An optimal production flow control problem with impulsive demand

We consider a system consisting of a single machine cell and producing one part type. The machine cell has a finite capacity and is reliable. We consider a finite planning horizon containing N impulsive demands. The demand occurs instantaneously. Each such demand is known by its size and when it occurs in the planning horizon. In order to keep the production as close to the demand as possible there is a trade off between building up inventory and letting customers wait. An optimal control problem is formulated to determine the optimal production strategy. Solution technique is developed via Pontryaginʹs Minimum Principle.