Abstract
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.
Highlights
Data envelopment analysis (DEA) is a linear programming method that was proposed by Charnes et al [3] to assess the performance of decision making units that use multiple inputs and produce multiple outputs
In most conventional DEA models, the internal structures of the production units are disregarded and the units are often considered as black boxes
To improve the overall and divisional efficiency scores obtained by Common set of weights (CSWs) on the basis of separation vector in basic two-stage network data envelopment analysis (NDEA), we suggest increasing the outputs of the second as well as reducing the inputs of the first stage
Summary
Data envelopment analysis (DEA) is a linear programming method that was proposed by Charnes et al [3] to assess the performance of decision making units that use multiple inputs and produce multiple outputs. To improve the overall and divisional efficiency scores obtained by CSWs on the basis of separation vector in basic two-stage NDEA, we suggest increasing the outputs of the second as well as reducing the inputs of the first stage (the intermediate measures stay unchanged). It is possible to present a different approach by considering input and output vectors as decision variables in the production set, instead of simultaneous decrease and increase in the inputs and outputs under evaluation unit, in such a way that the overall and the divisional efficiency scores obtained by CSWs on the basis of separation vector of the subunits are improved. As it can be observed, by applying CSWs method based on the separation vector, a better discrimination can be made between units and subunits.
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