Common set of weights and efficiency improvement on the basis of separation vector in two-stage network data envelopment analysis

Common set of weights (CSWs) method is one of the popular ranking methods in DEA which can rank efficient and inefficient units. Based on an identical criterion, the method selects the most favorable weight set for all units. An important issue is that in most common DEA models, the internal structure of the production units is ignored and the units are often considered as black boxes. In this paper, in order to evaluate the units and subunits in the two-stage NDEA based on an identical criterion, it is suggested to use CSWs method on the basis of separation vector. Our research contribution in this paper includes: (1) CSWs method is formulated in two-stage NDEA as a multiple objective fractional programming (MOFP) problem. (2) A method is suggested based on separation vector to change MOFP problem into single objective linear programming (SOLP) problem in two-stage NDEA. In the theorem, it is shown that the obtained solutions from MOFP and SOLP in two-stage NDEA are identical. (3) In the framework of the new models of two-stage NDEA, a process is introduced to improve efficiency evaluation by CSWs on the basis of separation vector which is based on the radial improvement of inputs and final outputs. Finally, an enlightening application is presented.