An integrated slacks-based super-efficiency measure in the presence of nonpositive data

Abstract

The slacks-based measure (SBM) and super-efficiency SBM (S-SBM) models are inoperable when inputs or outputs have zero or negative data. In this paper, a mixed-binary linear program integrating SBM and S-SBM is developed to handle zero and negative input and output values. The model is units invariant, unlike Tone and Chang et al. (2020)’s BP-SBM model. The model also addresses the limitations of modified SBM (MSBM) (Sharp et al., 2007) by dropping the requirement for minimum inputs and maximum outputs and avoids the sensitivity of the models using a range adjusted measure (RAM) to the range of the maximum and minimum values. Three sets of data are used to test the model and compare it with BP-SBM and the model proposed by Lin et al. (2019). The first data set is a simple illustration to simplify understanding of the data translation and application of the three models. The second data set comprises 30 Taiwanese electrical machinery listed firms and contains negative outputs. The third data set is the energy activities of 30 Chinese provinces with two bad outputs that are treated as negative data. The kernel density estimations show the distributions of efficiency scores as well as the Simar–Zelenyuk adapted Li tests for the model comparisons of the bootstrapped distributions for the latter two data sets. The results of these data sets validate the usefulness and practicability of our proposed approach.