Evaluating the efficiency of two-stage systems in presence of shared inputs and final outputs in the first stage: an non-cooperative approach

Traditional Data envelopment analysis (DEA) is a non-parametric approach that measures the efficiency of comparable black box systems. There is a weakness in traditional DEA that does not survey the internal structure of systems. Hence, for evaluating the efficiency of the systems with interior structure, Network DEA(NDEA) was introduced. Two-stage systems are a special case of network systems. Several approaches were developed for measuring the efficiency of these systems such as slacks-based measure approach. In this paper, we consider two-stage systems with shared inputs between stages and final output in stage 1 and we shall suggest the non-cooperative models for measuring the efficiency of these systems based on slacks-based measure approach. Then, we shall calculate the overall efficiency of these systems as the product of the efficiency scores of the two stages. Finally, an illustrative example has been presented.