Many cumulative problems are such that the horizon is fixed and cannot be delayed. In this situation, it often occurs that all the activities cannot be scheduled without exceeding the capacity at some points in time. Moreover, this capacity is not necessarily always the same during the scheduling period. This article introduces a new constraint for solving this class of problems. We adapt two filtering algorithms to our context: Sweep and P. Vilím's Edge-Finding algorithm. We emphasize that in some problems violations are imposed. We design a new filtering procedure specific to this kind of events. We introduce a search heuristic specific to our constraint. We successfully experiment our constraint.