DEA cross‐efficiency ranking method considering satisfaction and consensus degree

Abstract

Cross-efficiency evaluation in data envelopment analysis is an effective way to rank decision-making units (DMUs). However, different cross-efficiency evaluation models derived from different perspectives generate different cross-efficiency rankings. The information resulting from the various perspectives may be valuable and should not be ignored. In this paper, we propose an innovative composite method for ranking DMUs by calculating the Shannon entropy of the obtained cross-efficiency scores derived from the perspectives of satisfaction and consensus. Also, we adopt grey incidence analysis to compare the rankings of different cross-efficiency models. The calculation procedure using Shannon entropy and grey incidence analysis is illustrated on an example to generate the composite ranking result and compare it to other cross-efficiency model rankings. The cross-efficiency ranking using both satisfaction and consensus information provides a new comprehensive perspective in group evaluation. A practical example is used to show that the crossefficiency results obtained from the composite perspective of satisfaction and consensus should be widely accepted in practical decision-making.

The role of social start-ups in entrepreneurial behaviour: the search for efficiency

“…It is developed as an extension of DEA. Its use is suitable for the construction of synthetic indices (Martí and Puertas, 2020; Wu et al. , 2021; Guaita-Martínez et al.…”

An extended cross-efficiency evaluation method based on information entropy with an application to the urban logistics industry

“…Therefore, research on the CEE and SEE models has been constantly updated since their advent. Because the CEE model has no limit on the quantitative relationship between DMUs and indicators (Sun et al, 2020), it has been studied extensively in theory and application (Wu et al, 2021a(Wu et al, , 2021b.…”

“…The organic combination of self-and JM2 18,2 peer-evaluation mechanisms can reduce the subjectivity of the efficiency results and provide more valuable references for policymakers and decisionmakers (DMs). Of course, the traditional CEE method has its shortcomings, one of which is that its final result may be not unique due to the non-uniqueness of evaluating DMUs' input and output weights, causing ambiguity (Wu et al, 2021a(Wu et al, , 2021b. In order to overcome this problem, Doyle and Green (1994) proposed to build one secondary goal (SG) model, which could not only obtain unique final efficiency for all DMUs but also contribute to the theoretical research of the DEA method.…”

“…For example, Bian and Yang (2010) used information entropy to integrate efficiency values obtained from several proposed non-radial resource and environment DEA models for evaluating and ranking 30 provinces in China. The existing articles that obtain the CE values through the information entropy method are Nissi and Sarra (2018), Adhikari et al (2018), Liu et al (2021c) and Wu et al (2021aWu et al ( , 2021b. Specifically, the first computed the weights for DEA models according to the efficiency values obtained by them and then calculated the product sum of the weight and the efficiency value to obtain the CE.…”

“…The combination of self- and peer-evaluation mechanisms in the CEE method can distinguish all DMUs adequately, avoiding the overestimation result brought by self-evaluation. Besides, it can create a fair evaluation atmosphere (Wu et al , 2021a). In CEE method, a DMU is indeed the most efficient only if all DMUs evaluate it as the most efficient.…”