Uncertain Network Data Envelopment Analysis with ParallelStructure and Imprecisely Inputs and Outputs(Case Study: Social Security Organization)

Data Envelopment Analysis (DEA) is an effective method for evaluating therelative efficiency of decision-making units (DMUs). The classical approach considerseach organizational unit as a black box and limits evaluation to primary inputs and finaloutputs and neglects internal processes. This problem with the introduction and use ofDEA in network structures for more accurate performance analysis, taking into accountits internal processes, has been resolved. In most of the proposed models, the inputs andoutputs of DMUs are definite, but in many cases, those data cannot be measured in aprecise way. Therefore, this paper seeks to introduce a new model of Network DataEnvelopment Analysis with a parallel structure by considering inputs and outputs asuncertain variables. The approach used is to develop the mathematical model from atheoretical point of view, to prove the theoretical properties of the model, themathematical validity and its application.

In this paper, the assumptions of uncertainty theory and models of NetworkData Envelopment Analysis to evaluate DMUs with parallel structure and impreciseinputs and outputs.

According to the results of the implementation of the proposed model in theSocial Security Organization, the efficiency of all DMUs and its sub-system has beenevaluated between zero and one.

Due to the multiplicity of the sub-system, none of the 12-provincial socialsecurity managing directorates as DMUs were efficient (one efficiency score), but among313 branches, three branches were efficient. The final results of the implementation of theuncertain model proved the assumptions of the definitive model.