A tight MILP formulation based on multi-product valid inequalities for a lot-sizing problem

We consider a problem arising in the context of industrial production planning, namely the multi-product discrete lot-sizing and scheduling problem with sequence-dependent changeover costs. We aim at developing an exact solution approach based on a standard Branch & Bound procedure for this combinatorial optimization problem. To achieve this, we propose a new family of multi-product valid inequalities which enables us to better take into account in the mixed integer linear programming formulation the conflicts between different products simultaneously requiring production on the resource. We then present both an exact and a heuristic separation algorithm in order to identify the most violated valid inequalities to be added in the initial MILP formulation within a cutting-plane generation algorithm. We finally discuss preliminary computational results which confirm the practical usefulness of the proposed valid inequalities at strengthening the MILP formulation and at reducing the overall computation time.