Constraint-Based Scheduling
Edge Finding for Cumulative Scheduling
INFORMS Journal on Computing
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
O(n log n) overload checking for the cumulative constraint and its application
INAP'05 Proceedings of the 16th international conference on Applications of Declarative Programming and Knowledge Management
A resource cost aware cumulative
CSCLP'09 Proceedings of the 14th Annual ERCIM international conference on Constraint solving and constraint logic programming
Explanations for the cumulative constraint: an experimental study
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
A quadratic edge-finding filtering algorithm for cumulative resource constraints
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
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In scheduling using constraint programming we usually reason only about possible start times and end times of activities and remove those which are recognized as unfeasible. However often in practice there are more variables in play: variable durations of activities and variable resource capacity requirements. This paper presents a new algorithm for filtering maximum durations and maximum capacity requirements for discrete cumulative resources. It is also able to handle optional interval variables introduced in IBM ILOG CP Optimizer 2.0. Time complexity of the algorithm is ${\mathcal O}(n {\rm log} n)$. The algorithm is based on never published algorithm by Wim Nuijten and a on slightly modified e-feasibility checking algorithm by Armin Wolf and Gunnar Schrader. The later algorithm is also described in the paper.