Classifying flexible and integer data in two-stage network data envelopment analysis

In conventional DEA models, it is supposed real-valued inputs and outputs while every measure must be determined as an input or output. However, in some cases, there are flexible measures which can only take integer values in two-stage network DEA. In all previous researches has not been mentioned the classification flexible measures while some inputs, outputs, and flexible measures can only take integer values in two-stage network DEA. So in this paper, we propose integer-valued FNDEA approach is based on envelopment form of CCR that evaluates the relative efficiency of DMUs and determines the status of flexible measures in the presence of integer data in basic and general two-stage network structures. Our model can determine projection points of inputs, outputs, and flexible measures in the presence of integer data in two-stage network DEA. Numerical examples are used to illustrate the procedure.