Journal of Scheduling

, 12:299 | Cite as


Synthesizing partial order schedules by chaining
  • Nicola Policella
  • Amedeo Cesta
  • Angelo Oddi
  • Stephen F. Smith


Goal separation is often a fruitful approach when solving complex problems. It provides a way to focus on relevant aspects in a stepwise fashion and hence bound the problem solving scope along a specific direction at any point. This work applies goal separation to the problem of synthesizing robust schedules. The problem is addressed by separating the phase of problem solution, which may pursue a standard optimization criterion (e.g., minimal makespan), from a subsequent phase of solution robustification in which a more flexible set of solutions is obtained and compactly represented through a temporal graph, called a Partial Order Schedule ( \(\mathcal{POS}\) ). The key advantage of a \(\mathcal{POS}\) is that it provides the capability to promptly respond to temporal changes (e.g., activity duration changes or activity start-time delays) and to hedge against further changes (e.g., new activities to perform or unexpected variations in resource capacity).

On the one hand, the paper focuses on specific heuristic algorithms for synthesis of \(\mathcal{POS}\) s, starting from a pre-existing schedule (hence the name Solve-and-Robustify). Different extensions of a technique called chaining, which progressively introduces temporal flexibility into the representation of the solution, are introduced and evaluated. These extensions follow from the fact that in multi-capacitated resource settings more than one \(\mathcal{POS}\) can be derived from a specific fixed-times solution via chaining, and carry out a search for the most robust alternative. On the other hand, an additional analysis is performed to investigate the performance gain possible by further broadening the search process to consider multiple initial seed solutions.

A detailed experimental analysis using state-of-the-art rcpsp/max  benchmarks is carried out to demonstrate the performance advantage of these more sophisticated solve and robustify procedures, corroborating prior results obtained on smaller problems and also indicating how this leverage increases as problem size is increased.


Iterative improvement techniques Scheduling under uncertainty Constraint-based scheduling 


