A two-stage DEA approach for environmental efficiency measurement.

The slacks-based measure (SBM) model based on the constant returns to scale has achieved some good results in addressing the undesirable outputs, such as waste water and water gas, in measuring environmental efficiency. However, the traditional SBM model cannot deal with the scenario in which desirable outputs are constant. Based on the axiomatic theory of productivity, this paper carries out a systematic research on the SBM model considering undesirable outputs, and further expands the SBM model from the perspective of network analysis. The new model can not only perform efficiency evaluation considering undesirable outputs, but also calculate desirable and undesirable outputs separately. The latter advantage successfully solves the "dependence" problem of outputs, that is, we can not increase the desirable outputs without producing any undesirable outputs. The following illustration shows that the efficiency values obtained by two-stage approach are smaller than those obtained by the traditional SBM model. Our approach provides a more profound analysis on how to improve environmental efficiency of the decision making units.