By Rolf Fare, Shawna Grosskopf, Dimitris Margaritis

Info Envelopment research (DEA) is frequently missed in empirical paintings corresponding to diagnostic exams to figure out no matter if the information conform with expertise which, in flip, is critical in settling on technical switch, or discovering which varieties of DEA versions let facts modifications, together with facing ordinal data.

*Advances in facts Envelopment Analysis* specializes in either theoretical advancements and their functions into the size of effective potency and productiveness development, resembling 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 study and economics with a specific curiosity in creation concept and operations administration.

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

**Example text**

T. 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.

K , which is the ‘linear programming’ minimization problem. Hence the focus here is on the intensity variables z k , k = 1, . . , K . 2 Adjoint Transformations in DEA In the last section, we showed how the duality between input quantities and input prices was developed by Shephard (1953). Here we consider the more general case including both inputs and outputs with an emphasis on the DEA technology. Specifically, we introduce the adjoint transformation associated with this technology. Recall the technology matrix M consisting of input and output quantities.

M = y 11 · · · yk1 · · · y K 1 .. .. .. . . . 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.