The well-known Gouy-Stodola theoremstates that a device produces maximum useful power when working reversibly, that is with no entropy production inside the device. This statement then leads to a method of thermodynamic optimization based on entropy production minimization. Exergy destruction (difference between exergy of fuel and exhausts) is also given by entropy production inside the device. Therefore, assessing efficiency of a device by exergy analysis is also based on the Gouy-Stodola theorem. However, assumptions that had led to the Gouy-Stodola theorem are not satisfied in several optimization scenarios, e.g. non-isothermal steady-state fuel cells, where both entropy production minimization and exergy analysis should be used with caution. We demonstrate, using non-equilibrium thermodynamics, a few cases where entropy production minimization and exergy analysis should not be applied.