Fig. 1

Two efficiency frontiers for measuring unified efficiency. (a) The direction of NW (North-West) indicates a projection of K toward an efficiency frontier (A–B–C) that is incorporated into the conventional framework of DEA. (b) DEA environmental assessment incorporates the projection of SW (South–West) from K toward an efficiency frontier (G–H–D) under natural disposability and the projection of SE (South–East) from K toward an efficiency frontier (D–E–F) under managerial disposability. The projection of NW serves as a basis for the performance assessment of conventional DEA. The projection of NE (North-East) toward an efficient frontier (C–I) has been excluded from the conventional use. The proposed environmental assessment incorporates the projection toward NE along with an increase in components of an input vector. (c) NW + SW: natural disposability and NE + SE: managerial disposability. Both are incorporated in the proposed DEA environmental assessment. The two disposability concepts make a use of DEA different from the conventional use (by only NW direction for operational performance enhancement)