Estimating the directional scale elasticity of two-stage processes in the presence of undesirable outputs

Due to the complexity of the processes, analyzing the performance of the systems and examining the change in the scale of operations to improve productivity is a significant aspect. Therefore, in this research, a two-stage directional network data envelopment analysis approach is proposed to estimate the overall efficiency and the performance of each stage of two-stage processes, while undesirable outputs are produced in addition to desirable outputs. The proposed technology is based on the properties of the weak disposability of undesirable outputs and variable returns to scale. In addition, after presenting the response function, methods are proposed to calculate the right and left scale elasticities of overall efficient two-stage processes. In order to investigate the validity of the proposed method, a data set from 78 branches of the Iranian bank is used and their efficiency and scale elasticity are examined. The results show that the introduced method is useful and widely applicable to analyze the performance and scale of two-stage network systems in the presence of undesirable outputs.