Increasing the discriminatory power of DEA in the presence of the sample heterogeneity with cluster analysis and decision trees

Data envelopment analysis (DEA) is a widely used non-parametric data analytic tool discriminatory power of which is dependent on the homogeneity of the domain of the sample. In many real-life cases, however, the sample of the decision making units (DMU) could consist of two or more naturally occurring subsets, thus exhibiting clear signs of heterogeneity. In such situations, the discriminatory power of DEA is limited, for the nature of the relative efficiency of a DMU is likely to be influenced by its membership in a particular subset of the sample. In this study, we propose a three-step methodology allowing for increasing the discriminatory power of DEA in the presence of the heterogeneity of the sample. In the first phase, we use cluster analysis (CA) in order to test for the presence of the naturally occurring subsets in the sample. In the second phase DEA is used to calculate the relative efficiencies of the DMUs, as well as averaged relative efficiencies of each subset identified in the previous phase. Finally, we utilize decision tree (DT) induction in order to inquire into the subset-specific nature of the relative efficiencies of the DMUs in the sample. Illustrative example is provided.