Classifying flexible measures in two-stage network DEA and DEA-RA using novel slacks-based models

In conventional DEA models it has been assumed that each measure status is considered input or output. However, a performance measure in some cases can have input role for some DMUs and output role for others and is known as flexible measure. In this paper new slacks-based FNSBM models are proposed in general two-stage network DEA to determine the relative efficiency of units and the role of flexible measures. Then new radial FNDEA-R models and new slacks-based FNSBM-DEA-R models are developed in the presence of flexible measures based on the ratio of input components to output components or vice versa in the input and output orientation under constant returns to scale in general two-stage network. In our proposed models, flexible measures are determined as input or output to improve performance to maximize the relative efficiency of the DMU under evaluation. The FNDEA-R and FNSBM-DEA-R models versus FNSBM models prevent efficiency underestimation and pseudo inefficiency issues. The status of one flexible measure in the input-oriented and output-oriented FNDEA-R and FNSBM-DEA-R models may have different conclusions. The radial FNDEA and FNDEA-R models have unitsinvariant and the objective function of the FNSBM and FNSBM-DEA-R models are invariant with respect to the units of data. A numerical example is used to illustrate the procedures.