Download e-book for kindle: Advances in Data Envelopment Analysis by Rolf Fare, Shawna Grosskopf, Dimitris Margaritis

By Rolf Fare, Shawna Grosskopf, Dimitris Margaritis

ISBN-10: 9814644544

ISBN-13: 9789814644549

Info Envelopment research (DEA) is usually ignored in empirical paintings equivalent to diagnostic checks to figure out even if the knowledge conform with know-how which, in flip, is critical in deciding upon technical swap, or discovering which forms of DEA types enable facts alterations, together with facing ordinal data.

Advances in info Envelopment Analysis specializes in either theoretical advancements and their functions into the dimension of efficient potency and productiveness progress, reminiscent of its software to the modelling of time substitution, i.e. the matter of ways to allocate assets over the years, and estimating the "value" of a choice Making Unit (DMU).

Readership: complex postgraduate scholars and researchers in operations examine and economics with a selected curiosity in creation concept and operations administration.

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Y1M ··· yk M ··· yK M In the DEA world, for each DMU there is a given nonnegative intensity variable z k 0, k = 1, . . , K or z ∈ +K . If these are restricted only to be nonnegative, the resulting DEA technology will exhibit CRS (constant returns to scale). 19) or in terms of inequalities4 K T = (x, y) : z k x kn xn , n = 1, . . , N, z k ykm ym , m = 1, . . 20) k=1 K k=1 zk 0, k = 1, . . , K . Dual to input quantities are input prices and dual to output quantities are output prices. Dual to the intensity variables are their ‘prices’, here denoted 4 Note that we are a bit inconsistent with inputs, sometimes they are nonpositive and sometimes nonnegative.

7 For simplicity, assume that we have four data points, pi , i = 1, . . , 4 and suppose that this data satisfies the following relationship p1 − p2 > p3 − p4 . 18) Next, suppose that each pi has been transformed into qi = api + b, i = 1, . . , 4. 19) From the last two expressions we have q1 − q2 = ap1 − b − (ap2 − b) = a( p1 − p2 ) > a( p3 − p4 ) = ap3 − ap4 + b − b = q3 − q4 . 20) and the differences have a cardinal meaning. The affine transformation of data was interpreted as a linear approximation of the ordinal data h( p).

L(y) = {x : x can produce y}. 1) then the cost function is defined as C(y, w) = min{wx : x ∈ L(y)}. 2 We refer to L(y) as a subset of the primal or quantity space. The dual technology is a subset of the dual or price space. 3) where c is a given cost. The duality between the primal and dual technologies may be expressed in terms of distance functions defined over them. , if L(y) = {(x , x ) : x x 1 2 1 2 1 ⇔ x ∈ L(y). , the technology is Cobb–Douglas, then clearly a minimum does not exist if one price is zero; the isoquants approach the axes asymptotically.

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Advances in Data Envelopment Analysis by Rolf Fare, Shawna Grosskopf, Dimitris Margaritis

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