Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures

Cross-efficiency evaluation, an extension of data envelopment analysis (DEA), can eliminate unrealistic weighing schemes and provide a ranking for decision making units (DMUs). In the literature, the determination of input and output weights uniquely receives more attentions. However, the problem of choosing the aggressive (minimal) or benevolent (maximal) formulation for decision-making might still remain. In this paper, we develop a procedure to perform cross-efficiency evaluation without the need to make any specific choice of DEA weights. The proposed procedure takes into account the aggressive and benevolent formulations at the same time, and the choice of DEA weights can then be avoided. Consequently, a number of cross-efficiency intervals is obtained for each DMU. The entropy, which is based on information theory, is an effective tool to measure the uncertainty. We then utilize the entropy to construct a numerical index for DMUs with cross-efficiency intervals. A mathematical program is proposed to find the optimal entropy values of DMUs for comparison. With the derived entropy value, we can rank DMUs accordingly. Two examples are illustrated to show the effectiveness of the idea proposed in this paper.