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Diskretn. Anal. Issled. Oper., Ser. 1, 2006, Volume 13, Number 3, Pages 83–102 (Mi da37)  

This article is cited in 2 scientific papers (total in 2 papers)

Some properties of optimal schedules for the Johnson problem with preemption

S. V. Sevast'yanov, D. A. Chemisova, I. D. Chernykh

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: The properties are under study of the optimal schedules for the NP-hard Johnson problem with preemption. The length of an optimal schedule is shown to coincide with the total length of some subset of operations. These properties demonstrate that the optimal schedule of every instance of the problem can be found by a greedy algorithm (for the properly defined priority orders of operations on machines). This yields the first exact algorithm for the problem known since 1978. It is shown that the number of interruptions in a greedy schedule (and therefore, in the optimal schedule) is at most the number of operations, which is significantly better than the available upper bounds on the number of interruptions in the optimal schedule.

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English version:
Journal of Applied and Industrial Mathematics, 2007, 1:3, 386–397

Bibliographic databases:


Citation: S. V. Sevast'yanov, D. A. Chemisova, I. D. Chernykh, “Some properties of optimal schedules for the Johnson problem with preemption”, Diskretn. Anal. Issled. Oper., Ser. 1, 13:3 (2006), 83–102; J. Appl. Industr. Math., 1:3 (2007), 386–397

Citation in format AMSBIB
\Bibitem{SevCheChe06}
\by S.~V.~Sevast'yanov, D.~A.~Chemisova, I.~D.~Chernykh
\paper Some properties of optimal schedules for the Johnson problem with preemption
\jour Diskretn. Anal. Issled. Oper., Ser.~1
\yr 2006
\vol 13
\issue 3
\pages 83--102
\mathnet{http://mi.mathnet.ru/da37}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2289373}
\zmath{https://zbmath.org/?q=an:1249.90078}
\transl
\jour J. Appl. Industr. Math.
\yr 2007
\vol 1
\issue 3
\pages 386--397
\crossref{https://doi.org/10.1134/S1990478907030143}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548679863}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. A. Chemisova, “O svoistvakh optimalnykh raspisanii v zadache flow shop s preryvaniyami i proizvolnym regulyarnym kriteriem”, Diskretn. analiz i issled. oper., 16:3 (2009), 74–98  mathnet  mathscinet  zmath
    2. Sevastyanov S.V. Chemisova D.A. Chernykh I.D., “On Some Properties of Optimal Schedules in the Job Shop Problem with Preemption and an Arbitrary Regular Criterion”, Ann. Oper. Res., 213:1 (2014), 253–270  crossref  mathscinet  zmath  isi  elib  scopus
  • Дискретный анализ и исследование операций
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