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

The PLANWAR model is a new formulation to the multi-commodity, multi-plant, capacitated facility location problem that seeks to locate a number of production plants and distribution centers so that total operating costs for the distribution network are minimized. An important component of a firmʹs physical distribution strategy is its network strategy, which defines the physical flow of commodities (products) from production plants to warehouses and from warehouses to customer zones. A frequent objective when designing a network strategy is to determine the least total cost system design such that all customer demand is satisfied subject to limitations imposed by production capacities for plants and storage capacities for warehouses. We present a mixed integer programming model, PLANWAR, and provide an efficient heuristic solution procedure for this supply chain management problem. Distribution system design problems commonly occurs 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.