Reasoning with Conditional Time-intervals

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Reasoning with conditional time-intervals representing activities or tasks that may or may not be executed in the final schedule is crucial in many scheduling applications. In Constraint-Based Scheduling, those problems are usually handled by defining new global constraints over classical integer variables. The approach described in this paper takes a different perspective by introducing a new type of variable (namely a time-interval variable) that intrinsically embeds the notion of conditionality. This dual perspective facilitates the modelling process while ensuring a strong constraint propagation and an efficient search in the engine. The approach forms the foundations of the new generation of scheduling model and algorithms provided in ILOG CP Optimizer.