A selection process of input and output factors using partial efficiency in data envelopment analysis

The improper use of input and output factors in DEA has a critical and negative impact on the efficiency measurement and the discernment of decision making units (DMUs): hence the proper selection process of the factors should precede the actual applications of DEA. In this paper, we propose a new approach to selecting proper factors based on Tofallis' partial efficiency evaluation method. With the approach, the factors are clustered by measuring their respective partial efficiencies and analyzing the rank correlations of them. The method and procedure we propose in this paper are then applied to measure the efficiencies of the public libraries in Seoul District area, and the results show that the proposed approach can provide meaningful information to improve discernment of the DMUs while using fewer input factors (and less information). The proposed method can be effectively used in the situation where the number of the DMUs to be considered is relatively small compared to the number of available input and output factors, which usually lessens the power to identify the inefficient units in DEA.