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

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

Keywords:

Data envelopment analysis , Efficiency , Two stage system , Non-cooperative , Slacks - based measure