A new method for analyzing industrial energy systems is presented in this paper. The major part of this method is two graphical tools, namely, "retrofit R-curve" and "grassroots R-curve". The new method can be applied for three major scenarios. The retrofit R-curve is dedicated for the operational management and retrofit of utility systems. The R-curve will indicate how the existing operation could be improved without capital investment. For retrofit, the analysis of this scenario will denote, through steam marginal prices, which steam is the most valuable steam worth saving and how much can be saved. The steam marginal prices determined from the method can be used as the basis for steam level switching and heat-exchanger network retrofit. The grassroots R-curve is built on the basis of a hypothetical ideal utility system without imposing capacity limits for equipment; thus, it can indicate ideal fuel utilization. This curve is used for debottlenecking the existing utility system when new processes are added and/or the throughput needs to be increased. The analysis of this scenario will indicate the most economic modifications to cope with significant changes in heat and power demand. These two curves are easy to construct and simple to understand, but they are powerful, in providing insights and perspectives for improving existing energy systems.