Abstract
The original radial VRS super-efficiency model in DEA excludes the DMU under evaluation from the reference set. However, it must lead to the problem of infeasibility specifically when the DMU under consideration is at the extremity of the frontier. In this paper, a modified nonradial VRS super-efficiency model is established. The super-efficiency model in the presence of nonradial measurement still maintains some good properties, and the original radial VRS super-efficiency model infeasibility can also be detected through it. Our model with nonradial measurement can help decision makers allocate input resources and arrange production activities because it finds an efficient benchmark DMU, which is different from the reference DMU under radial measurement.
Highlights
Data envelopment analysis (DEA), first introduced by Charnes et al [1] and extended by Banker et al [2], is an effective nonparametric technique for measuring the relative efficiency of peer decision-making units (DMUs) with multiple inputs and outputs. eir initial models based upon the constant returns to scale (CRS) and variable returns to scale (VRS) are commonly referred to as the CCR model and the BCC model, respectively. ey compute scalar efficiency scores with a range of zero to unity which indicate how efficient each DMU has performed as compared to other DMUs in converting inputs to outputs and determine efficient level or position for each DMU under evaluation among all DMUs
To break the tie of efficient DMUs and further enhance the discrimination power of DEA, Andersen and Petersen [11] proposed a new model according to the CCR model, which is called super-efficiency model where the DMU under evaluation is excluded from the reference set
Under the condition of VRS, the super-efficiency model may be infeasible when some efficient DMUs are under evaluation, while the super-efficiency model under CRS does not suffer the problem of infeasibility
Summary
Data envelopment analysis (DEA), first introduced by Charnes et al [1] and extended by Banker et al [2], is an effective nonparametric technique for measuring the relative efficiency of peer decision-making units (DMUs) with multiple inputs and outputs. eir initial models based upon the constant returns to scale (CRS) and variable returns to scale (VRS) are commonly referred to as the CCR model and the BCC model, respectively. ey compute scalar efficiency scores with a range of zero to unity which indicate how efficient each DMU has performed as compared to other DMUs in converting inputs to outputs and determine efficient level or position for each DMU under evaluation among all DMUs. They proposed a modified VRS super-efficiency model to yield a super-efficiency score that characterizes both the radial efficiency and input saving/output surplus. Lee et al [21] first point out that zero output data will not lead to infeasibility of the output-oriented super-efficiency models developed in the studies of Cook et al [16], Lee et al [17], and Chen and Liang [18].
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