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

Document Type : Research Paper


1 Prof., Department of Industrial Management, Faculty of Management University of Tehran, Tehran, Iran.

2 Ph.D. Candidate, Department of Industrial Management, Faculty of Management, University of Tehran, Tehran, Iran.

3 MSc., Department of Executive Management, University of Payame Nour, Babol, Iran.


Objective: Data Envelopment Analysis (DEA) is an effective method for evaluating the
relative efficiency of decision-making units (DMUs). The classical approach considers
each organizational unit as a black box and limits evaluation to primary inputs and final
outputs and neglects internal processes. This problem with the introduction and use of
DEA in network structures for more accurate performance analysis, taking into account
its internal processes, has been resolved. In most of the proposed models, the inputs and
outputs of DMUs are definite, but in many cases, those data cannot be measured in a
precise way. Therefore, this paper seeks to introduce a new model of Network Data
Envelopment Analysis with a parallel structure by considering inputs and outputs as
uncertain variables. The approach used is to develop the mathematical model from a
theoretical point of view, to prove the theoretical properties of the model, the
mathematical validity and its application.
Methods: In this paper, the assumptions of uncertainty theory and models of Network
Data Envelopment Analysis to evaluate DMUs with parallel structure and imprecise
inputs and outputs.
Results: According to the results of the implementation of the proposed model in the
Social Security Organization, the efficiency of all DMUs and its sub-system has been
evaluated between zero and one.
Conclusion: Due to the multiplicity of the sub-system, none of the 12-provincial social
security managing directorates as DMUs were efficient (one efficiency score), but among
313 branches, three branches were efficient. The final results of the implementation of the
uncertain model proved the assumptions of the definitive model.


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