Performance evaluation is important in education for finding the weaknesses of an institution for making necessary improvement. Universities have the missions of exploring and transmitting knowledge, where the former is accomplished via research and the latter via teaching. They play the key role in economic development and the improvement of human life. In response to this, self-evaluation of universities is required by the Ministry of Education of Taiwan, with the aim of enhancing the performance of the universities in Taiwan. National Cheng Kung University is one of the leading universities in Taiwan. To main the  leading position, the academic departments are evaluated to identify their weaknesses and strengths. One major difficulty in inter-department comparison is the diversity of the departments. To take this into account, several performance indicators are considered, including total credit hours, publications, and external grants. Moreover, each department has flexibilities in selecting the indicators to emphasize. The conventional way of applying a set of subjectively pre-determined weights, called a priori weights, is replaced by a posteriori weights reflected from the observed data in an objective manner to calculate the weighted sum for comparison. The empirical study of National Cheng Kung University indicates that, in general, colleges of soft sciences perform better in teaching, while colleges of hard sciences perform better in research.