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distance to that frontier for the individual observations. The frontier is
piecewise linear and is formed by tightly enveloping the data points of the
observed 'best practice' activities in the observations, i.e. the most efficient
farms in the sample. DEA uses the distance to the frontier as a measure of
efficiency. Relative performance to the frontier provides a score for each
farm from 0 (worst performance), to 1 (best performance). For a review of
the general advantages of the DEA technique over other, parametric,
approaches see, for example, Seiford and Thrall (1990) and Färe et al.
(1994; 1996).
In this chapter, we consider the technical efficiency (TE) of a farm
to be represented by the ratio of the best technical performance in the data
set to the technical performance of that particular farm. Assuming that for
sustainability, the use of indirect energy should be minimised, we used an
input-oriented DEA model aiming at minimising the input level given the
output level. Following the general approach, we assumed that the input is
strongly disposable, i.e. the input level can be reduced at no cost. The DEA
model used is described in the equation set (2.1a)-(2.1e).
where
-th farm; Y is a
p n matrix of p outputs produced by the n farms; is the intensity vector
of the weights attached to the n farms for the construction of the virtual
comparison unit for farm j ;
is the Farrell-Debreu measure of efficiency of the
j
1 vector of quantities of output
produced by farm j; B is a mn matrix of m inputs used by the n farms,
and
is a
p ×
j.
The efficiency of the n farms is assessed by solving n LP models,
in which the vectors and are adapted each time another farm j is
considered. From constraint (2.1c) follows that can never exceed unity.
A solution for that is less than unity indicates that a weighted
combination of other farms in the sample exists that produces at least the
same amount of output but with fewer inputs. Constraint (2.1d) is added
because variable returns to scale are assumed.
In this chapter, technical efficiency (TE) is calculated according to
model (1) using Onfront (Färe and Grosskopf 1998). The input that is taken
into account is measured as the amount of indirect energy use in chemical
is the vector of these inputs for farm
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