Generating Robust Partial Order Schedules

  • Nicola Policella
  • Angelo Oddi
  • Stephen F. Smith
  • Amedeo Cesta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3258)


This paper considers the problem of transforming a resource feasible, fixed-times schedule into a partial order schedule (POS) to enhance its robustness and stability properties. Whereas a fixed-times schedule is brittle in the face of unpredictable execution dynamics and can quickly become invalidated, a POS retains temporal flexibility whenever problem constraints allow it and can often absorb unexpected deviation from predictive assumptions. We focus specifically on procedures for generating Chaining FormPOSs, wherein activities competing for the same resources are linked into precedence chains. One interesting property of a Chaining Form POS is that it is “makespan preserving” with respect to its originating fixed-times schedule. Thus, issues of maximizing schedule quality and maximizing schedule robustness can be addressed sequentially in a two-step scheduling procedure. Using this approach, a simple chaining algorithm was recently shown to provide an effective basis for transforming good quality solutions into POSs with good robustness properties. Here, we investigate the possibility of producing POSs with better robustness and stability properties through more extended search in the space of Chaining Form POSs. We define two heuristics which make use of a structural property of chaining form POSs to bias chaining decisions. Experimental results on a resource-constrained project scheduling benchmark confirm the effectiveness of our approach.


Schedule Problem Start Time Precedence Constraint Project Schedule Resource Unit 
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.
    Cesta, A., Oddi, A., Smith, S.F.: Profile Based Algorithms to Solve Multiple Capacitated Metric Scheduling Problems. In: Proceedings of AIPS 1998 (1998)Google Scholar
  2. 2.
    Artigues, C., Roubellat, F.: A polynomial activity insertion algorithm in a multi-resource schedule with cumulative constraints and multiple modes. European Journal of Operational Research 127, 297–316 (2000)MATHCrossRefGoogle Scholar
  3. 3.
    Leus, R., Herroelen, W.: Stability and Resource Allocation in Project Planning. IIE Transactions 36, 667–682 (2004)CrossRefGoogle Scholar
  4. 4.
    Policella, N., Smith, S.F., Cesta, A., Oddi, A.: Generating Robust Schedules through Temporal Flexibility. In: Proceedings of ICAPS 2004 (2004)Google Scholar
  5. 5.
    Bartusch, M., Mohring, R.H., Radermacher, F.J.: Scheduling project networks with resource constraints and time windows. Annals of Operations Research 16, 201–240 (1988)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Leon, V., Wu, S., Storer, R.: Robustness measures and robust scheduling for job shops. IIE Transactions 26, 32–43 (1994)CrossRefGoogle Scholar
  7. 7.
    Ginsberg, M.L., Parkes, A.J., Roy, A.: Supermodels and Robustness. In: Proceedings of AAAI 1998 (1998)Google Scholar
  8. 8.
    Kolisch, R., Schwindt, C., Sprecher, A.: Benchmark instances for project scheduling problems. In: Weglarz, J. (ed.) Project Scheduling - Recent Models, Algorithms and Applications, pp. 197–212. Kluwer, Boston (1998)Google Scholar
  9. 9.
    Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)MATHGoogle Scholar
  10. 10.
    Aloulou, M.A., Portmann, M.C.: An Efficient Proactive Reactive Scheduling Approach to Hedge against Shop Floor Disturbances. In: Proceedings of MISTA 2003 (2003)Google Scholar
  11. 11.
    Artigues, C., Billaut, J., Esswein, C.: Maximization of solution flexibility for robust shop scheduling. European Journal of Operational Research (2004) (to appear)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Nicola Policella
    • 1
  • Angelo Oddi
    • 1
  • Stephen F. Smith
    • 2
  • Amedeo Cesta
    • 1
  1. 1.Institute for Cognitive Science and TechnologyItalian National Research CouncilRomeItaly
  2. 2.The Robotics InstituteCarnegie Mellon UniversityPittsburghUSA

Personalised recommendations