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 bet
ween building up inventory and letting customers wait. An optimal cont
rol problem is formulated to determine the optimal production strategy
. Solution technique is developed via Pontryagin's Minimum Principle.