Formulating the single machine sequencing problem with release dates as a mixed integer program
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
Artificial Intelligence - Special issue on knowledge representation
Scheduling with release dates on a single machine to minimize total weighted completion time
Discrete Applied Mathematics
Optimal speedup of Las Vegas algorithms
Information Processing Letters
Scheduling identical parallel machines to minimize total weighted completion time
CO89 Selected papers of the conference on Combinatorial Optimization
Algorithm performance and problem structure for flow-shop scheduling
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Single Machine Scheduling with Release Dates
SIAM Journal on Discrete Mathematics
Embedding Relaxations in Global Constraints for Solving TSP and TSPTW
Annals of Mathematics and Artificial Intelligence
Optimization-Oriented Global Constraints
Constraints
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Arc Consistency for Global Cardinality Constraints with Costs
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
An Arc-Consistency Algorithm for the Minimum Weight All Different Constraint
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Time-Indexed Formulations for Machine Scheduling Problems: Column Generation
INFORMS Journal on Computing
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Computers and Operations Research
A global constraint for total weighted completion time for cumulative resources
Engineering Applications of Artificial Intelligence
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We introduce a novel global constraint for the total weighted completion time of activities on a single unary capacity resource. For propagating the constraint, we propose an O(n 4) algorithm 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. We then apply the constraint to the multi-machine job shop scheduling problem with total weighted completion time. Our experiments show an order of magnitude reduction in search effort over the standard weighted-sum constraint and demonstrate that the way in which the job weights are associated with activities is important for performance.