# Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis

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### "Some Models for Estimating Technica..." refers background or methods in this paper

...Once again, however, we emphasize that we are proceeding directly from observational data in our fine tuning of the CCR developments found in Charnes, Cooper and Rhodes (1978a). Mix and scale variations are likely to occur together in such observational data and so safeguards are required, as in our minimum extrapolation postulate, insofar as we cannot effect a separation of scale variations as in the formal theory of economics....

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...The linear programming problems in (14) and (15) are employed to estimate the overall technical and scale efficiencies of a DMU. The linear programming formulations in (19A) and (20A) take into account the possibility that the average productivity at the most productive scale size may not be attainable for other scale sizes at which a particular DMU may be operating. These formulations estimate the pure technical efficiency of a DMU at the given scale of operation. The estimation of most productive scale size in DEA is discussed in Banker (1984). Figure 3 illustrates these concepts of technical and scale efficiencies....

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...I This could describe the CCR efficiency measure, except that each ur and vi in U and V is only required to be nonnegative rather than strictly positive. See (1). The positivity requirement would be obtained, however, if we followed the nonArchimedean formulation and development in Charnes, Cooper and Rhodes (1979),13 as we shall do below....

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...REMARK. Fare and Lovell (1978) discuss the relationship between Farrell's efficiency measure and Shephard's distance measure....

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...This results in a characterization of the DMUs associated with P2 and P3 as being "equally inefficient" relative to the DMU associated with PI. This characterization may be satisfactory in some cases. In other cases we may want to "fine tune" the developments in Charnes, Cooper and Rhodes (1978a) so that we can locate differences such as are portrayed in the P2 and P3 situations....

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