By Abraham Charnes, William W. Cooper, Arie Y. Lewin, Lawrence M. Seiford
This ebook represents a milestone within the development of information Envelop ment research (DEA). it's the first reference textual content which incorporates a complete evaluate and comparative dialogue of the elemental DEA versions. the advance is anchored in a unified mathematical and graphical remedy and comprises crucial modeling ex tensions. moreover, this is often the 1st e-book that addresses the particular strategy of accomplishing DEA analyses together with combining DEA and 1 parametric strategies. The publication has 3 different designated beneficial properties. It lines the functions pushed evolution and diffusion of DEA versions and extensions throughout disciplinary barriers. It encompasses a complete bibliography to function a resource of references in addition to a platform for extra strengthen ments. And, ultimately, the facility of DEA research is proven via fifteen novel functions which should still function an suggestion for destiny functions and extensions of the technique. The starting place of this e-book used to be a convention on New makes use of of DEA in 2 administration and Public coverage which used to be held on the IC Institute of the collage of Texas at Austin on September 27-29, 1989. The convention used to be made attainable via NSF furnish #SES-8722504 (A. Charnes and a couple of W. W. Cooper, co-PIs) and the help of the IC Institute.
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Extra info for Data Envelopment Analysis: Theory, Methodology, and Applications
For DMUs , using BCCp-I with (Xo, Yo) = (5, 3) determines a convex combination of the vectors (Xi, Y i), i = 1, ... 5 that is not below y = 3 (= Yo) and that allows as much shrinkage of Xo as possible. ,* = (2/3, 113, 0, 0, 0, 0, 0). _ ... - . P6 0L---~2----~4----~6----~8----1~0--~12X Figure 2-5. Table 2-2. Envelopment surface for the BCC-Input model. Solution Values for the Input-Oriented BCC Model Primal Problem (BCCp-I) DMU ()* s+ 1 1 1 0 0 0 0 0 2 3 4 5 6 7 1 1 7115 1/2 3/5 1 0 s 0 0 0 0 0 0 0 Dual Problem (BBCD-I) A w~ J f1 v uo Al = 1 A2 = 1 A3 = 1 A4 = 1 Al = 2/3, A2 = 113 Al = 1 A3 = 1 1 1 1/6 1/3 114 113 1/15 e 3/20 112 113 116 119 115 1/4 1/10 2/3 -2/3 -3/4 -5/3 4/15 !
DMU7 . Essentially, the various models for DEA each seek to establish which subsets of n DMUs determine parts of an envelopment surface. As will be seen, the geometry of this envelopment surface is prescribed by the specific DEA model employed. To be efficient, the point Pj corresponding to DMUj must lie on this surface. Units that do not lie on the surface are termed inefficient, and the DEA analysis identifies the sources and amounts of inefficiency and/or provides a summary measure of relative efficiency.
2. BCC Output Orientation As can be seen from the formulation below, the essential difference between the previous input-oriented BCC model and the output-oriented BCC model is that the LP now maximizes on ¢ to achieve proportional output augmentation. Here the normalizing constraint for the multiplier form (the dual problem) now involves ,uYo, while vXo appears in the objective function. t. Zo =
Data Envelopment Analysis: Theory, Methodology, and Applications by Abraham Charnes, William W. Cooper, Arie Y. Lewin, Lawrence M. Seiford