
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Corresponding author

Correspondence to Philippe Baptiste.

Additional information

P. Baptiste and C. Dürr: Supported by the NSF/CNRS grant 17171 and ANR/Alpage.

P. Brucker: Supported by INTAS Project 00-217 and by DAAD PROCOPE Project D/0427360.

M. Chrobak: Supported by NSF grants CCR-0208856 and INT-0340752.

S. A. Kravchenko: Supported by the Alexander von Humboldt Foundation.

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Baptiste, P., Brucker, P., Chrobak, M. et al. The complexity of mean flow time scheduling problems with release times. J Sched 10, 139–146 (2007). https://doi.org/10.1007/s10951-006-0006-4

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  • DOI: https://doi.org/10.1007/s10951-006-0006-4

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