By Rolf Fare, Shawna Grosskopf, Dimitris Margaritis

Info Envelopment research (DEA) is usually ignored in empirical paintings resembling diagnostic exams to figure out no matter if the knowledge conform with expertise which, in flip, is critical in picking technical swap, or discovering which forms of DEA types enable information changes, together with facing ordinal data.

*Advances in facts Envelopment Analysis* specializes in either theoretical advancements and their purposes into the size of effective potency and productiveness progress, comparable to 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 call Making Unit (DMU).

Readership: complex postgraduate scholars and researchers in operations learn and economics with a selected curiosity in construction thought and operations administration.

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**Additional resources for Advances in Data Envelopment Analysis**

**Example text**

Z1 y11 + z 2 y21 y1 z 1 y12 + z 2 y22 y2 z1 x1 + z 2 x2 z1, z2 x 0, where x may be given as an observed DMU’s input use. Thus following Färe, Grosskopf and Margaritis (2011), we can extend the diet problem to include inputs. We begin by considering the DEA profit maximization problem. t. z k xkn x n , n = 1, . . , N z k ykm ym , m = 1, . . , M k=1 K k=1 zk 0, k = 1, . . , K . 9 This assumption is for simplicity, multiple inputs may be included. 10 This formulation exhibits constant returns to scale, which under competition yields maximum zero profit.

This is illustrated in the duality figure in Section 2 of this chapter. , M w p = (wp)M = q where M qk = N pm ykm − m=1 wn x kn , k = 1, . . , 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 .

N, k=1 K z k ykm yk m , m = 1, . . , M, 0 k = 1, . . , K k=1 zk K z k = 1. k=1 Note that since the unit of measurement of inputs changes from xkn to an x kn , the directional vector must also change from gn to an gn , maintaining the same unit of measurement for inputs and directions. March 10, 2015 8:49 Advances in Data Envelopment Analysis - 9in x 6in b2007-ch02 page 31 Chapter 2. 36) k=1 may be rewritten as K K z k x kn + bn an k=1 zk an xk n + bn − βan gn . 39) k=1 which is the original input constraint, demonstrating that the directional (DEA) input distance function is invariant with respect to affine data transformations, assuming VRS.