Production flow control under finite capacity

The authors study the problem of minimizing in-process inventory cost under finite capacity constraints and for a continuous time-varying demand. They present the properties of the optimal control in the most general case and prove that it belongs to a finite set of feasible controls. They also prove that under some additional assumptions the optimal control can be characterized analytically. The multiproduct problem is examined. They propose a numerical application which is presented to illustrate the analytical results