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Operations Research Proceedings 1994 pp 168–172Cite as

Two, Three, Many or the Complexity of Scheduling with Fixed Number of Jobs

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Part of the book series: Operations Research Proceedings ((ORP,volume 1994))

Zusammenfassung

Im Beitrag wird die Kompliziertheit der Scheduling-Probleme in job-shop-, flow-shop- und mixed-shop-Bedienungssystemen zusammenfassend dargestellt, wenn die Anzahl der Aufträge n kleiner oder gleich der Anzahl der Maschinen m ist. Fast alle Scheduling-Aufgaben mit zwei Aufträgen können in Polynomialzeit für beliebiges reguläres Kriterium gelöst werden, aber diese Aufgaben mit drei Aufträgen sind binär NP-hard. Die Ausnahme bilden die Aufgabe mit zwei Aufträgen im m-Maschinen mixed-shop-System ohne Unterbrechung der Operationen, die binär NP-hard für beliebiges nichttriviales reguläres Kriterium ist sowie die Aufgabe mit n-Aufträgen im m-Maschinen open-shop-System mit Unterbrechung der Operationen, die polynomial lösbar für die Minimierung der Gesamtbearbeitungszeit ist.

Summary

The paper surveys the complexity of job-shop, flow-shop, open-shop and mixed-shop scheduling problems when the number of jobs n is less or equal to the number of machines m. Almost all shop-scheduling problems with two jobs can be solved in polynomial time for any given regular criterion, but those with three jobs are binary NP-hard. The exceptions are the two job m machine mixed-shop problem without operation preemptions, which is binary NP-hard for any non-trivial regular criterion, and the n job m machine open-shop problem with allowed operation preemptions, which is polynomially solvable for minimizing makespan.

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Author information

Authors and Affiliations

  1. Minsk, Belarus

    Yuri N. Sotskov

Authors
  1. Yuri N. Sotskov
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Editor information

Editors and Affiliations

  1. Wirtschaftsinformatik und Operations Research, Universität zu Köln, Pohligstraße 1, D-50969, Köln, Germany

    Ulrich Derigs (Lehrstuhl) (Lehrstuhl)

  2. Mathematisches Institut, Universität zu Köln, Weyertal 80, D-50931, Köln, Germany

    Achim Bachem

  3. Institut für Betriebswirtschaftslehre, Christian-Albrechts-Universität zu Kiel, Olshausenstraße 40, D-24118, Kiel, Germany

    Andreas Drexl

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© 1995 Springer-Verlag Berlin Heidelberg

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Sotskov, Y.N. (1995). Two, Three, Many or the Complexity of Scheduling with Fixed Number of Jobs. In: Derigs, U., Bachem, A., Drexl, A. (eds) Operations Research Proceedings 1994. Operations Research Proceedings, vol 1994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79459-9_31

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  • DOI: https://doi.org/10.1007/978-3-642-79459-9_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58793-4

  • Online ISBN: 978-3-642-79459-9

  • eBook Packages: Springer Book Archive

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