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The conventional data envelopment analysis was first introduced in 1978 by Charnes, Cooper, and Rhodes (1978), in evaluating the efficiency of a set of peer organizations called decision-making units (DMUs) that consume multiple inputs to generate various outputs. DEA methods have been widely accepted as an effective technique in identifying and separating efficient DMUs from inefficient ones. But the conventional DEA intrinsically aims to identify efficient DMUs and the efficient frontier, so the use of DEA is not enough for discriminating between efficient DMUs. In terms of ranking DMUs, many authors show that conventional DEA is not an appropriate method in many situations. Consequently, the researchers and practitioners have faced a question, “Which DEA method should we use for ranking DMUs effectively and consistently?” Publication and research work have grown substantially, resulting in significant advancements in its methodologies, models, and real-world applications (see Cook and Seiford, 2009; Chen et al., 2019).
Charnes et al. (1978) demonstrate how to change a fractional linear measure of efficiency into a linear programming (LP) format to measure efficiency scores (ESs) of DMUs. In the conventional DEA (C-DEA), a relative efficiency is defined as the ratio of the sum of weighted outputs to the sum of weighted inputs. The C-DEA solves an LP formulation for each DMU to be rated, and the weights assigned to each linear aggregation are obtained by solving the corresponding LP. The DMUs in the C-DEA to be assessed should be relatively homogeneous. As the whole technique is based on a comparison of each DMU with all the remaining ones, a considerable large set of DMUs is necessary for the assessment to be meaningful (Ramanathan, 2006). The C-DEA eventually determines which of the DMUs make efficient use of their inputs and produce most outputs and which DMUs do not. The significant function that the conventional DEA model can do is to separate efficient DMUs from inefficient DMUs. For the inefficient DMUs, the analysis can quantify what levels of improved performance should be attainable. Also, the study indicates where an inefficient DMU might look for benchmarking help as it searches for ways to improve. Recently, Cao et al. (2020) introduce the concept of the anti-strike ability of a single DMU and provide a new ranking method of DMUs. Shahghobadi (2020) presents a method for performance assessment of units so that a large number of units are not evaluated as efficient, but there is at least one efficient unit. Toloo et al. (2020) contend that the number of performance factors (inputs and outputs) plays a decisive role when applying DEA to real-world applications.
The C-DEA produces a single, complete measure of performance for each DMU. The highest efficiency score among all the DMUs would identify the most efficient DMU(s), and every other DMU would be evaluated by comparing its ratio to the DMU with the highest one. A significant weakness of the C-DEA-based assessment comes out because a considerable number of DMUs out of the set of DMUs to be rated can be classified as efficient, and all efficient DMUs are considered to be equal. The nature of the self-evaluation of C-DEA allows each DMU to be evaluated with its most favorable weights. Thus, to maximize the self-efficiency, the conventional DEA model intentionally ignores unfavorable inputs/outputs. The DEA-based methods are developed to measure the relative efficiency of DMUs with multiple inputs and outputs. If DMUs have a single output and a single input, any DEA ranking method is necessary. As the number of inputs and/or outputs of DMUs to be rated increases, the weaknesses of DEA-related methods become more apparent since the DEA method can overlook the weights assigned to unfavorable inputs or outputs