A Solution Approach for Agricultural Service Center Location Problem Using TOPSIS, DEA and SAW Techniques - Technology Management for Sustainable Production and Logistics - page 34

2.7 Simple Additive Weighting (SAW) Technique

Simple Additive Weighting (SAW) method is one of the most popular and most
widely used methods because of its simplicity (Shakouri et al. 2014 ). It assumes
additive aggregation of decision outcomes, which is controlled by weights
expressing the importance of attributes. SAW uses all attribute values of an
alternative and uses the regular arithmetical operations of multiplications and
summations.
Usually the results of MADM methods are different, so their results should be
compared and best rank for alternatives selected. Friedman test can be applied to
compare different related samples. If the results of Friedman test showed that there
is no meaningful difference between rankings, so to use the benefits of all devel-
oped MADM methods, the median of all ranking for each alternative can be used.
Otherwise the best ranking method should be selected.

2.8 New MADM Technique

Since the mentioned MADM methods might be able to lead to best solution,
another MADM methodology developed for them. In this technique first a hierar-
chical model is developed to create decision attributes for ASCLP. The summary
of proposed MADM method has been shown in Fig. 5 .
To find the priority of the ASC location selection attributes, a FAHP survey was
designed and performed. The local weights of relative importance are computed
to the attributes against the objectives; and also the global weights, which are the
relative importance attributes against the goal. To derive the global weight of each
attribute, its local weight was multiplied by the local weight of each corresponding
objectives (Zangeneh et al. 2014 ).
To select best candidate location for ASCs, some sub-attribute for each location
attribute were defined which can easily be measured. The Eq. 14 can be used for
calculating the value of each attribute for each candidate location:

p

ǜ

χ ij =

C k ∀ i , j

(14)

k = 1

where, k is the index of sub-attribute, and ˜ C k is the normalized value of sub-

attribute k .
Since the unit of the sub-attributes is different, to sum and use them in formula-
tions they are converted them to a normal range between one and zero before cal-
culation of decision parameters using the Eq. 15 :

C k = C k − min C k
max C k − min C k

∀ i , j

(15)