In this paper, we consider an Energy Scheduling Problem given by a set of non-preemptive tasks, each requiring a resource usage limited in maximum and minimum, and satisfying its time window constraint (release date and deadline) with a total energy requirement (time x resource usage). Our goal consists in getting an optimized usage pro le of each task over an interval horizon in order to respect all the constraints. To deal with all this, we associate two main concepts, linear programming and energetic reasoning. We try to introduce into a linear program, the idea that the resource usage pro le of each task scheduled inside a set of time window intervals, once started, must respect all its energy constraints. So the problem consists in connecting the energetic constraints with a linear program. We want to discern if this is possible, trying at the same time to design an effcient solving approach.

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