Large industrial sites commonly contain multiple production and utility systems. In practice, integrated optimization is often not possible because the necessary complete information cannot be exchanged between the systems. Often, industrial sites optimize the operation of production and utility systems sequentially without any feedback, which leads to suboptimal operation.

In this paper, we propose a method to coordinate between production and utility systems in a multi-leader multi-follower Stackelberg game. The proposed method does not require complete information exchange. The only information exchanged in one feedback loop is the energy demand and demand-dependent energy cost.

In two case studies, the method reduces the total production cost by 7.6% and 3.4% compared to the common sequential optimization. These cost savings correspond to 84% and 88% of the potential cost savings by an integrated optimization. In summary, the proposed method reduces cost significantly, while only incomplete information is exchanged between production and utility systems.

大型工业场所通常包含多个生产和公用事业系统。实际上，集成优化通常是不可能的，因为无法在系统之间交换必要的完整信息。通常，工业现场会在没有任何反馈的情况下按顺序优化生产和公用事业系统的运行，这会导致运行不佳。

在本文中，我们提出了一种在多领导者多跟从Stackelberg游戏中协调生产系统和公用事业系统的方法。所提出的方法不需要完整的信息交换。在一个反馈回路中交换的唯一信息是能源需求和与需求有关的能源成本。

在两个案例研究中，与常见的顺序优化相比，该方法将总生产成本降低了7.6％和3.4％。通过集成优化，这些成本节省分别相当于潜在成本节省的84％和88％。总之，提出的方法可显着降低成本，同时在生产系统和公用事业系统之间仅交换不完整的信息。