A Relaxation of the Cumulative Constraint
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
A unified framework for partial and hybrid search methods in constraint programming
Computers and Operations Research
Solving a large-scale precedence constrained scheduling problem with elastic jobs using tabu search
Computers and Operations Research
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Allocation and scheduling of Conditional Task Graphs
Artificial Intelligence
Why cumulative decomposition is not as bad as it sounds
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Event-based MILP models for resource-constrained project scheduling problems
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A new o(n2log n) not-first/not-last pruning algorithm for cumulative resource constraints
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Explaining the cumulative propagator
Constraints
Explanations for the cumulative constraint: an experimental study
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
Not-First and not-last detection for cumulative scheduling in O(n3 log n)
INAP'05 Proceedings of the 16th international conference on Applications of Declarative Programming and Knowledge Management
A constraint integer programming approach for resource-constrained project scheduling
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
On the complexity of global scheduling constraints under structural restrictions
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Inrecent years, constraint satisfaction techniques have been successfullyapplied to ’’disjunctive‘‘ scheduling problems, i.e., schedulingproblems where each resource can execute at most one activityat a time. Less significant and less generally applicable resultshave been obtained in the area of ’’cumulative‘‘ scheduling.Multiple constraint propagation algorithms have been developedfor cumulative resources but they tend to be less uniformly effectivethan their disjunctive counterparts. Different problems in thecumulative scheduling class seem to have different characteristicsthat make them either easy or hard to solve with a given technique.The aim of this paper is to investigate one particular dimensionalong which problems differ. Within the cumulative schedulingclass, we distinguish between ’’highly disjunctive‘‘ and ’’highlycumulative‘‘ problems: a problem is highly disjunctive when manypairs of activities cannot execute in parallel, e.g., becausemany activities require more than half of the capacity of a resource;on the contrary, a problem is highly cumulative if many activitiescan effectively execute in parallel. New constraint propagationand problem decomposition techniques are introduced with thisdistinction in mind. This includes an O(n^2) ’’edge-finding‘‘algorithm for cumulative resources (where n is thenumber of activities requiring the same resource) and a problemdecomposition scheme which applies well to highly disjunctiveproject scheduling problems. Experimental results confirm thatthe impact of these techniques varies from highly disjunctiveto highly cumulative problems. In the end, we also propose arefined version of the ’’edge-finding‘‘ algorithm for cumulativeresources which, despite its worst case complexity in O(n^3),performs very well on highly cumulative instances.