The degree of robustness based on hierarchical DEA

Abstract

Data envelopment analysis (DEA) is a method that is used to evaluate the efficiency values of decision-making units (DMUs), and several methods to evaluate the robustness of efficiency against the changes in specific input or output items has been developed. Although, it is difficult to figure out how robust efficiency values of DMUs are quantitatively considering all input and output items. To overcome this problem, we propose a degree of robustness, τ, based on a hierarchical DEA model. The proposed degree is formulated based on the efficiency value of each combination of input and output items, the number of input and output items of each combination, and parameter p. This parameter p represents the degree of importance on non-characteristic nodes relative to that of the characteristic nodes. The robustness of efficiency considering all input and output items can be evaluated by the proposed degree.