Slacks-based measures of efficiency and super-efficiency in presence of nonpositive data

SBM and Super-SBM models will not function correctly when zero data or negative data appear in the inputs or outputs. This paper generalizes the SBM model and Super-SBM model so that zero data and negative data can be dealt with. Nonpositive SBM extends SBM, and Nonpositive Super-SBM extends Super-SBM. Both Nonpositive SBM and Nonpositive Super-SBM can deal with negative data and zero data. If the data are positive, Nonpositive SBM and Nonpositive Super-SBM are the same as SBM and Super-SBM, respectively. Nonpositive Super-SBM does not guarantee that the projection is Pareto efficient. A two-stage approach like that in [7] is proposed to resolve this issue. Nonpositive Super-SBM is employed to identify input savings and output surpluses, which are incorporated into the Modified Nonpositive SBM so that the Pareto efficient projection can be determined. The super-efficiency measure proposed by Fang et al. [7] and Lin et al. [11] do not account for the slacks identified at the second stage when the super-efficiency obtained at the first stage is larger than one. We will propose a composite super-efficiency index to resolve such issue. (C) 2021 Elsevier Ltd. All rights reserved.