Abstract
Edge-finding and energetic reasoning are well known filtering rules used in constraint based disjunctive and cumulative scheduling during the propagation of the resource constraint. In practice, however, edge-finding is most used (because it has a low running time complexity) than the energetic reasoning which needs O（n3） time-intervals to be considered (where n is the number of tasks). In order to reduce the number of time-intervals in the energetic reasoning, the maximum density and the minimum slack notions are used as criteria to select the time-intervals. The paper proposes a new filtering algorithm for cumulative resource constraint, and titled energetic extended edge finder of complexity O（n3）. The new algorithm is a hybridization of extended edge-finding and energetic reasoning: more powerful than the extended edge-finding and faster than the energetic reasoning. It is proven that the new algorithm subsumes the extended edge-finding algorithm. Results on Resource Constrained Project Scheduling Problems (RCPSP) from BL set and PSPLib librairies are reported. These results show that in practice the new algorithm is a good trade-off between the filtering power and the running time on instances where the number of tasks is less than 30.
Highlights
Scheduling is the process of assigning resources to tasks or activities over the time
The filtering power of this algorithm is less than the one of the energetic reasoning, but in practice, it is a good trade-off between the filtering power and the running time
The time bounds of task intervals used in the edge-finding for detection and adjustment are used in an energetic reasoning
Summary
Scheduling is the process of assigning resources to tasks or activities over the time. There exist many types of scheduling problems following the tasks properties (preemptive or non-preemptive), the type of resources (disjunctive or cumulative) and the objective function (makespan, time late...). When a unique cumulative resource with non-preemptive tasks is considered, the problem is called cumulative scheduling problem (CuSP). A solution of a CuSP instance is an assignment of valid start time si to each task i in such a way that resource constraints are satisfied i.e.,. The inequalities in (1) ensure that each task is assigned a feasible start and end time, while (2) enforces the resource constraint. The global constraint CUMULATIVE embeds many filtering algorithms. Energetic reasoning, edge-finding and timetabling are the most used
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