A modified slacks-based super-efficiency measure in the presence of negative data. (September 2019) - Lin, Ruiyue; Yang, Wei; Huang, Huiling
Highlights: We propose a slacks-based super-efficiency measure which is feasible and can deal with negative data. Our approach yields a strongly Pareto efficient projection for each DMU. Our approach identifies the saving or excess of each input and the surplus or shortfall of each output by slacks. Our approach is monotonous, units-invariant and translation-invariant for both inputs and outputs. Our approach overcomes the limitations of radial super-efficiency models and extends Super SBM to the situation with negative data. Abstract: As a non-radial super-efficiency model, Super slacks-based measure (SBM) can rank efficient decision making units (DMUs) while it cannot deal with negative data. This paper proposes an improved Super SBM model and the corresponding improved SBM model under the condition of variable returns to scale, both of which are feasible and allow input-output variables to take negative values. Based on them, a two-stage approach is provided, which has the following advantages in the presence of negative data: compared with radial super-efficiency models capable of dealing with negative data, it can judge the efficiency of DMUs just by the resulting super-efficiency score; it yields a strongly Pareto efficient projection for each DMU; for inefficient DMUs, it provides better target; for efficient DMUs with the super-efficiency score greater than one, it reduces or expands at least one of outputs or inputs to reach the super-efficiency frontier; it is monotonous, units-invariant and translation invariant for both inputs and outputs. The proposed method successfully overcomes the drawbacks of the current super-efficiency models capable of handling negative data and extends Super SBM to the situation where negative data exist.