The document discusses multiple criteria decision making (MCDM) approaches. It introduces several common MCDM methods: the weighted score method, TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method, and Analytic Hierarchy Process (AHP). It then provides a detailed example of how to apply the weighted score method and TOPSIS method to a problem of selecting the best car based on criteria like style, reliability, fuel economy, and cost.

1. 1
Multi-Criteria Decision
Making
MCDM Approaches
Membuat Keputusan Menggunakan
Pelbagai Kriteria

2. 2
PENGENALAN
Zeleny (1982) dalam bukunya “Multiple
Criteria Decision Making” mengatakan:
“Telah menjadi lebih susah untuk melihat
dunia di sekeliling kita secara uni-dimensi
dan menggunakan satu kriteria penilaian
sahaja”
Sebenarnya kita selalu berdepan dengan keadaan untuk
membuat keputusan berdasarkan banyak kriteria.

3. 3
Banyak masalah samada dipihak kerajaan,
swasta atau individu akan melibatkatkan
pelbagai objektif atau kriteria.
Contoh: bagaimana hendak mencari kawasan
untuk loji nuklear, objektif terlibat mungkin
merangkumi:
• Keselamatan (Safety)
• Kesihatan (Health)
• Alam Sekitar (Environment)
• Kos (Cost)
PENGENALAN

4. 4
Contoh Masalah-masalah Pelbagai
Kriteria
Dalam kajian kes R&D, (Moore et. al
1976), telah mengenalpasti objektif
berikut:
• Keuntungan.
• Pertumbuhan & kepelbagaian produk.
• Peningkatan kadar milikan dalam pasaran.
• Mempertahankan keupayaan teknikal.
• Reputasi & Imej.
• Penyelidikan yang menjangka persaiagan.

5. 5
Memilih calon isteri/ suami. Kriteria
termasuklah:
• Ugama (30%)
• Cantik/ Tampan (20%)
• Kekayaan (10%)
• Keturunan / Family status (10%)
• Pendidikan (20%)
• Maskahwin/ Hantaran (10%)
% - Wajaran (weightages)
Contoh Masalah-masalah Pelbagai
Kriteria

6. 6
Terdapat konflik dalam kriteria tersebut –
semua kriteria kecuali Maskawin
menggambarkan prinsip semakin tinggi nilai
semakin baik.
Persoalannya bagaimana kita hendak ubahsuai
@ “normalize” kriteria supaya menjadi sama
dengan kriteria lain?
Supaya semua penilaian kita menjadi konsisten
dan angka akhir akan memberikan satu skor
yang bermakna.
Contoh Masalah-masalah Pelbagai
Kriteria

7. 7
Dalam penilaian projek pun melibatkan proses
yang sama:
1. “Problem Tree”
2. “Objective Tree”
3. Strategi
4. Kenalpasti projek/ program
5. Penilaian setiap projek/program
6. Membuat keputusan - MCDM
Contoh Masalah-masalah Pelbagai
Kriteria

8. 8
Contoh Matrik Keputusan Pelbagai Kriteria
Contoh MCDM

9. 9
Approaches For MCDM
Several approaches for MCDM exist. We
will cover the following:
• Weighted score method.
• TOPSIS method
• Analytic Hierarchy Process (AHP)
• Goal programming ?

10. 10
Weighted score method
Determine the criteria for the problem
Determine the weight for each criteria.
The weight can be obtained via survey,
AHP, etc.
Obtain the score of option i using each
criteria j for all i and j
Compute the sum of the weighted score
for each option .

11. 11
Weighted score method
In order for the sum to make sense all criteria
scale must be consistent, i.e.,
More is better or less is better for all criteria
Example:
In the wife selection problem, all criteria
(Religion, Beauty, Wealth, Family status, Family
relationship, Education) more is better
If we consider other criteria (age, dowry) less is
better

12. 12
Weighted score method
Let Sijscore of option i using criterion j
wj weight for criterion j
Si score of option i is given as:
Si = Σ wj Sij
j
The option with the best score is selected.

