DEA cross-efficiency evaluation considering undesirable output and ranking priority: a case study of eco-efficiency analysis of coal-fired power plants

Data envelopment analysis cross-efficiency evaluation has been widely accepted as a useful tool for performance evaluation and ranking of decision making units. However, the non-uniqueness of optimal weights is a problem that has reduced the usefulness of this powerful method. In addition, current studies generally have not considered the situation in which undesirable outputs appear in the data envelopment analysis cross-efficiency evaluation. To solve these problems, firstly, we present an equitable model for efficiency evaluation of decision-making units with undesirable outputs and introduce a technique for cross-efficiency evaluation considering undesirable outputs. Then, a ranking priority model is proposed considering the decision making units' intentions of pursuing the best ranking positions. In addition, an aggressive model is given to guarantee the uniqueness of the optimal solution. The proposed approach can not only solve the problem of non-uniqueness of optimal weights in data envelopment analysis cross-efficiency evaluation but also considers undesirable outputs and ranking preferences of the decision-making units. Finally, the proposed approach is applied for eco-efficiency analysis of coal-fired power plants in a big data environment, and the results show that most coal-fired power plants in China have not performed well.