Dea based multiple criteria evaluation and the multivariate statistics analysis for ranking units

Data envelopment analysis (DEA) method was originally designed to evaluate the efficiency of decision making units (DMUs), and it classifies the units merely into two dichotomic groups: efficient and inefficient ones. The purpose of the paper is to combine the multiple criteria evaluation with DEA and to fully rank the evaluation units from the most efficient one to the least efficient one as classified by DEA. In this paper we develop two new multivariate statistics analysis DEA based models for multiple criteria evaluation. Both of the methods could solve multiple criteria evaluation problem, which includes three types of index (cost, benefit, and fixed), and provide a full ranking of the efficient and inefficient units on the same scale based on the maximal correlation between the linear combinations of inputs and outputs sets where their common weights are computed by maximizing the eigenvalue of a quadruple matrix product; or based on the ratio between the composite output and the composite input where their common weights are computed by a new nonlinear optimization of the goodness of separation between two groups. We also demonstrate this method for evaluation and full ranking through an example.