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


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 ,


SAW, Cont.







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

=

=




Weight Product Method, Cont.


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)


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=−= ∑

=

−−


TOPSIS, Cont.

5. Calculate similarities to positive-idealsolution

6. Rank preference order

miSS

SC

ii

ii ,...,1 ,

)( *

*=

+

=−

−




TOPSIS, Cont.






Apichat Sopadang: MADM -

Scoring Method 17

ELECTRE METHOD

Management Science

Multiple Attribute Decision Making

By

Dr. Apichat Sopadang


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


Outrank Relationship


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}




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









A2 and A4 can be eliminated

multiple attribute decision making

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