Acta Informatica

, Volume 24, Issue 5, pp 513–524 | Cite as

Minimizing mean flow-time with parallel processors and resource constraints

  • J. Błażewicz
  • W. Kubiak
  • H. Röck
  • J. Szwarcfiter


The problem to be considered is one of scheduling nonpreemptable tasks in multiprocessor systems when tasks need for their processing processors and other limited resources, and when mean flow time is the system performance measure. For each task the time required for its processing and the amount of each resource which it requires, are given. Special attention is paid to the computational complexity of algorithms for determining the optimal schedules for different assumptions concerning the environment. For the case of scheduling independent, arbitrary length tasks when each task may require a unit of an additional resource of one type, an O(n3) algorithm is given. For more complicated resource requirements, however, it is proved that the problem under consideration is NP-hard in the strong sense, even for the case of two processors.


Computational Complexity Information Theory Computational Mathematic Computer System System Organization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Błażewicz, J.: Deadline scheduling of tasks with ready times and resource constraints. Inf. Proc. Lett. 8, 60–63 (1979)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Błażewicz, J.: Scheduling tasks on parallel processors under resource constraints to minimize mean finishing time. Methods Oper. Res. 35, 67–72 (1979)zbMATHGoogle Scholar
  3. 3.
    Błażewicz, J., Barcelo, J., Kubiak, W., Röck, H.: Scheduling tasks on two processors with deadlines and additional resources. Eur. J. Oper. Res. 26, 364–370 (1986)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Błażewicz, J., Drabowski, M., Weglarz, J.: Scheduling multiprocessor tasks to minimize schedule length. IEEE Trans. Comput. C-35, 389–393 (1986)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Błażewicz, J., Ecker, K.: A linear time algorithm for restricted bin packing and scheduling problems. Oper. Res. Lett. 2, 80–83 (1983)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Błażewicz, J., Lenstra, J.K., Rinnooy Kan, A.H.G.: Scheduling subject to resource constraints: classification and complexity. Discrete Appl. Math. 5, 11–24 (1983)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Bruno, J.L.: Scheduling algorithms for minimizing the mean weighted flow-time criterion. In: Computer and Job/Shop Scheduling Theory, Coffman, E.G., Jr. (ed.). New York: Wiley 1976Google Scholar
  8. 8.
    Bruno, J., Coffman, E.G., Jr., Sethi, R.: Scheduling independent tasks to reduce mean finishing time. Commun. ACM 17, 382–387 (1974)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Garey, M.R., Johnson, D.S.: Complexity results for multiprocessor scheduling under resource constraints. SIAM J. Comput. 4, 397–411 (1975)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: a Guide to the Theory of NP-Completeness. San Francisco: Freeman 1979zbMATHGoogle Scholar
  11. 11.
    Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling theory: a survey. Ann. Discrete Math. 5, 287–326 (1979)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Johnson, D.S.: The NP-completeness column; an ongoing guide. J. Algorithms 4, 189–203 (1983)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Lenstra, J.K., Rinnooy Kan, A.H.G.: Scheduling theory since 1981: an annotated bibliography. In: M.O.H. Eighertaigh, J.K. Lenstra, A.H.G. Rinnooy Kan (eds.), Combinatorial Optimization: Annotated Bibliographies. Chichester: Wiley 1985zbMATHGoogle Scholar
  14. 14.
    McNaughton, R.: Scheduling with deadlines and loss functions. Management Sci. 12, 1–12 (1959)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Möhring, R.H.: Scheduling problems with a singular solution. Ann. Discrete Math. 16, 225–339 (1982)MathSciNetGoogle Scholar
  16. 16.
    Radermacher, F.J.: Kapazitätsoptimierung in Netzplänen. Mathematical Systems in Economics. Vol. 40. Meisenheim: Verlag Anton Hain 1978zbMATHGoogle Scholar
  17. 17.
    Radermacher, F.J.: Scheduling of project networks. Ann. Oper. Res. 4, 227–252 (1985/86)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Röck, H.: Some new results in flow shop scheduling. Zeitschr. Oper. Res. 28, 1–16 (1984)MathSciNetGoogle Scholar
  19. 19.
    Słowinski, R.: L'ordonnancement des tâches preémptives sur les processeurs indépendants en présense de ressources supplémentaires. RAIRO Inf. 15, 155–166 (1981)zbMATHGoogle Scholar
  20. 20.
    Ullman, J.D.: Complexity of Sequencing Problems. In: Computer and Job/Shop Scheduling Theory. Coffman, E.G., Jr. (ed.). New York: Wiley 1976Google Scholar
  21. 21.
    De Werra, D.: Preemptive scheduling, linear programming and network flows. SIAM J. Algebraic Discrete Methods 5, 11–20 (1984)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • J. Błażewicz
    • 1
  • W. Kubiak
    • 2
  • H. Röck
    • 3
  • J. Szwarcfiter
    • 4
  1. 1.Instytut AutomatykiPolitechnika PoznańskaPoznańPoland
  2. 2.Instytut InformatykiPolitechnika GdańskaGdańskPoland
  3. 3.Institut für Quantitative MethodenTechnische Universität BerlinBerlin
  4. 4.Universidade Federal de Rio de JaneiroRio de JaneiroBrazil

Personalised recommendations