Solving to Optimality a Discrete Lot-Sizing Problem Thanks to Multi-product Multi-period Valid Inequalities

We consider a problem related to industrial production planning, namely the multi-product discrete lot-sizing and scheduling problem with sequence-dependent changeover costs. This combinatorial optimization is formulated as a mixed-integer linear program and solved to optimality by using a standard Branch & Bound procedure. However, the computational efficiency of such a solution approach relies heavily on the quality of the bounds used at each node of the Branch & Bound search tree. To improve the quality of these bounds, we propose a new family of multi-product multi-period valid inequalities and present both an exact and a heuristic separation algorithm which form the basis of 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.