Energy efficiency is one of the main pathways for energy security and environmental protection. In fact, the International Energy Agency asserts that without energy efficiency, 70% of targeted emission reductions are not achievable. Despite this clarity, enhancing the energy efficiency introduce significant challenge toward process operation. The reason is that the methods applied for energy-saving pose the process operation at the intersection of safety constraints. The present research aims at uncovering the trade-off between safe operation and energy efficiency; an optimization framework is developed that ensures process safety and simultaneously optimizes energy-efficiency, quantified in economic terms. The developed optimization framework is demonstrated for a solid oxide fuel cell (SOFC) power generation system. The significance of this industrial application is that SOFC power plants apply a highly degree of process integration resulting in very narrow operating windows. However, they are subject to significant uncertainties in power demand. The results demonstrate a strong trade-off between the competing objectives. It was observed that highly energy-efficient designs feature a very narrow operating window and limited flexibility. For instance, expanding the safe operating window by 100% will incur almost 47% more annualized costs. Establishing such a trade-off is essential for realizing energy-saving.