Abstract: Considering the problem that traditional DEA model cannot evaluate the relative performance of the matrix-type system effectively, the production possibility set is defined and the network DEA model is established for matrix-type system in this paper. It is proved that the DMUs are weak DEA efficiency if and only if all subsystems of the DMUs are weak DEA efficiency. Using data of ten electric power companies in the United States of America, the network DEA model is tested. The results show that the new model can make up for the drawbacks of the traditional DEA model on ignoring the internal structures. The new model can also evaluate divisional efficiency scores, which can help decision makers to detect the sub-processes needed to be evaluated. Furthermore, the new model provides a new idea for evaluating the relative performance of the complex systems.

Key words: matrix-type organization, network DEA, divisional efficiency, overall efficiency