Efficiency analysis in multi-stage network DEA-R models

In many organizations and financial institutions, it is in many cases more cost and time efficient to access ratio data. Therefore, it is of great importance to evaluate the performance of decision-making units (DMUs) which only have access to ratios of inputs to outputs or vice versa (for instance, ratio of employees to students, ratio of assets to liabilities and ratio of doctors to patients). In this paper, we will propose two-stage network DEA-R model with multi-objective linear programming (MOLP) structures. Then, introducing a production possibility set (PPS) in each network stage, we will compare efficiency values in network DEA and DEA-R. In the end, through an applied study on 22 medical centers which treat special patients in three stages, we will suggest an output-oriented multi-stage network DEA-R model under assumption of CRS technology. The medical centers are evaluated in all three stages based on overall network efficiency. The results of the analysis are presented and a future research in this field is discussed in the final section of the paper.