We introduce a novel global constraint for the total weighted completion time of activities on a single unary capacity resource. For propagating the constraint, an O(n 4) algorithm is proposed, which makes use of the preemptive mean busy time relaxation of the scheduling problem. The solution to this problem is used to test if an activity can start at each start time in its domain in solutions that respect the upper bound on the cost of the schedule. Empirical results show that the proposed global constraint significantly improves the performance of constraint-based approaches to single-machine scheduling for minimizing the total weighted completion time. Since our eventual goal is to use the global constraint as part of a larger optimization problem, we view this performance as very promising. We also sketch the application of the global constraint to cumulative resources and to problems with multiple machines.


Schedule Problem Completion Time Single Machine Global Constraint Total Weighted Tardiness 
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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • András Kovács
    • 1
    • 3
  • J. Christopher Beck
    • 2
  1. 1.Projet Contraintes, INRIA RocquencourtFrance
  2. 2.Dept. of Mechanical and Industrial Engineering, University of TorontoCanada
  3. 3.Computer and Automation Research Institute, Hungarian Academy of Sciences 

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