  In this paper, we address the task of setting up an optimal production plan
taking into account an uncertain demand. The energy system is represented by a
system of hyperbolic partial differential equations (PDEs) and the uncertain
demand stream is captured by an Ornstein-Uhlenbeck process. We determine the
optimal inflow depending on the producer's risk preferences. The resulting
output is intended to optimally match the stochastic demand for the given risk
criteria. We use uncertainty quantification for an adaptation to different
levels of risk aversion. More precisely, we use two types of chance constraints
to formulate the requirement of demand satisfaction at a prescribed probability
level. In a numerical analysis, we analyze the chance-constrained optimization
problem for the Telegrapher's equation and a real-world coupled gas-to-power
network.
