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In an energy system, it is important to identify the origin of residue formation in order to implement actions to reduce their formation or to eliminate them as well as to evaluate their impact on the production costs of the system. In the exergetic cost theory, although there are several criteria to allocate the cost formation of residues to the productive components, no unique indication on the best choice has been defined yet. In this paper, the production exergy costs are determined by allocating the residue cost formation to the irreversibilities of the productive components from which they originate. This criterion, based on the Gouy–Stodola theorem, is an extension of the criterion of entropy changes, and unlike this, it avoids the existence of a negative production cost. This criterion is applied to a combined cycle of three pressure levels, and the production exergy costs are compared with the criteria of entropy changes, distributed exergy, and entropy. The results of the proposed criterion are in agreement with the compared criteria.