Two-stage data envelopment analysis: An enhanced Russell measure model

Data envelopment analysis (DEA) is a non-parametric method in Operations Research and Economics for measuring the relative efficiency of peer decision making units (DMUs) that have multiple inputs and outputs. In many situations, DMUs can have a two-stage structure where the first stage uses inputs to produce outputs (called intermediate measures) that then become the inputs to the second stage. In recent studies on two-stage production processes, authors used the radial DEA models to measure the efficiency of the whole process and the efficiencies of individual two stages. In these models, due to the existence of intermediate measures, the usual procedure of adjusting the inputs or outputs by the efficiency scores for an inefficient DMU does not necessarily yield an efficient DMU. In this paper, we introduce a non-radial enhanced Russell measure (ERM) model on two-stage production processes by taking into account a relationship of the two stages. Unlike the radial two-stage DEA models, the new approach enables us to determine the efficient projections for inefficient DMUs within the framework of two-stage-DEA. An example of the non-life insurance industry in Taiwan is applied to compare the new measure to a recent two-stage DEA model.