Environmental Efficiency Evaluation of the Xiangjiang River Basin: A DEA Cross-Efficiency Approach With Social Network

Cross-efficiency in data envelopment analysis is widely used for performance evaluation of decision-making units (DMUs), but it neglects the reference relationship between each pair of DMUs. In order to address the problem, this paper introduces the concept of social network to clearly describe the reference relationship between DMUs and then a fully ranking can be made. A novel cross-efficiency approach is developed by integrating social network analysis in this study. Firstly, we propose a pairwise comparison model based on cross-efficiency evaluation to identify the superiority and inferiority between any pair of DMUs. Secondly, based on pairwise comparison, we build a non-weighted directed social network where a direction generates from one DMU to another DMU if the former one references the latter one. Each edge in the unweighted social network captures the learning procedure from worse-performance DMU to better-performance DMU. Comparing with traditional cross-efficiency approaches, our proposed approach considers the reference relationship among DMUs rather than only cross-efficiency scores. Thus, the importance of each DMU in the network can be measured by its centrality. Finally, the proposed approach is employed to environmental efficiency evaluation of the cities along the Xiangjiang River Basin, then, some beneficial universal policies have been summarized.