Nonparametric Model Specifications The DEA method allows for the calculation of the relative ef-
ficiency of the data, and does not provide any information on the
absolute efficiency. The most efficient DMUs are those situated on
the frontier, the others can reach this allocation if: They reduce
the inputs, while maintaining a constant output; they increase
the outputs, while maintaining the inputs constant; and they per-
form a combination of the two previous solutions [3]. According to
Vincová [26] in nonparametric models, we evaluate n productive
units, DMUs, where each DMU takes m different inputs to produce
s different outputs. Our proposed measure of the efficiency of any
UMU is obtained as the maximum of a ratio of weighted outputs to
weighted inputs subject to the condition that the similar ratios for
every DMU be less than or equal to unity [15]. The models must
include all characteristics considered, i.e. the weights of all inputs
and outputs must be greater than zero. Such a model is defined as a
linear divisive programming model:
Maximize ho=
1
1
uryro
vixio
s r m i =
=
∑
∑
(6)
Subject to:
1
1
uryrj
vixij
s r m i =
=
∑
∑
< 1; j=1, 2, …, n; ur, Vi> 0; r = 1, …, s; i = 1, …, m.
Here the y
rj
, x
ij
(all positive) are the known outputs and inputs
attached to each j
th
DMU and the u
r
, vi> 0 are the variable weights
to be determined by the solution of this problem e.g., by the data on
all of the DMU’s which are being used as a reference set. According
to [4], a unit will be efficient if and only if this ratio equals one, oth
-
erwise it will be considered as relatively inefficient.
