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7/31/2019 Multiple Attribute Decision Making
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Apichat Sopadang: MADM -
Scoring Method 1
SCORING METHODS
Management Science
Multiple Attribute Decision Making
By
Dr. Apichat Sopadang
Apichat Sopadang: MADM - ScoringMethod 2
Scoring Methods
Transformation of a vector to an appropriatescalar value
Formulate an index to represent itseffectiveness => wind-chill factor, graduateschool admission index
Two scoring techniques: The SimpleAdditive Weighting method (SAW) and theWeighted Product method
Apichat Sopadang: MADM - ScoringMethod 3
Simple Additive Weighting(SAW) Method
Best know and most widely used method Uses all n attribute values of an alternative
and uses the regular arithmetical operations
of multiplication and addition
The attribute values must be both numerical
and comparable
∑=
==
n
j
ij ji mir wV 1
,...,1 ,
Apichat Sopadang: MADM - ScoringMethod 4
SAW, Cont.
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Apichat Sopadang: MADM - ScoringMethod 5
Apichat Sopadang: MADM - ScoringMethod 6
Apichat Sopadang: MADM - ScoringMethod 7
Apichat Sopadang: MADM - ScoringMethod 8
Weight Product Method
Transformation is not necessary when we use
multiplication among attribute values
The weights become exponents associated with
each attribute value
Positive power for benefit attributes and negative
power for cost attributes
mi x
x
AV
AV R
j
j
w
j
n
j
w
ij
n
jii ,...,1 ,
)()(
)(
*
1
1
* ==
=
Π
Π
=
=
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Apichat Sopadang: MADM - ScoringMethod 9
Weight Product Method, Cont.
Apichat Sopadang: MADM - ScoringMethod 10
TOPSIS
Technique for Order Preference by Similarity to
Ideal Solution (TOPSIS)
Ideal solution is usually unattainable or infeasible
DM’s utilities decrease monotonically when an
alternative moves away from this ideal
TOPSIS defines an index called similarity to thepositive-ideal solution (proximity to positive and
remoteness to negative values)
Apichat Sopadang: MADM - ScoringMethod 11
TOPSIS, Cont.
1. Calculate normalized ratings2. Calculate weight normalized ratings
3. Identify positive-ideal and negative-ideal
solutions
4. Calculate separation measures
,)(1
2**∑=
−=
n
j
jijivvS mivvS
n
j
jiji ,...,1 ,)(1
2=−= ∑
=
−−
Apichat Sopadang: MADM - ScoringMethod 12
TOPSIS, Cont.
5. Calculate similarities to positive-idealsolution
6. Rank preference order
miSS
SC
ii
ii ,...,1 ,
)( *
*=
+
=−
−
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Apichat Sopadang: MADM - ScoringMethod 13
TOPSIS, Cont.
Apichat Sopadang: MADM - ScoringMethod 14
Apichat Sopadang: MADM - ScoringMethod 15
Apichat Sopadang: MADM - ScoringMethod 16
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Apichat Sopadang: MADM -
Scoring Method 17
ELECTRE METHOD
Management Science
Multiple Attribute Decision Making
By
Dr. Apichat Sopadang
Apichat Sopadang: MADM - ScoringMethod 18
ELECTRE
Elimination et Choice Translating Reality
Outrank relationship A1($13000, 18MPG), A2($16000, 21MPG) and
A3($18000, 25MPG) => nondominate
(A1 R A2) and (A2 R A3) but not imply that (A1 R A3)
Pairwise comparison
It examines both the degree to which the preferenceweights are in agreement with pairwise dominancerelationships and the degree to which weightedevaluations differ from each other
Apichat Sopadang: MADM - ScoringMethod 19
Outrank Relationship
Apichat Sopadang: MADM - ScoringMethod 20
Procedure of ELECTRE.
1. Calculate the normalized decision matrix2. Calculate the weighted normalized decision
matrix
3. Determine the concordance and
discordance set
C ( p,q) = { j|v pj ≥ vqj}
D( p,q) = { j|v pj < vqj}
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Apichat Sopadang: MADM - ScoringMethod 21
Procedure of ELECTRE.
4. Calculate the concordance matrix
5. Calculate the discordance matrix
6. Determine the concordance dominancematrix
7. Determine the discordance dominance
matrix8. Determine the aggregate dominance matrix
9. Eliminate the less favorable alternativeApichat Sopadang: MADM - Scoring
Method 22
Apichat Sopadang: MADM - ScoringMethod 23
Apichat Sopadang: MADM - ScoringMethod 24
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Apichat Sopadang: MADM - ScoringMethod 26
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Apichat Sopadang: MADM - ScoringMethod 28
A2 and A4 can be eliminated
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