A thermodynamic analysis is presented by means of mathematical formulation to examine the performance of the most common types of heat engines including Otto, Diesel, and Brayton cycles, at the regime of minimum entropy generation. All engines are subject to internal and external irreversibilities. It is shown that minimum entropy production criterion neither correlates with maximum thermal efficiency design nor with maximum work output criterion. The results demonstrate that the production of entropy is not necessarily equivalent to the energy losses taking place in real devices. (C) 2013 Elsevier Inc. All rights reserved.