This work reports the analyses of some thermodynamic systems with the concepts of entropy generation, entropy generation numbers and revised entropy generation number, as well as exergy destruction number and exergy-work conversion efficiency that are proposed in this paper. The applicability of entropy generation minimization (EGM) is conditional if the optimization objective is the output power. The EGM leads to the maximum output power when the net exergy flow rate into the system is fixed, but it may not be appropriate if the net exergy flow rate into the system is not fixed. On the other hand, smaller exergy destruction number always corresponds to larger exergy-work conversion efficiency. The refrigeration cycle with the reverse Carnot engine is also analyzed in which mechanical work is input. The result shows that the EGM leads to the largest COP if the temperature of the high temperature heat source is fixed. (C) 2013 Elsevier Ltd. All rights reserved.