Data Envelopment Analysis (DEA) is a non-parametric method that doesn't require any prior information to measure the relative performance of decision-making units (DMUs). However, standard DEA models use different weight vectors for evaluating DMUs, so comparing and ranking DMUs on the same basis are impossible. In order to evaluate and rank DMUs on a common basis, the common weights DEA model was proposed, and many studies on the common weights of DEA have been conducted so far. In most studies, they usually determined the weights to minimize the difference between ideal values obtained from different weight vectors and real values obtained from common weights. The problem of these methods is that the standard of evaluation deflects because a few specific DMUs play a decisive role in minimizing the difference in common weights determination.
This paper proposed the clustering method based on the property of production and suggested the common weight DEA model using the cluster analysis. First of all, it suggested an equation model finding the unique global reference set of each DMU, then clustered DMUs by the information of global reference set. From the given clustering results, the relative importance of each DMU is calculated and at the final stage, the common weights are calculated from a new model taking into account this relative importance.
The clustering method and the common weights DEA model were applied to and analyzed with numerical examples of previous studies. Through the comparison between the results of both the proposed DEA model and the previous model, the validity of the proposed model was discussed.
The proposed common weights DEA model based on cluster analysis will be effective in evaluating and ranking the efficiency of DMUs, and this does not require any extra information. And, the clustering method proposed can be introduced to several application fields, such as finding benchmarks for each DMU, detection of isolated DMUs, and so on. We can consider the combination of the clustering algorithm and other common weights determination algorithms.
The results of the above study were published under the title of "A new common weights DEA model based on cluster analysis" (https://doi.org/10.1007/s12351-024-00838-5) in "Operational Research".
