Cross Efficiency Evaluation Based On The Importance Of Output

DEA cross efficiency is very effective in the judgment and ranking of decision-making units(DMUs), and plays a significant role to evaluate the efficiency of multi-input and multi-output pattern. However, the traditional DEA cross efficiency method most studies the desirable output problems(only the products that bring the companies economic benefits are considered). In actual situations, the undesirable output problems, such as the pollution, defective goods and the occupational injury, are more common. Therefore research of undesirable output is becoming increasingly important.The purpose of this study is to introduce the evaluation with undesirable output into cross DEA Efficiency. In consideration with undesirable output study, there will be the following questions:(1) the profit brought by desirable output and the pollution control expenses brought by undesirable output are different, namely there are difference of output significance;(2) the desirable and undesirable outputs of DMUs have their own production efficiency and the production frontiers of desirable and undesirable outputs are different;(3) there are interaction between desirable output and undesirable output.After full consideration and detailed analysis, this paper proposes the concepts of significance coefficient and part efficiency to quantify these problems. By combining the traditional DEA cross efficiency model of desirable output with undesirable output, the paper establishes a new model, the importance of desirable output and undesirable output and mutual influenced between them has been considered. The experimental result shows that the efficiency of DMUs are affected by three factors: input, desirable output and undesirable output. Input links the desirable output and the undesirable output while the desirable output and the undesirable output directly affect the ranks of DMUs. The final result of the experiment meets the expected requirements, so it is possible to use this approach to evaluate such issues.