Optimal location of production centers, interconnected materials and products allocation

This paper deals with a complex problem, consisting of the selection of production centers, the allocation of materials and products as well as the consideration of the production levels. Production centers may be located at different sites, i.e. nodes of a graph. Multiple components or raw materials are transported to the production centers and a variety of final products may be manufactured and distributed from them. Each product has specific unit requirements of component materials. There are multiple supply centers for each type of material and demand centers for each product, i.e. nodes of the graph, with capacity or demand limits. All distances between nodes of the graph i.e. supply, demand and production centers, are known. Transportation costs may be nonlinear functions of distance. Other variables like costs or profits are considered. The optimisation criterion may be the cost required for demand satisfaction or the profit. The problem is formulated as a linear programming model.