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On the solution region for certainscheduling problems with preemption

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Abstract

The paper deals with parallel machine and open shop scheduling problems with pre-emptions and an arbitrary nondecreasing objective function. An approach to describing the solution region for these problems and to reducing them to minimization over polytopes is proposed. Properties of the solution regions for certain problems are investigated. It is proved that open shop problems with unit processing times are equivalent to certain parallel machine problems, where preemption is allowed at arbitrary times. A polynomial algorithm is presented, transforming a schedule of one type into a schedule of the other type.

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References

  1. E. Balas, On the facial structure of scheduling polyhedra, Mathematical Programming Study 24 (1985)179–218.

    Google Scholar 

  2. I. Bárány and T. Fiala, Nearly optimum solution of multimachine scheduling problems, Szigma 15 (1982)177–191 (in Hungarian).

    Google Scholar 

  3. P. Brucker, B. Jurisch and M. Jurisch, Open shop problems with unit time operations, ZOR 37 (1993)59–73.

    Google Scholar 

  4. J. Bruno, E.G.L. Coffman and R. Sethi, Scheduling independent tasks to reduce mean finishing time, Comm. ACM 17(1974)382–387.

    Article  Google Scholar 

  5. J. Du and J. Y.-T. Leung, Minimizing mean flow time in two-machine open shops and flow shops, Journal of Algorithms 14(1993)24–44.

    Article  Google Scholar 

  6. R.E. Graham, E.L. Lawler, J.K. Lenstra and A.H.G. Rinnooy Kan, Optimization and approximation in deterministic sequencing and scheduling: A survey, Ann. Discrete Math. 5(1979)287–326.

    Article  Google Scholar 

  7. A.M. Livshits and V.I. Rublinecky, On comparitive complexity of some discrete optimization problems, Computational Mathematics and Computers 3(1972)78–85 (in Russian).

    Google Scholar 

  8. R. McNaughton, Scheduling with deadlines and loss functions, Manag. Sci. 6(1959)1–12.

    Article  Google Scholar 

  9. M. Queyranne and A.S. Schulz, Polyhedral approaches to machine scheduling, Report No. 408 1994, Technische Universität Berlin, Berlin, 1994.

    Google Scholar 

  10. V.A. Strusevich, Minimizing sum of completion times for the open shop, Vestnik BGU, Seria 1, fiz., mat., mekch. 1(1988)44–46 (in Russian).

    Google Scholar 

  11. V.S. Tanaev, Preemptions in deterministic processing systems with parallel identical machines, Vestsi AN BSSR, Seria Fiz.-Mat. Nauk 6(1973)44–48 (in Russian).

    Google Scholar 

  12. V.S. Tanaev, Symmetric functions in scheduling theory, Izv. Akad. Nauk. Belarusi. Ser. Fiz.-Mat. Nauk 1992, nos. 5–6(1992)97–102 (in Russian).

  13. T. Tautenhahn, Open-shop Probleme mit Einheitsbearbeitungszeiten, Ph.D. Thesis, Otto-von-Guericke Universität, Magdeburg, 1993 (in German).

    Google Scholar 

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Authors
  1. Heidemarie Bräsel
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  2. Natalia Shakhlevich
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Bräsel, H., Shakhlevich, N. On the solution region for certainscheduling problems with preemption. Annals of Operations Research 83, 1–22 (1998). https://doi.org/10.1023/A:1018999711765

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