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Preemptive job-shop scheduling problems with a fixed number of jobs

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Abstract.

It is shown that the two machine preemptive job-shop problem with mean flow-time or makespan objective function and three jobs is NP-hard. This contrasts the fact that the nonpreemptive versions of these problems are polynomially solvable if the number of jobs is arbitrary but fixed. It is also shown that the preemptive problems can be solved pseudopolynomially if both the number of machines and the number of jobs is fixed.

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Authors and Affiliations

  1. FB Mathematik/Informatik, Universität Osnabrück, D-49069 Osnabrück, Germany (e-mail: peter@mathematik.uni-osnabrueck.de), , , , , , DE

    Peter Brucker

  2. Institute of Engineering Cybernetics, Surganov Str. 6, 220012 Minsk, Belarus (e-mail: kravchen@newman.basnet.minsk.by; sotskov@newman.basnet.minsk.by), , , , , , XX

    Svetlana A. Kravchenko & Yuri N. Sotskov

Authors
  1. Peter Brucker
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  2. Svetlana A. Kravchenko
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  3. Yuri N. Sotskov
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Manuscript received: November 1996/final version received: January 1998

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Brucker, P., Kravchenko, S. & Sotskov, Y. Preemptive job-shop scheduling problems with a fixed number of jobs. Mathematical Methods of OR 49, 41–76 (1999). https://doi.org/10.1007/PL00020906

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  • DOI: https://doi.org/10.1007/PL00020906

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