  This article studies a hyperbolic conservation law that models a highly
re-entrant manufacturing system as encountered in semi-conductor production.
Characteristic features are the nonlocal character of the velocity and that the
influx and outflux constitute the control and output signal, respectively. We
prove the existence and uniqueness of solutions for $L^1$-data, and study their
regularity properties. We also prove the existence of optimal controls that
minimizes in the $L^2$-sense the mismatch between the actual and a desired
output signal. Finally, the time-optimal control for a step between equilibrium
states is identified and proven to be optimal.

Optimization and Control