Lagrangean decomposition of a Lot-Sizing problem into Facility Location and Multi-commodity Flow

This paper describes the way a multi-item, multi-plant Lot-Sizing problem with transfer costs and capacities may be reformulated according to a multi-commodity flow formalism, and decomposed, through Lagrangean Relaxation, into a master Facility Location problem and a slave Minimal Cost Multi-commodity Flow problem. This decomposition framework gives rise in a natural way to the design of a relax/project approximate algorithm, and it ends with numerical experiments.