Skip to main content

Interval Analysis in Scheduling

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNPSE,volume 3709)

Abstract

This paper reconsiders the most basic scheduling problem, that of minimizing the makespan of a partially ordered set of activities, in the context of incomplete knowledge. While this problem is very easy in the deterministic case, its counterpart when durations are interval-valued is much trickier, as standard results and algorithms no longer apply. After positioning this paper in the scope of temporal networks under uncertainty, we provide a complete solution to the problem of finding the latest starting times and floats of activities, and of locating surely critical ones, as they are often isolated. The minimal float problem is NP-hard while the maximal float problem is polynomial. New complexity results and efficient algorithms are provided for the interval-valued makespan minimization problem.

Keywords

  • Schedule Problem
  • Activity Network
  • Critical Path
  • Precedence Constraint
  • Longe Path

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/11564751_19
  • Chapter length: 15 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   149.00
Price excludes VAT (USA)
  • ISBN: 978-3-540-32050-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   189.00
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dechter, R., Meiri, I., Pearl, J.: Temporal constraint networks. Artif. Intell. 49, 61–95 (1991)

    MATH  CrossRef  MathSciNet  Google Scholar 

  2. Morris, P., Muscettola, N., Vidal, T.: Dynamic control of plans with temporal uncertainty. In: IJCAI, pp. 494–502 (2001)

    Google Scholar 

  3. Vidal, T., Fargier, H.: Handling contingency in temporal constraint networks: from consistency to controllabilities. JETAI 11, 23–45 (1999)

    MATH  CrossRef  Google Scholar 

  4. Morris, P.H., Muscettola, N.: Managing temporal uncertainty through waypoint controllability. In: IJCAI, pp. 1253–1258 (1999)

    Google Scholar 

  5. Khatib, L., Morris, P., Morris, R., Rossi, F.: Temporal constraint reasoning with preferences. In: IJCAI, pp. 322–327 (2001)

    Google Scholar 

  6. Kelley, J., Walker, M.: Critical path planning and scheduling. In: Proc. of the Eastern Joint Comp. Conf., pp. 160–172 (1959)

    Google Scholar 

  7. Chanas, S., Zieliński, P.: The computational complexity of the criticality problems in a network with interval activity times. Eur. J. Oper. Res. 136, 541–550 (2002)

    MATH  CrossRef  Google Scholar 

  8. Dubois, D., Fargier, H., Fortin, J.: Computational methods for determining the latest starting times and floats of tasks in interval-valued activity networks. J. Intell. Manuf. (2005) (to appear)

    Google Scholar 

  9. Buckley, J.: Fuzzy PERT. In: Applications of fuzzy set methodologies in industrial engineering, pp. 103–114. Elsevier, Amsterdam (1989)

    Google Scholar 

  10. Dubois, D., Fargier, H., Fortemps, P.: Fuzzy scheduling: modeling flexible constraints vs. coping with incomplete knowledge. Eur. J. Oper. Res. 147, 231–252 (2003)

    MATH  CrossRef  MathSciNet  Google Scholar 

  11. Dubois, D., Fargier, H., Galvagnon, V.: On latest starting times and floats in activity networks with ill-known durations. Eur. J. Oper. Res. 147, 266–280 (2003)

    MATH  CrossRef  MathSciNet  Google Scholar 

  12. Chanas, S., Kamburowski, J.: The use of fuzzy variables in pert. Fuzzy Set Syst. 5, 1–19 (1981)

    CrossRef  MathSciNet  Google Scholar 

  13. Chanas, S., Dubois, D., Zieliński, P.: On the sure criticality of tasks in activity networks with imprecise durations. IEEE T. Syst. Man Cy. B 34, 393–407 (2002)

    CrossRef  Google Scholar 

  14. Zieliński, P.: On computing the latest starting times and floats of activities in a network with imprecise durations. Fuzzy Set Syst. 150, 53–76 (2005)

    MATH  CrossRef  Google Scholar 

  15. Kolisch, R., Sprecher, A.: Psplib - a project scheduling library. Eur. J. Oper. Res. 96, 205–216 (1996)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fortin, J., Zieliński, P., Dubois, D., Fargier, H. (2005). Interval Analysis in Scheduling. In: van Beek, P. (eds) Principles and Practice of Constraint Programming - CP 2005. CP 2005. Lecture Notes in Computer Science, vol 3709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11564751_19

Download citation

  • DOI: https://doi.org/10.1007/11564751_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29238-8

  • Online ISBN: 978-3-540-32050-0

  • eBook Packages: Computer ScienceComputer Science (R0)