Constraint propagation and decomposition techniques for highly disjunctive and highly cumulative project scheduling problems

  • Philippe Baptiste
  • Claude Le Pape
Session 6
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1330)


In recent years, constraint satisfaction techniques have been successfully applied to “disjunctive” scheduling problems, i.e., scheduling problems where each resource can execute at most one activity at a time. Less significant and less generally applicable results have been obtained in the area of “cumulative” scheduling. Multiple constraint propagation algorithms have been developed for cumulative resources but they tend to be less uniformly effective than their disjunctive counterparts. Different problems in the cumulative scheduling class seem to have different characteristics that make them either easy or hard to solve with a given technique. The aim of this paper is to investigate one particular dimension along which problems differ. Within the cumulative scheduling class, we distinguish between “highly disjunctive” and “highly cumulative” problems: a problem is highly disjunctive when many pairs of activities cannot execute in parallel, e.g., because many activities require more than half of the capacity of a resource; on the contrary, a problem is highly cumulative if many activities can effectively execute in parallel. New constraint propagation and problem decomposition techniques are introduced with this distinction in mind. This includes an O(n2) “edge-finding” algorithm for cumulative resources, and a problem decomposition scheme which applies well to highly disjunctive project scheduling problems. Experimental results confirm that the impact of these techniques varies from highly disjunctive to highly cumulative problems.


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  1. A. Aggoun and N. Beldiceanu [1993], Extending CHIP in Order to Solve Complex Scheduling and Placement Problems, Mathematical and Computer Modelling 17:57–73.Google Scholar
  2. D. Applegate and W. Cook [1991], A Computational Study of the Job-Shop Scheduling Problem, ORSA Journal on Computing 3(2):149–156.Google Scholar
  3. Ph. Baptiste and C. Le Pape [1995], A Theoretical and Experimental Comparison of Constraint Propagation Techniques for Disjunctive Scheduling, Proc. 14th International Joint Conference on Artificial Intelligence.Google Scholar
  4. P. Brucker, S. Knust, A. Schoo, and O. Thiele [1997], A Branch and Bound Algorithm for the Resource-Constrained Project Scheduling Problem, Working Paper, University of Osnabrück, 1997.Google Scholar
  5. J. Carlier and B. Latapie [1991], Une méthode arborescente pour résoudre les problèmes cumulatifs, RAIRO Recherche opérationnelle / Operations Research 25(3):311–340.Google Scholar
  6. J. Carlier and E. Néron [1996], A New Branch-and-Bound Method for Solving the Resource-Constrained Project Scheduling Problem, Proc. International Workshop on Production Planning and Control.Google Scholar
  7. J. Carlier and E. Pinson [1990], A Practical Use of Jackson's Preemptive Schedule for Solving the Job-Shop Problem, Annals of Operations Research 26:269–287.Google Scholar
  8. Y. Caseau and F. Laburthe [1995], Disjunctive Scheduling with Task Intervals, Technical Report, Ecole Normale Supérieure.Google Scholar
  9. Y. Caseau and F. Laburthe [1996a], Cumulative Scheduling with Task Intervals, Proc. Joint International Conference and Symposium on Logic Programming.Google Scholar
  10. Y. Caseau and F. Laburthe [1996b], CLAIRE: A Parametric Tool to Generate C++ Code for Problem Solving, Working Paper, Bouygues, Direction Scientifique.Google Scholar
  11. A. Cesta and A. Oddi [1996], Gaining Efficiency and Flexibility in the Simple Temporal Problem, Proc. 3rd International Workshop on Temporal Representation and Reasoning.Google Scholar
  12. E. Demeulemeester and W. Herroelen [1992], A Branch-and-Bound Procedure for the Multiple Resource-Constrained Project Scheduling Problem, Management Science 38(12):1803–1818.Google Scholar
  13. M. R. Garcy and D. S. Johnson [1979], Computers and Intractability. A Guide to the Theory of NP-Completeness, W. H. Freeman and Company.Google Scholar
  14. M. Gondran and M. Minoux [1984], Graphs and Algorithms, John Wiley and Sons.Google Scholar
  15. R. Kolisch, A. Sprecher, and A. Drexl [1995], Characterization and Generation of a General Class of Resource-Constrained Project Scheduling Problems, Management Science 41(10):1693–1703.Google Scholar
  16. C. Le Pape [1994], Implementation of Resource Constraints in ILOG SCHEDULE: A Library for the Development of Constraint-Based Scheduling Systems, Intelligent Systems Engineering 3(2):55–66.Google Scholar
  17. C. Le Pape and Ph. Baptiste [1996], Constraint Propagation Techniques for Disjunctive Scheduling: The Preemptive Case, Proc. 12th European Conference on Artificial Intelligence.Google Scholar
  18. C. Le Pape and Ph. Baptiste [1997], A Constraint Programming Library for Preemptive and Non-Preemptive Scheduling, Proc. 3rd International Conference on the Practical Application of Constraint Technology.Google Scholar
  19. O. Lhomme [1993], Consistency Techniques for Numeric CSPs, Proc. 13th International Joint Conference on Artificial Intelligence.Google Scholar
  20. W. P. M. Nuijten [1994], Time and Resource Constrained Scheduling: A Constraint Satisfaction Approach, PhD Thesis, Eindhoven University of Technology.Google Scholar
  21. J. H. Patterson [1984], A Comparison of Exact Approaches for Solving the Multiple Constrained Resource Project Scheduling Problem, Management Science 30(7):854–867.Google Scholar
  22. M. Perregaard [1995], Branch and Bound Methods for the Multi-Processor Job Shop and Flow Shop Scheduling Problem, MSc Thesis, University of Copenhagen.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Philippe Baptiste
    • 1
    • 2
  • Claude Le Pape
    • 1
  1. 1.Bouygues, Direction ScientifiqueSaint-Quentin-en-Yvelines
  2. 2.UMR CNRS 6599, Université de Technologie de CompiègneFrance

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