By Abraham Charnes, William W. Cooper, Arie Y. Lewin, Lawrence M. Seiford
This booklet represents a milestone within the development of information Envelop ment research (DEA). it's the first reference textual content which incorporates a complete overview and comparative dialogue of the elemental DEA types. the improvement is anchored in a unified mathematical and graphical remedy and contains crucial modeling ex tensions. additionally, this can be the 1st e-book that addresses the particular technique of undertaking DEA analyses together with combining DEA and 1 parametric suggestions. The booklet has 3 different exact good points. It strains the functions pushed evolution and diffusion of DEA versions and extensions throughout disciplinary barriers. It contains a complete bibliography to function a resource of references in addition to a platform for extra improve ments. And, ultimately, the ability of DEA research is verified via fifteen novel functions which should still function an notion for destiny functions and extensions of the technique. The foundation of this booklet was once a convention on New makes use of of DEA in 2 administration and Public coverage which was once held on the IC Institute of the collage of Texas at Austin on September 27-29, 1989. The convention was once made attainable via NSF provide #SES-8722504 (A. Charnes and a couple of W. W. Cooper, co-PIs) and the aid of the IC Institute.
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Extra resources for Data Envelopment Analysis: Theory, Methodology, and Applications
As can be readily verified from the formulation given below, the Units Invariant Multiplicative model of Charnes, Cooper, Seiford, and Stutz (1983) results from the application of the Additive model to the logarithms of the original data values. Hence all interpretations and comments from the previous section again apply, but now in the transformed space (Log(X), Log(Y». t. v » ____ s+ >0> = Log(Yo) Log(X) ,I. + s- = Log(Xo) Log(Y) ,I. - ____ 1,1. t. = =- 310 IlTLog(Yo) - vTLog(Xo) + ---- ---- Uo IlTLog(Y) - vTLog(X) + uol :s;; 0 _fJT ~-1 -vT:s;; 110 free -I 30 CONCEPTS, MODELS, AND COMPUTATION However, two additional observations are worthwhile.
In this interpretation, Vo plays the role of a y intercept. From table 2-3, the closest supporting hyperplane for DMU5 has the equation jy - ~x + 1 = 0, which forms the facet of the envelopment surface joining DMU2 and DMU3 . , ¢*Yo. As illustrated in figure 2-6, DMU5 is projected onto the point (5, 6j). Solving BCCD-O for the other DMUs yields the envelopment surface 'in figure2-6, where the remaining inefficient points are projected onto those segments of supporting hyperplanes that envelop the convex hull.
Introduction Data Envelopment Analysis (DEA) is a body of concepts and methodologies that have now been incorporated in a collection of models with accompanying interpretive possibilities as follows: the CCR ratio model (1978) (i) yields an objective evaluation of overall efficiency and (ii) identifies the sources and estimates the amounts of the thusidentified inefficiencies; 2. the BCC model (1984) distinguishes between technical and scale inefficiencies by (i) estimating pure technical efficiency at the given scale of operation and (ii) identifying whether increasing decreasing, or constant returns to scale possibilities are present for further exploitation; 3.
Data Envelopment Analysis: Theory, Methodology, and Applications by Abraham Charnes, William W. Cooper, Arie Y. Lewin, Lawrence M. Seiford