Application Expanding Of Data Envelopment Analysis And Relative Research On Principal Component Analysis

Data Envelopment Analysis (DEA), as developed by A.Charnes and W.W.Cooper et al., is an effective optimization method used for measuring the relative efficiency of DMUs. Since C2R model that was the first DEA model was based in 1978,relational academic study is ceaselessly developed and the realm of applications is increasingly widened. The works of this paper are application expanding of DEA and relative research on PCA. The works of this paper are composing of two parts. Firstly,the paper expatiates on basic theories and its basic model –C2R model. By way of an attempt on applications of DEA in the other fields and in chemical technology experiment, the relation between reactant and product just as input and output in economics, based on this, the paper applies DEA for evaluating the method of orthogonal experiment into chemical technology experiment design in order to find out feasible and operational conditions of the experiment. Analysis of the example shows that DEA is an efficient method to evaluate chemical technology experiment design, and its computation is brief and easy. DEA is a beneficial supplement to evaluate orthogonal experiment. Moreover DEA has been widely used not only for evaluateing efficient and noneffective units in the data set, but also for ranking of DMUs with several inputs and several outputs. Recently, Zhu proposed a ranking procedure using the PCA and showed that there is a consistency between the rankings obtained from DEA and PCA for the data set considered in his article by Spearman correlation test. However, it is shown in this article that in certain instances, DEA and PCA may yield inconsistent rankings. On the second place, the other work of this paper is that the PCA ranking approach adopted by Zhu is slightly modified by incorporating aspects, which were not considered in Zhu's model. Numerical results reveal that both approaches produce consistent ranking with DEA when the data set has a small number of efficient units but, when a majority of the DMUs are efficient, only the modified approach shows a consistency with DEA ranking. Therefore, caution should be paid when Zhu's proposal is applied to other data sets and the modified PCA model may offset this disadvantage. Consistent and useful results and information are derived from the comparison of the two methods.