From the perspective of input and output, the DEA-Tobit method is used to improve the corporate social responsibility input and corporate performance layer by layer, and the maximum likelihood estimation of the optimal solution is verified according to the DEA censored data. The empirical analysis of corporate social responsibility performance of listed manufacturing companies in Shanghai and Shenzhen stock market shows that the overall investment in corporate social responsibility optimization has more obvious fluctuation characteristics than the amount of corporate social responsibility. Meanwhile, corporate philanthropic responsibility input has more obvious fluctuation than corporate ethical responsibility in the improvement of corporate performance.

Starting from the input and output of scientific research in universities, data envelopment analysis (DEA) calculating the relative efficiency of scientific research of universities was used, and the membership function in fuzzy math was used to process DEA results and the evaluation class was determined. By empirically analyzing the research efficiency of 31 domestic universities, the results showed that the scale of the scientific research efficiency of 20 universities was appropriate. And by adjusting the input or output of the other eleven universities, the scientific research efficiency became appropriate. The results of evaluates research efficiency of universities could provide a scientific basis for optimizing scientific research resources.

Because of the "free rider" problem, the corporate lacked of the initiative when they had to undertake the social responsibility. Basing on the corporate theory of the new institutional economics, the reasons were analyzed. Moreover, to solve this problem, an institution to incent corporations to undertake proactively social responsibility was designed and such an institution was proved to realize the Nash equilibrium can be achieved Pareto optimality not only in a deterministic environment but also in the uncertain environment.