The purpose of this paper is to evaluate the efficiency of a network of natural gas power plants using the Data Envelopment Analysis approach. The network is modeled as a linear system with multiple inputs and outputs. As inputs one could consider, for instance, the age of a plant, the total number of hours that a plant is in operation during each year, etc. As outputs the model considers the electrical energy delivered per year, the number of hours that the plant is not in operation, etc. The proposed approach does not only evaluate each plant relative to the other ones, but it also `produces' policy making scenarios that would enable plant managers to improve the plant's operational characteristics. Computational results based on real-world data are presented and discussed. Relationships between efficiency scores and various inputs/outputs are also investigated and some interesting trends are identified.