Ranking decision making units with the integration of the multi-dimensional scaling algorithm into PCA-DEA

Abstract

Data envelopment analysis (DEA) has being used commonly in a variety of fields since it was developed, and its development continues through interacting with other techniques. Since the method can be applied to multiple inputs and outputs, it interacts with multivariate statistical methods. Principle component analysis (PCA) is a multivariate analysis method used to destroy the independence structure between variables or to reduce the number of dimensions. In literature, PCA and DEA are compared for ranking decision making units. Then, PCA-DEA procedure was modified. In this study, the multidimensional scaling (MDS) algorithm, which is one of the commonly used methods in multivariate statistics, is integrated to the PCA-DEA method to rank the decision making units (DMUs). According to Spearman rank correlation, the proposed method gives a higher correlation with super efficiency compared to other methods.

Keywords

• Data envelopment analysis,ranking problem,multivariate statistics,principle component analysis,multi-dimensional scaling

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