Data Envelopment Analysis for Evaluating Structure of Input and Output Items

SUMMARY Data envelopment analysis (DEA) is an evaluation method that allows analysts to evaluate the efficiencies of decision making units (DMUs) with multiple input and output items. When DMUs are evaluated only in terms of efficiency, analysts cannot evaluate how efficient combinations of input and output items are. In order to evaluate the efficiencies of such combinations, we propose a method that is based on DEA in order to evaluate the structure of the efficiency for input and output items based on the conventional hierarchical approach. The proposed method is composed of four steps. In Step 1, dividing the data set, we construct a hierarchical structure. In Step 2, efficiency values are calculated for each divided data set. In Step 3, nodes are integrated, and they are visualized in Step 4. Based on the visualization, analysts can evaluate the characteristics of a DMU structurally and find the second most efficient items and key items that improve efficiency when they are added to other items. A numerical example with a data set from the 2010 Quality of Life Index (35 DMUs, one input and five output items) is used to illustrate the features of the proposed method.