A multi-commodity, multi-plant, capacitated facility location problem: Formulation and efficient heuristic solution

Distribution system design problems commonly occur in the following form: A number of production plants supply warehouses with multiple products which in turn distribute these products to customer outlets based on their specified demand quantities of the different products. It is required to select the optimum set of plants and warehouses from a potential set and plan production capacities, warehouse capacities and quantities shipped so that the total operating costs of the distribution network are minimized. This paper is a computational study to investigate the value of coordinating production and distribution planning. We present a mixed integer programming formulation for the capacitated plant and warehouse supply chain management problem and propose an efficient heuristic based on Lagrangian relaxation of the problem.