Abstract
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.
Highlights
Data Envelopment Analysis (DEA)—originally developed by Charnes, Cooper, and Rhodes (CCR) [1]—is an effective method for evaluating the efficiencies of decision making units (DMUs) with the same inputs and outputs
The advantages of the approach proposed in this paper are that it is always feasible for calculating cross-efficiency, the multiple optimum solutions for DEA weights can be ignored, and the uncertainty of cross-efficiency intervals are considered in discrimination of DMUs
Weights that result in different cross-efficiency scores, and to different ranking results of
Summary
Data Envelopment Analysis (DEA)—originally developed by Charnes, Cooper, and Rhodes (CCR) [1]—is an effective method for evaluating the efficiencies of decision making units (DMUs) with the same inputs and outputs. Existing order relations for interval numbers are used to identify dominance relations among DMUs and a ranking result of DMUs is derived These approaches perform the cross-efficiency evaluation without choosing the DEA weights. Use the DEA entropy model to calculate the intervals of all cross-efficiency values with imprecise inputs and outputs, and all DMUs are evaluated and ranked based upon the distance to ideal positive cross efficiency. The current approaches for cross-efficiency evaluation are often averaging the entries of the cross-efficiency matrix column-wise for comparison of DEA efficient units, or concentrate on how to determine DEA weights uniquely In these cases, the problem of choosing the aggressive (minimal) or benevolent (maximal) formulation for decision-making might still remain.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
