By Avcibas, Memon, Sankur, Sayood

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1 . 1 DMU A B C D E F G H Input 2 3 3 4 5 5 6 8 Output 1 3 2 3 4 2 3 5 We can evaluate the efficiency of DMU A, by solving the LP problem below: A > max subject to 6—u 2f = 1 u<2v 2u < 3v An < bv Zu < ^v {A) (C) (E) (G) 3u 3u 2u 5u < < < < 3v 4v 5v Sv (B) (D) (F) (H) where all variables are constrained to be nonnegative. 5). 5. 5, the best possible weights for DMU A, in each of the above constraints. Thus the performance of B is used to characterize A and rates it as inefficient even with the best weights that the data admit for A.

5 0. Region P 1. 17) The objective function u -> max yields the same solutions as 1/u -> min, so the problem is to find the minimum t for which the following line touches the region P : A{vilu)^2{v2lu)^t. 3 we see that t = 1 (and hence u = 1) represents the optimal line for D, showing that D is efficient. It is also easy to see that D is efficient for any weight {vi^ V2) on the fine segment (P25 ^3)- This observation leads to the conclusion that the optimal (t'l, V2) for D is not unique. 3. 1 at the end of this Chapter.

The resulting ratio would then yield an index for evaluating efficiencies. 6. ) This simplifies matters for use, to be sure, but raises a host of other questions such as justifying the 5 to 1 ratio for doctor vs. nurse and/or the 3 to 1 ratio of the weights for inpatients and outpatients. Finally, and even more important, are problems that can arise with the results shown - since it is not clear how much of the efficiency ratings are due to the weights and how much inefficiency is associated with the observations.

### A Progressive Lossless Near-Lossless Image Compression Algorithm by Avcibas, Memon, Sankur, Sayood

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