A Lagrangean relaxation based heuristic for logistics network design
Résumé
We consider a logistics network design problem with multiple periods, echelons, facilities and commodities. The initial network has some operating facilities and a set of potential locations to settle new ones. Over a strategic horizon, the optimisation model aims at locating operating facilities; planning the capacity, the production levels and the product flows. This problem is modelled as a mixed integer linear programme (MILP) with binary variables associated to facility status and continuous variables associated to material flows. The proposed scheme is based on the lagrangean relaxation of some coupling constraints. A decomposition level is performed by considering the main echelons: suppliers / plants; plants / warehouses and customers; warehouses / customers. characteristics of the corresponding echelon The resolution of this decomposed problem provides a lower bound. On the other hand, the feasible solutions provide upper bounds that can be improved by applying a D.C. (Difference of Convex Functions) algorithm for MILP. A procedure for updating lagrangean multipliers is also proposed. All these elements are combined to build an iterative heuristic for solving the original problem. Stopping conditions are based on the classical gap between the two bounds.