Multi-product valid inequalities for the discrete lot-sizing and scheduling problem

Céline Gicquel (1) , Michel Minoux (2)

1 LRI - Laboratoire de Recherche en Informatique
2 DECISION

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 Cut & Branch procedure for this combinatorial optimization problem. To achieve this, we propose a new family of multi-product valid inequalities which corresponds to taking into account the conflicts between different products simultaneously requiring production on the resource. We then present both an exact and a heuristic separation algorithm which form the basis of a cutting-plane generation algorithm. We finally discuss computational results which confirm the practical usefulness of the proposed inequalities at strengthening the MILP formulation and at reducing the overall computation time.

Mots clés: Production planning; Lot-sizing; Mixed-integer linear programming; Valid inequalities

Domaines: Informatique [cs]

Céline Gicquel, Michel Minoux. Multi-product valid inequalities for the discrete lot-sizing and scheduling problem. Computers and Operations Research, 2015, 54, pp.12-20. ⟨10.1016/j.cor.2014.08.022⟩. ⟨hal-01262267⟩