  1. Aloulou, M. A., & Portmann, M. C. (2005). An efficient proactive-reactive scheduling approach to hedge against shop floor disturbances. In G. Kendall, E. Burke, S. Petrovic, & M. Gendreau (Eds.), Multidisciplinary scheduling: theory and applications (pp. 223–246). New York: Springer. CrossRefGoogle Scholar
  2. Artigues, C., Billaut, J. C., & Esswein, C. (2005). Maximization of solution flexibility for robust shop scheduling. European Journal of Operational Research, 165(2), 314–328. CrossRefGoogle Scholar
  3. Bartusch, M., Mohring, R. H., & Radermacher, F. J. (1988). Scheduling project networks with resource constraints and time windows. Annals of Operations Research, 16, 201–240. CrossRefGoogle Scholar
  4. Cesta, A., & Oddi, A. (2001). Algorithms for dynamic management of temporal constraints networks (Tech. rep.). ISTC-CNR, Institute for Cognitive Science and Technology, Italian National Research Council. Google Scholar
  5. Cesta, A., Oddi, A., & Smith, S. F. (1998). Profile based algorithms to solve multiple capacitated metric scheduling problems. In Proceedings of the 4th international conference on artificial intelligence planning systems, AIPS-98 (pp. 214–223). Google Scholar
  6. Cesta, A., Oddi, A., & Smith, S. F. (2002). A constraint-based method for project scheduling with time windows. Journal of Heuristics, 8(1), 109–136. CrossRefGoogle Scholar
  7. Chapman, D. (1987). Planning for conjuctive goals. Artificial Intelligence, 32(3), 333–377. CrossRefGoogle Scholar
  8. Cheng, C., & Smith, S. F. (1994). Generating feasible schedules under complex metric constraints. In Proceedings of the 12th national conference on artificial intelligence, AAAI-94 (pp. 1086–1091). Menlo Park: AAAI Press. Google Scholar
  9. Chien, S. A., Muscettola, N., Rajan, K., Smith, B. D., & Rabideau, G. (1998). Automated planning and scheduling for goal-based autonomous spacecraft. IEEE Intelligent Systems, 13(5), 50–55. CrossRefGoogle Scholar
  10. Currie, K., & Tate, A. (1991). O-plan: The open planning architecture. Artificial Intelligence, 52(1), 49–86. CrossRefGoogle Scholar
  11. Do, M. B., & Kambhampati, S. (2003). Improving temporal flexibility of position constrained metric temporal plans. In Proceedings of the 13th international conference on automated planning & scheduling, ICAPS’03 (pp. 42–51). Google Scholar
  12. Fox, M., & Long, D. (2003). PDDL2.1: An extension to PDDL for expressing temporal planning domains. Journal of Artificial Intelligence Research, 20, 61–124. Google Scholar
  13. Fox, M., Gerevini, A., Long, D., & Serina, I. (2006a). Plan stability: replanning versus plan repair. In Proceedings of the 16th international conference on automated planning and scheduling, ICAPS 06 (pp. 212–221). Google Scholar
  14. Fox, M., Howey, R., & Long, D. (2006b). Exploration of the robustness of plans. In Proceedings of the 21st national conference on artificial intelligence, AAAI 06 (pp. 834–839). Google Scholar
  15. Godard, D., Laborie, P., & Nuitjen, W. (2005). Randomized large neighborhood search for cumulative scheduling. In Proceedings of the 15th international conference on automated planning and scheduling, ICAPS 2005 (pp. 81–89). Google Scholar
  16. Kambhampati, S., Knoblock, C. A., & Yang, Q. (1995). Planning as refinement search: a unified framework for evaluating design tradeoffs in partial order planning. Artificial Intelligence, 76(1–2), 167–238. CrossRefGoogle Scholar
  17. Kolisch, R., Schwindt, C., & Sprecher, A. (1998). Benchmark instances for project scheduling problems. In J. Weglarz (Ed.), Project scheduling—recent models, algorithms and applications (pp. 197–212). Boston: Kluwer Academic. Google Scholar
  18. Laborie, P., & Ghallab, M. (1995). Planning with sharable resource constraints. In Proceedings of 14th international joint conference on artificial intelligence, IJCAI-95 (pp. 1643–1651). Google Scholar
  19. Laborie, P., & Godard, D. (2007). Self-adapting large neighborhood search: application to single-mode scheduling problems. In Proceedings of 3rd multidisciplinary international scheduling conference: theory and applications, MISTA-07. Google Scholar
  20. Leus, R., & Herroelen, W. (2004). Stability and resource allocation in project planning. IIE Transactions, 36(7), 667–682. CrossRefGoogle Scholar
  21. Muscettola, N. (2002). Computing the envelope for stepwise-constant resource allocations. In Lecture notes in computer science: Vol. 2470. Principles and practice of constraint programming, 8th international conference, CP 2002 (pp. 139–154). Berlin: Springer. CrossRefGoogle Scholar
  22. Policella, N., Oddi, A., Smith, S. F., & Cesta, A. (2004a). Generating robust partial order schedules. In M. Wallace (Ed.), Lecture notes in computer science : Vol. 3258. Principles and practice of constraint programming, 10th international conference, CP 2004 (pp. 496–511). Berlin: Springer. Google Scholar
  23. Policella, N., Smith, S. F., Cesta, A., & Oddi, A. (2004b). Generating robust schedules through temporal flexibility. In Proceedings of the 14th international conference on automated planning & scheduling, ICAPS’04 (pp. 209–218). Google Scholar
  24. Policella, N., Wang, X., Smith, S. F., & Oddi, A. (2005). Exploiting temporal flexibility to obtain high quality schedules. In Proceedings of the twentieth national conference on artificial intelligence, AAAI-05 (pp. 1199–1204). Google Scholar
  25. Policella, N., Cesta, A., Oddi, A., & Smith, S. F. (2007). From precedence constraint posting to partial order schedules. AI Communications, 20(3), 163–180. Google Scholar
  26. Rasconi, R., Cesta, A., & Policella, N. (2008). Validating scheduling approaches against executional uncertainty. Journal of Intelligent Manufacturing (in press). Google Scholar
  27. Resende, M., & Ribeiro, C. (2002). Greedy randomized adaptive search procedures. In F. Glover & G. Kochenberger (Eds.), Handbook of metaheuristics (pp. 219–249). Dordrecht: Kluwer Academic. Google Scholar
  28. Smith, S. F., & Cheng, C. (1993). Slack-based heuristics for constraint satisfactions scheduling. In Proceedings of the 11th national conference on artificial intelligence, AAAI-93 (pp. 139–144). Menlo Park: AAAI Press. Google Scholar
  29. Wu, S. D., Beyon, E. S., & Storer, R. H. (1999). A graph-theoretic decomposition of the job shop scheduling problem to achieve scheduling robustness. Operations Research, 47(1), 113–124. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Nicola Policella
    • 1
  • Amedeo Cesta
    • 2
  • Angelo Oddi
    • 2
  • Stephen F. Smith
    • 3
  1. 1.European Space AgencyDarmstadtGermany
  2. 2.ISTC-CNRNational Research Council of ItalyRomeItaly
  3. 3.The Robotics InstituteCarnegie Mellon UniversityPittsburghUSA

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