Skip to main content
SpringerLink
Log in

Scheduling under Uncertainty: Optimizing against a Randomizing Adversary

  • Conference paper
  • First Online:
Book cover Approximation Algorithms for Combinatorial Optimization (APPROX 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1913))

Abstract

Deterministic models for project schedulingand control suf- fer from the fact that they ssume complete inform tion and neglect random influences that occur during project execution. A typical con- sequence is the underestimation of the expected project duration and cost frequently observed in practice. To cope with these phenomena, we consider schedulingmodels in which processingtimes are random but precedence and resource constraints are fixed. Scheduling is done by poli- cies which consist of an an online process of decisions that are based on the observed past and the a priori knowledge of the distribution of pro- cessing times. We give an informal survey on different classes of policies and show that suitable combinatorial properties of such policies give in- sights into optimality, comput tional methods, and their approximation behavior. In particular, we present recent constant-factor approximation algorithms for simple policies in machine scheduling that are based on suitable polyhedral relaxation of the performance space of policies.

Supported by Deutsche Forschungsgemeinschaft under grant Mo 346/3-3 and by German Israeli Foundation under grant I-564-246.06/97.

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. P. Brucker, A. Drexl, R. H. Möhring, K. Neumann, and E. Pesch. Resource-constrained project scheduling:Not tion, classiffication, models, nd methods. European J. Oper. Res., 112(1):3–41, 1999.

    Article  MATH  Google Scholar 

  2. D. R Fulkerson. Expected critical path lengths in PERT networks. Oper. Res., 10:808–817, 1962.

    MATH  Google Scholar 

  3. K. D. Glazebrook and J. Niño-Mora. Schedulingmulticlass queuingnetworks on parallel servers:Approxim te nd he vy-traffic optimility of Klimov’s rule. In R. Burkard and G. Woeginger, editors, Algorithms — ESA’97, 5th Annual Eu-ropean Symposium pages 232–245. Springer-Verlag, Lecture Notes in Computer Science, vol. 1284, 1997.

    Google Scholar 

  4. M. H. Goldwasser and R. Motwani. Complexity measures for ssembly sequences. International Journal of Computational Geometry and Applications To apear.

    Google Scholar 

  5. R. L. Graham. Bounds on multiprocessingtiminganom lies. Bell Systems Tech. Journal 45:1563–1581, 1968.

    MATH  Google Scholar 

  6. L. A. Hall, A. S. Schulz, D. B. Shmoys, and J. Wein. Schedulingto minimize average completion time:off-line and on-line approximation algorithms. Mathematics Oper. Res., 22(3):513–544, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  7. U. Heller. On the shortest overall duration in stochastic project networks. Methods Oper. Res., 42:85–104, 1981.

    MATH  Google Scholar 

  8. G. Igelmund and F. J. Radermacher. Preselective strategies for the optimization of stochastic project networks under resource constr ints. Networks 13:1–28, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  9. R. H. Möhring and F. J. Radermacher. Introduction to stochastic schedulingproblems. In K. Neumann and D. Pallaschke, editors, Contributions to Operations Re-search, Proceedings of the Oberwolfach Conference on Operations Research, 1984 pages 72–130. Springer-Verlag, Lecture Notes in Economics and Mathematical Systems, vol. 240, 1985.

    Google Scholar 

  10. R. H. Möhring, F. J. Radermacher, and G. Weiss. Stochastic scheduling problems II. Set strategies. Z. Oper. Res. Ser. A 29:65–104, 1985.

    MATH  MathSciNet  Google Scholar 

  11. . R. H. Möhring, A. S. Schulz, and M. Uetz. Approxim tion in stoch stic scheduling: the power of LP-b sed priority policies. J. Assoc. Comp. Mach., 46(6):924–942, 1999.

    MATH  Google Scholar 

  12. R. H. Möhring, M. Skutella, and F. Stork. Scheduling with AND/OR precedence constraints. Technical Report 646, Technische Universität Berlin, Fachbereich Mathematik, Berlin, Germany, 1999. Revised July 2000.

    Google Scholar 

  13. R. H. Möhring, M. Skutell, and F. Stork. Forcing rel tions for AND/OR precedence constr ints. In Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA pages 235–236, 2000.

    Google Scholar 

  14. R. H. Möhring and F. Stork. Linear preselective strategies for stochastic project scheduling. Technical Report 612, Technische Universität Berlin, Fachbereich Mathematik, Berlin, Germany, 1998. To appear in and Mathematical Methods of Operations Research.

    Google Scholar 

  15. F. J. Radermacher. Analytical vs. combin torial characteriz tions of well-behaved strategies in stochastic scheduling. Methods Oper. Res., 53:467–475, 1986.

    MathSciNet  Google Scholar 

  16. 16. J. Sgall. On-line scheduling. In A. Fiat and G. J. Woeginger, editors, Online Algorithms: The State of the Art pages 196–231. Springer-Verlag, Lecture Notes in Computer Science, vol. 1442, 1998.

    Chapter  Google Scholar 

  17. F. Stork. A branch-nd-bound lgorithm for minimizing expected m kespan in stoch stic project networks with resource constraints. Technical Report 613, Technische Universität Berlin, Fachbereich Mathematik, Berlin, Germany, 1998.

    Google Scholar 

  18. G. Weiss and M. Pinedo. Schedulingt sks with exponential service times on non-identical processors to minimize various cost functions. J. Appl. Prob., 17:187–202, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  19. U. Zwick and M. Paterson. The complexity of Mean Payoff. Games on graphs. Theor. Comp. Sc., 158:343–359, 1996.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität Berlin, 10623, Berlin, Germany

    Rolf H. Möhring

Authors
  1. Rolf H. Möhring
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Christian-Albrechts-Universität zu Kiel Institut für Informatik und praktische Mathematik Olshausenstr, 40, 24098, Kiel, Germany

    Klaus Jansen

  2. Computer Science Department, University of Maryland, A.V. Williams Bldg College Park, MD 20742, USA

    Samir Khuller

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Möhring, R.H. (2000). Scheduling under Uncertainty: Optimizing against a Randomizing Adversary. In: Jansen, K., Khuller, S. (eds) Approximation Algorithms for Combinatorial Optimization. APPROX 2000. Lecture Notes in Computer Science, vol 1913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44436-X_3

Download citation

  • DOI: https://doi.org/10.1007/3-540-44436-X_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67996-7

  • Online ISBN: 978-3-540-44436-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation