Skip to main content
SpringerLink
Log in

Parallel Machine Scheduling under Uncertainty

  • Conference paper
Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alon, N., Azar, Y., Woeginger, G.J., Yadid, T.: Approximation Schemes for Scheduling on Parallel Machines. Journal of Scheduling 1, 55–66 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brucker, P.: Scheduling Algorithms, 5th edn. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  3. Chekuri, C., Khanna, S.: On Multi-dimensional Packing Problems. SIAM Journal on Computing 33, 837–851 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Garey, M.R., Johnson, D.S.: “Strong” NP-Completeness Results: Motivation, Examples, and Implications. Journal of the ACM 25, 499–508 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  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. Graham, R.L.: Bounds on Multiprocessing Timing Anomalies. SIAM Journal of Applied Mathematics 17, 416–429 (1969)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. Kouvelis, P., Yu, G.: Robust Discrete Optimization and its applications. Kluwer Academic Publishers (1997)

    Google Scholar 

  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. Luce, R., Raiffa, H.: Games and Decisions: Introduction and a Critical Survey. Wiley (1957)

    Google Scholar 

  12. Sahni, S.K.: Algorithms for Scheduling Independent Tasks. Journal of the ACM 23, 116–127 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zuckerman, D.: Linear Degree Extractors and the Inapproximability of Max Clique and Chromatic Number. Theory of Computing 3, 103–128 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Industrial Engineering and Management, Wrocław University, of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Adam Kasperski

  2. Faculty of Fundamental Problems of Technology, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Adam Kurpisz & Paweł Zieliński

Authors
  1. Adam Kasperski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adam Kurpisz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paweł Zieliński
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute — IONA College,, 10801, New Rochelle, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kasperski, A., Kurpisz, A., Zieliński, P. (2012). Parallel Machine Scheduling under Uncertainty. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31724-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31723-1

  • Online ISBN: 978-3-642-31724-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation