Composition by DEA Distance to the Frontier - Probabilistic Composition of Preferences, Theory and Applications - page 50

Chapter 6
Composition by DEA Distance
to the Frontier

Abstract In the preceding chapter the composition of the preferences according to
the different criteria was made by rules that do not weight the criteria. These rules
were based on different points of view formulated in terms of joint probabilities. A
different approach to avoid a previous determination of weights, based on multi-
variate distances to the frontiers, is considered in this chapter.

Keywords Data envelopment analysis Frontier Human development index

6.1 Data Envelopment Analysis

Data Envelopment Analysis (DEA) emerged in the late 1970s, with the work of
Charnes et al. ( 1978 ). The basic idea behind DEA consists of comparing the
alternatives corresponding to production units by evaluating their ef ciency in

terms of ratios between linear combinations of the values of outputs and inputs,
with coef

cients varying freely.
If there is only one product from a unique resource, the ef ciency is naturally

measured by the ratio between the amount of output produced and the amount of
resource employed to produce it. In the case of multiple inputs combined to produce
different amounts of different products, a similar ratio can be employed if it is
possible, by means of unitary prices or any other type of coef

cients, to obtain a
unique aggregate measure of output produced and another unique aggregate mea-
sure of input employed.
DEA is employed to measure the ef ciency when there is freedom of choice of

coef ciency of a production unit is then

measured by the distance between the ratio obtained applying to its outputs and inputs
the most favorable coef

cients to combine outputs and inputs. The ef

cients and the highest ratio that would be obtained applying

the same coef cients to outputs and inputs observed in some competing alternative.

A mathematical programming algorithm is employed to determine this optimal
distance from the productivity ratio associated with the alternative under evaluation
to the productivity ratios in the frontier of highest productivities. An alternative is
considered ef

cient and receives an ef ciency score of 1 if its vector of inputs and