Parallel Machine Scheduling under Uncertainty

  • Adam Kasperski
  • Adam Kurpisz
  • Paweł Zieliński
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 300)

Abstract

In this paper a parallel machine scheduling problem with uncertain processing times is discussed. This uncertainty is modeled by specifying a scenario set containing K distinct processing time scenarios. The ordered weighted averaging aggregation (OWA) operator, whose special cases are the maximum and Hurwicz criteria, is applied to compute the best schedule. Some new positive and negative approximation results concerning the problem are shown.

Keywords

scheduling parallel machines uncertain processing times OWA operator robust optimization 
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References

  1. 1.
    Alon, N., Azar, Y., Woeginger, G.J., Yadid, T.: Approximation Schemes for Scheduling on Parallel Machines. Journal of Scheduling 1, 55–66 (1998)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Brucker, P.: Scheduling Algorithms, 5th edn. Springer, Heidelberg (2007)MATHGoogle Scholar
  3. 3.
    Chekuri, C., Khanna, S.: On Multi-dimensional Packing Problems. SIAM Journal on Computing 33, 837–851 (2004)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Garey, M.R., Johnson, D.S.: “Strong” NP-Completeness Results: Motivation, Examples, and Implications. Journal of the ACM 25, 499–508 (1978)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W. H. Freeman and Company (1979)Google Scholar
  6. 6.
    Graham, R.L.: Bounds on Multiprocessing Timing Anomalies. SIAM Journal of Applied Mathematics 17, 416–429 (1969)MATHCrossRefGoogle Scholar
  7. 7.
    Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems: theoretical and practical results. Journal of the ACM 34, 144–162 (1987)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kouvelis, P., Daniels, R.L., Vairaktarakis, G.: Robust scheduling of a two-machine flow shop with uncertain processing times. IIE Transactions 32, 421–432 (2000)Google Scholar
  9. 9.
    Kouvelis, P., Yu, G.: Robust Discrete Optimization and its applications. Kluwer Academic Publishers (1997)Google Scholar
  10. 10.
    Lenstra, J.K., Rinnooy Kan, A., Brucker, P.: Complexity of Machine Scheduling Problems. In: Hammer, P., Johnson, E.L., Korte, B.H., Nemhauser, G.L. (eds.) Studies in Integer Programming, Annals of Discrete Mathematics, vol. 1, pp. 343–363. North-Holland Publishing Company (1977)Google Scholar
  11. 11.
    Luce, R., Raiffa, H.: Games and Decisions: Introduction and a Critical Survey. Wiley (1957)Google Scholar
  12. 12.
    Sahni, S.K.: Algorithms for Scheduling Independent Tasks. Journal of the ACM 23, 116–127 (1976)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Yager, R.R.: On Ordered Weighted Averaging Aggregation Operators in Multi-Criteria Decision Making. IEEE Transactions on Systems, Man and Cybernetics 18, 183–190 (1988)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Zuckerman, D.: Linear Degree Extractors and the Inapproximability of Max Clique and Chromatic Number. Theory of Computing 3, 103–128 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Adam Kasperski
    • 1
  • Adam Kurpisz
    • 2
  • Paweł Zieliński
    • 2
  1. 1.Institute of Industrial Engineering and ManagementWrocław University, of TechnologyWrocławPoland
  2. 2.Faculty of Fundamental Problems of TechnologyWrocław University of TechnologyWrocławPoland

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