A new approach in the network DEA models for measurement of productivity of decision-making units using multi-objective programming method

So far, numerous studies have been developed to evaluate the performance of “Decision-Making Units (DMUs)” through “Data Envelopment Analysis (DEA)” and “Network Data Envelopment Analysis (NDEA)” models in different places, but most of these studies have measured the performance of DMUs by efficiency criteria. The productivity is considered as a key factor in the success and development of DMUs and its evaluation is more comprehensive than efficiency evaluation. Recently, studies have been developed to evaluate the productivity of DMUs through the mentioned models but firstly, the number of these studies especially in NDEA models is scarce, and secondly, productivity in these studies is often evaluated through the “productivity indexes”. These indexes require at least two time periods and also the two important elements of efficiency and effectiveness in these studies are not significantly evident. So, the purpose of this study is to develop a new approach in the NDEA models using “Multi-Objective Programming (MOP)” method in order to measure productivity of DMUs through efficiency and effectiveness “simultaneously, in one stage, in a period, and interdependently”. “Simultaneous and single-stage” study provides the advantage of sensitivity analysis in the model. One case study demonstrates application of the proposed approach in the branches of a Bank. Using proposed approach revealed that it is possible for a branch to be efficient by considering its subdivisions separately but not be efficient by considering the conjunction between its subdivisions. In addition, a branch may be efficient by considering the conjunction between its subdivisions but not be productive. Efficient branches are not necessarily productive, but productive branches are also efficient.