A global constraint for total weighted completion time for cumulative resources

The criterion of total weighted completion time occurs as a sub-problem of combinatorial optimization problems in such diverse areas as scheduling, container loading and storage assignment in warehouses. These applications often necessitate considering a rich set of requirements and preferences, which makes constraint programming (CP) an effective modeling and solving approach. On the other hand, basic CP techniques can be inefficient in solving models that require inference over sum type expressions. In this paper, we address increasing the solution efficiency of constraint-based approaches to cumulative resource scheduling with the above criterion. Extending previous results for unary capacity resources, we define the COMPLETIONm global constraint for propagating the total weighted completion time of activities that require the same cumulative resource. We present empirical results in two different problem domains: scheduling a single cumulative resource, and container loading with constraints on the location of the center of gravity. In both domains, the proposed constraint propagation algorithm out-performs existing propagation techniques

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A global constraint for total weighted completion time

Abstract. 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.

A global constraint for total weighted completion time

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/sup 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.Anglai