Exergy analysis, which provides means of calculating efficiency losses in industrial devices, is reviewed, and the area of its validity is carefully discussed. Consequently, a generalization is proposed, which holds also beyond the area of applicability of exergy analysis. The generalization is formulated within the framework of classical irreversible thermodynamics, and interestingly it leads to minimization of a functional different from entropy production. Fuel cells, osmotic power plants and heat engines are analyzed within the theory. In particular, the theory is demonstrated on a toy model of solid oxide fuel cells quantitatively. Eventually, a new general algorithm of thermodynamic optimization is proposed. (C) 2014 Elsevier Ltd. All rights reserved.