An optimal investment and inventory policy

The relation between the optimal production level and the optimal investment in a flexible manufacturing machine will be the subject of this paper. The study concerns the production of N families of products on one production machine. The investment level in a particular production machine is assumed to depend on both the intra and inter family set-up times. The optimal production level will be shown to depend on the optimal investment choice made and as such on both the intra- and inter-family set-up times. The results show the necessity of coordination between several departments, as for instance the production planning department and financial department, of an organization. Moreover it will be argued that circumstances exist in which mathematical models can be used in a more qualitative level of analysis.