By William W. Cooper

Data Envelopment research: A complete textual content with types, purposes, References, And DEA-Solver software program, 2d version is designed to supply a scientific advent to DEA and its makes use of as a multifaceted device for comparing difficulties in numerous contexts. each one bankruptcy accompanies its advancements with uncomplicated numerical examples and discussions of exact functions. Emphasis is put on the use in addition to an knowing of DEA and the subjects during this publication were chosen and taken care of therefore. the 1st 9 chapters hide the fundamental rules of DEA and the ultimate seven chapters are extra complicated therapy of DEA. those ultimate chapters have been thoroughly revised into new chapters, reflecting contemporary advancements that drastically expand the ability and scope of DEA and result in new instructions for learn and DEA makes use of. including the 1st ten chapters of the fundamental ideas, they are going to supply scholars and researchers with a fantastic realizing of the technique, its makes use of and its potential.

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**Example text**

A. ). A. Simon (1991) Models of My Life (New York: Basic Books). xxxviii DATA ENVELOPMENT ANALYSIS Glossary of symbols X, y, X X €. R" A G i^™x" x^, AJ e ej / rank(A) X)"_i Aj Small letters in bold face denote vectors. a; is a point in the n dimensional vector space R". A is a matrix with m rows and n columns. The symbol -^ denotes transposition. e denotes a row vector in which all elements are equal to 1. ej is the unit row vector with the j-th element 1 and others 0. I is the identity matrix.

I + 151t;2 ~ 19ui + 131^2 ' An easier route would be to solve the following problem. 7) 16 DATA ENVELOPMENT ANALYSIS subject to ISOiti + 50u2 IQui + 131112 " lOOtti + 90M2 20U1 + 151U2 ~ with ui,U2,vi,V2 > 0. The choice of ui,U2 and wi,W2 should maximize the ratio for Hospital B, so no better choice can be made from this manager's standpoint. As shown in the next chapter, this nonlinear programming problem can be replaced by the following linear program. max 150ui 4- 50u2 subject to 150ui + 50u2 < 19t;i + ISlwa lOOui + 90u2 < 20t;i + 151W2 19^;i + 131t;2 = 1 and all variables are constrained to be positive.

11). 1 (CCR-Efiiciency) 1. DMUo is CCR-efficient if 9* = 1 and there exists at least one optimal {v*,u*), with V* > 0 and u* > 0. 2. Otherwise, DMUo is CCR-inefficient. BASIC CCR MODEL 25 Thus, CCR-inefRciency means that either (i) 9* < 1 or (M) 6* = 1 and at least one element of {v*,u*) is zero for every optimal solution of (LPo). 2, and a detailed description of CCR-efficiency will be given in Chapter 3. Now we observe the case where DMUo has 9* < 1 (CCR-inefiicient). 9) for which the weight {v*,u*) produces equahty between the left and right hand sides since, otherwise, 9* could be enlarged.