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《Mathematics in Practice and Theory》 2019-15
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A Note on the Scale Efficiency Index Method in Data Envelopment Analysis

QUAN Shan-shan;HAN Wei-yi;School of Economic and Management, Harbin Institute of Technology;  
The original scale efficiency index method is introduced in order to analyze returns to scale(RTS).Since this method is based on input oriented models,it is contrary to the definition of RTS.The analysis of RTS should be analyzed based on output oriented models.And it is very necessary to convert the method based on input-oriented models to the one based on output-oriented models.Firstly,we proved that the rules of the original method are also applicable to the method based on the output-oriented models in theory no matter what two methods are different essentially.Secondly,it is theoretically proved that the input-oriented BCC model is not equivalent to the output-oriented BCC model,which means that two methods are not equivalent.Thirdly,an example is given to show that two methods will lead to different computational results,and the fundamental reasons are analyzed in theory.The above conclusion shows that two methods are different in two aspects:projection method and computational result.Therefore,the analysis of returns to scale should be based on output oriented models.
【Fund】: 国家自然科学基金(51878026);; 中央高校基本科研业务费专项资金(HIT.HSS.201406)
【CateGory Index】: F224
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