By Rolf Fare, Shawna Grosskopf, Dimitris Margaritis

Information Envelopment research (DEA) is frequently missed in empirical paintings comparable to diagnostic checks to figure out even if the knowledge conform with expertise which, in flip, is necessary in determining technical swap, or discovering which varieties of DEA types enable information ameliorations, together with facing ordinal data.

*Advances in facts Envelopment Analysis* makes a speciality of either theoretical advancements and their purposes into the size of effective potency and productiveness development, similar to its program to the modelling of time substitution, i.e. the matter of the way to allocate assets over the years, and estimating the "value" of a choice Making Unit (DMU).

Readership: complicated postgraduate scholars and researchers in operations examine and economics with a selected curiosity in construction conception and operations administration.

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K . 36) March 10, 2015 8:49 Advances in Data Envelopment Analysis - 9in x 6in b2007-ch03 page 49 Chapter 3. DEA and Intensity Variables 49 Thus the unit price of intensity variable k or DMU k is its revenue minus cost or its profit, so pricing DMUs is achieved by evaluating their profits. To illustrate our result, consider the inner product of q ∈ +K and z ∈ +K , K qk z k . 37) k=1 Thus for any z k 0, setting it equal to one and the other elements equal to zero, shows that qk is the unit price of that DMU.

T. z k xkn λxk n , n = 1, . . , N z k ykm yk m , m = 1, . . , M 0, k = 1, . . , K . , Grosskopf, S. and Margaritis, D. If k is efficient its score is one, and the problem above provides its value. If it is inefficient, then z k = 0 and x k will be projected onto the isoquant11 of L(y k ) which consists of convex combinations of other DMUs whose intensity variables are positive. As an illustration we include the example from Färe, Grosskopf and Margaritis (2012). They assume that there are three DMUs which use two inputs to produce a single output, with the data given below.

1 On Shephard’s Duality Theory To illustrate the difference between the duality familiar from linear programming to that in production theory we start by presenting Shephard’s original duality between cost and production, Shephard (1953). , sets of input vectors x ∈ +N required to produce y. 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.