We consider the multi-product discrete lot-sizing and scheduling problem with sequence-dependent changeover costs. We propose a new family of multi-product valid inequalities which enables us to better take into account in the MILP formulation the conflicts between di erent products simultaneously requiring production on the resource. We then present both an exact and a heuristic separation algorithm for these valid inequalites. We fi nally discuss some preliminary computational results which con firm the practical usefulness of the proposed valid inequalities at strengthening the MILP formulation.