Production flow control: Balancing facilities under fixed initial inventory conditions

An optimal control approach to continuous-time aggregate production planning problems is presented for cases of balancing multiple facilities against arbitrarily changing demand profiles. The dynamics of such a system is modeled by input and output inventory flows through facilities of finite capacity. Initially fixed input and output inventory flows through facilities of finite capacity. Initially fixed input inventory levels in the system are drained by controllable production rates. The objective is to track a given customer demand while minimizing the surplus of the output inventory. The optimal behaviour of the system is studied with the aid of the maximum principle. The analytical properties of the optimal solution which are obtained are then invoked to construct a fast numerical algorithm.