Dynamic task sequencing in temporal problems with uncertainty

In classical planning and scheduling approaches, a task schedule is £rst designed off line, then executed on line, simply releasing tasks at times compatible with temporal domains of their starting time-points. When durations of tasks are uncertain, one wishes to keep as much ¤exibility on line as possible so as to release each task according to effective durations taken by previous ones. One also wishes to ensure off line that the on-line schedule will be feasible whatever the uncertain durations will be, which has been called temporal controllability of the plan. Such proactive reasoning both leads to predictice schedules that are more robust when executed on line, and also to easier and more effective on-line rescheduling when needed. Going further, the notion of sequentiability has been de£ned with respect to resource constraints. It means here the ability to decide on line the sequencing of tasks that use the same discrete resource, according to effective durations taken by previous ones. In the nonuncertain framework, algorithms exist to prune the search and detect so-called forbidden precedences among tasks. In this paper we show how these techniques can be extended in temporal problems with uncertainty.