In this article, 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 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.

中文翻译：

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需求不确定的双曲线供应系统中机会约束的最优流入控制

在本文中，我们解决了考虑不确定需求的情况下制定最佳生产计划的任务。能量系统由双曲型偏微分方程组表示，不确定的需求流由Ornstein-Uhlenbeck过程捕获。我们根据生产者的风险偏好确定最佳流入量。结果输出旨在针对给定的风险标准最佳地匹配随机需求。我们使用不确定性量化来适应不同级别的风险规避。更准确地说，我们使用两种类型的机会约束来以规定的概率水平制定需求满足的要求。在数值分析中，我们分析了电报机的机会约束优化问题