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

Author

Listed:
  • Peter Brucker
  • Svetlana A. Kravchenko
  • Yuri N. Sotskov

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. Copyright Springer-Verlag Berlin Heidelberg 1999

Suggested Citation

  • Peter Brucker & Svetlana A. Kravchenko & Yuri N. Sotskov, 1999. "Preemptive job-shop scheduling problems with a fixed number of jobs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(1), pages 41-76, March.
    • Handle: RePEc:spr:mathme:v:49:y:1999:i:1:p:41-76
    DOI: 10.1007/PL00020906
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    Citations

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    Cited by:

    1. Martin Middendorf & Vadim G. Timkovsky, 1999. "Transversal Graphs for Partially Ordered Sets: Sequencing, Merging and Scheduling Problems," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 417-435, December.
    2. Peter Brucker & Yu Sotskov & Frank Werner, 2007. "Complexity of shop-scheduling problems with fixed number of jobs: a survey," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 461-481, June.
    3. Yuri N. Sotskov, 2020. "Mixed Graph Colorings: A Historical Review," Mathematics, MDPI, vol. 8(3), pages 1-24, March.

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