This paper introduces a new method to prune the domains of the variablesin constrained optimization problems where the objective function is defined by a sumy = ∑xi , and where the integer variables x i are subject to difference constraintsof the form xj - xi ≤ c. An important application area where such problems occur is deterministic scheduling with the mean flow time as optimality criteria.This new constraint is also more general than a sum constraint defined on a set of ordered variables. Classical approaches perform a local consistency filtering after each reduction ofthe bound of y. The drawback of these approaches comes from the fact that the constraints are handled independently.We introduce here a global constraint that enables to tackle simultaneously the whole constraint system, and thus, yields a more effective pruningof the domains of the x i when the bounds of y are reduced.An efficient algorithm,derived from Dijkstra's shortest path algorithm, is introduced to achieve interval consistency on this global constraint.