Erkie Asmare 1 and Andualem Begashaw


Nonparametric Model Specifications



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Review on Parametric and Nonparametric M (2)

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.

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