Fuzzy C-means based data envelopment analysis for mitigating the impact of units’ heterogeneity

Data envelopment analysis (DEA) is a non-parametric model that is developed for evaluating the relative efficiency of a set of homogeneous decision-making units that each unit transforms multiple inputs into multiple outputs. However, usually the decision-making units are not completely similar. The purpose of this paper is to propose an algorithm for DEA applications when considered DMUs are non-homogeneous.

To reach this aim, an algorithm is designed to mitigate the impact of heterogeneity on efficiency evaluation. Using fuzzy C-means algorithm, a fuzzy clustering is obtained for DMUs based on their inputs and outputs. Then, the fuzzy C-means based DEA approach is used for finding the efficiency of DMUs in different clusters. Finally, the different efficiencies of each DMU are aggregated based on the membership values of DMUs in clusters.

Heterogeneity causes some positive impact on some DMUs while it has negative impact on other ones. The proposed method mitigates this undesirable impact and a different distribution of efficiency score is obtained that neglects this unintended impacts.

The proposed method can be applied in DEA applications with a large number of DMUs in different situations, where some of them enjoyed the good environmental conditions, while others suffered from bad conditions. Therefore, a better assessment of real performance can be obtained.

The paper proposed a hybrid algorithm combination of fuzzy C-means clustering method with classic DEA models for the first time.