دانلود رایگان مقاله انگلیسی رتبه بندی DMU ها با استفاده از سطوح بالا و پایین راندمان نرمال در تحلیل پوشش داده ها - الزویر 2018

ABSTRACT

In data envelopment analysis, the existing methods for measuring the relative efficiencies of decision making units (DMUs) are to compare DMUs relative to the best or the worst of all DMUs. In this paper, we consider both the best DMU and the worst DMU as the reference DMUs and propose the normalized efficiency. Further, from the optimistic and pessimistic viewpoints, we construct two DEA models to obtain the upper and lower bounds of the normalized efficiency and then achieve an interval efficiency evaluation to rank all DMUs completely. Finally, two examples are presented to illustrate the performance of the interval efficiency evaluation.

Conclusion

The CCR model measures the best relative efficiency of a DMU by maximizing the ratio of the weighted outputs to the weighted inputs under the constraint that the maximum ratio of all DMUs is 1. Hence, all DMUs are compared relative to the best DMU. Considering that a superior object must be far from the worst object as well as being close to the best, we evaluate DMUs relative to the worst DMU as well as the best DMU. Then, we propose the normalized efficiency and achieve the best normalized efficiency and the worst normalized efficiency respectively. Further, we build the interval efficiency evaluation and rank all DMUs completely based on the upper and lower bounds of the normalized efficiency. Compared with the traditional DEA methods, our evaluation method has some attractive advantages. First of all, for the given input and output weights, the normalized efficiency is obtained by normalizing the output-input ratio of a DMU, and it measures the position of a DMU in the interval built by the best DMU and the worst DMU. Hence, it is fairer for all DMUs to compare the normalized efficiencies. Second, from the optimistic viewpoint and the pessimistic viewpoint, we achieve the upper and lower bounds of the normalized efficiency respectively. It is more comprehensive to evaluate DMUs by considering the best normalized efficiency and the worst normalized efficiency simultaneously. Last but not least, based on the interval efficiency, we can rank all DMUs with the assessor’s given level of optimism. Although the assessor’s level of optimism could affect the ranking of all DMUs, yet there exists an interval of the parameter α such that the ranking is stable.