A study of the input/output variable characteristics in DEA

Since Charnes et al. [“Measuring the efficiency of decision making units,” European Journal of Operational Research, 2, 429–444 (1978)] proposed the concept of data envelopment analysis (DEA), many papers have been published using DEA. However, not many of these papers discuss the fundamental characteristics of input and output variables. For instance, the differing relationships among variables are rarely discussed, nor is there any discussion about the effects on evaluating efficiency when data variables are transformed. If the data used for analysis are misused, the relative efficiency among different departments or organizations can be affected. Thus, a clarification of the relative relationships among different variables is essential in order to achieve accuracy in using DEA. This article, therefore, aims to discuss these issues through a focus on the characteristics of input and output variables used in DEA. By means of mathematical analysis, this research proposes four theorems, together with two examples, to discuss the characteristics of the input and output variable in DEA. We put forward seven findings which demonstrate how DEA can be misunderstood and misused. Through these findings, this study seeks to prevent future research from making mistakes through misuse of data.