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This study pursues to compare the two types of cost efficiency model based on DEA. Two types of DEA are derived by the two different approaches by Farrell_Debreu and Tone. Based on two concepts, Two different DEA model are derived. The characteristics and difference of two are looked up. Based on the simple numerical case, The efficient rates, the rankings, the reference sets are different. The model based on Tone`s approach shows the more cheap attainable target cost level. DEA model set by Tone is superior in measuring cost efficiency, but Farrell_Debreu type DEA model is better to explain data in technical efficiency. So, it is required to use the results of DEA more carefully.

A Comparative Case Study of Cost Efficiency DEA Model based on the Farrell_Debreu's and Tone's approach