13. 13
Weighted Score Method
The method can be modified by using
U(Sij) and then calculating the weighted
utility score.
To use utility the condition of separability
must hold.
Explain the meaning of separability:
U(Si) = Σ wj U(Sij)
U(Si) ≠ U(Σ wj Sij)

14. 14
Example Using Weighted Scoring
Method
Objective
• Selecting a car
Criteria
• Style, Reliability, Fuel-economy
Alternatives
• Civic Coupe, Saturn Coupe, Ford Escort,
Mazda Miata

15. 15
Weights and Scores
Weight 0.3 0.4 0.3 Si
Style Reliability Fuel Eco.
Saturn
Ford
7 9 9
8 7 8
9 6 8
Civic
Mazda 6 7 8
8.4
7.6
7.5
7.0

16. 16
TOPSIS METHOD
Technique of Order Preference by
Similarity to Ideal Solution
This method considers three types of
attributes or criteria
• Qualitative benefit attributes/criteria
• Quantitative benefit attributes
• Cost attributes or criteria

17. 17
TOPSIS METHOD
In this method two artificial alternatives are
hypothesized:
Ideal alternative: the one which has the best
level for all attributes considered.
Negative ideal alternative: the one which has
the worst attribute values.
TOPSIS selects the alternative that is the closest
to the ideal solution and farthest from negative
ideal alternative.

18. 18
Input to TOPSIS
TOPSIS assumes that we have m alternatives
(options) and n attributes/criteria and we have
the score of each option with respect to each
criterion.
Let xij score of option i with respect to
criterion j
We have a matrix X = (xij) m×n matrix.
Let J be the set of benefit attributes or criteria
(more is better)
Let J' be the set of negative attributes or
criteria (less is better)

19. 19
Steps of TOPSIS
Step 1: Construct normalized decision
matrix.
This step transforms various attribute
dimensions into non-dimensional
attributes, which allows comparisons
across criteria.
Normalize scores or data as follows:
rij = xij/ (Σx2
ij) for i = 1, …, m; j = 1, …, ni

20. 20
Steps of TOPSIS
Step 2: Construct the weighted normalized
decision matrix.
Assume we have a set of weights for each
criteria wj for j = 1,…n.
Multiply each column of the normalized
decision matrix by its associated weight.
An element of the new matrix is:
vij = wj rij

21. 21
Steps of TOPSIS
Step 3: Determine the ideal and negative ideal
solutions.
Ideal solution.
A* = { v1
*
, …, vn
*
}, where
vj
*
={ max (vij) if j ∈ J ; min (vij) if j ∈ J' }
i i
Negative ideal solution.
A' = { v1', …,vn' }, where
v' = { min (vij) if j ∈ J ; max (vij) if j ∈ J' }
i i

22. 22
Steps of TOPSIS
Step 4: Calculate the separation measures for
each alternative.
The separation from the ideal alternative is:
Si
*
= [ Σ (vj
*
– vij)2
] ½
i = 1, …, m
j
Similarly, the separation from the negative ideal
alternative is:
S'i = [ Σ (vj' – vij)2
] ½
i = 1, …, m
j

23. 23
Steps of TOPSIS
Step 5: Calculate the relative closeness to
the ideal solution Ci
*
Ci
*
= S'i / (Si
*
+S'i ) , 0 < Ci
*
< 1
Select the option with Ci
*
closest to 1.
WHY ?

24. 24
Applying TOPSIS Method to
Example
Weight 0.1 0.4 0.3 0.2
Style Reliability Fuel Eco.
Saturn
Ford
7 9 9 8
8 7 8 7
9 6 8 9
Civic
Mazda 6 7 8 6
Cost

25. 25
Applying TOPSIS to Example
m = 4 alternatives (car models)
n = 4 attributes/criteria
xij = score of option i with respect to criterion j
X = {xij} 4×4 score matrix.
J = set of benefit attributes: style, reliability, fuel
economy (more is better)
J' = set of negative attributes: cost (less is better)

26. 26
Steps of TOPSIS
Step 1(a): calculate (Σx2
ij )1/2
for each column
Style Rel. Fuel
Saturn
Ford
49 81 81 64
64 49 64 49
81 36 64 81
Civic
Mazda
Cost
Σxij
2
i
(Σx2
)1/2
36 49 64 36
230 215 273 230
15.17 14.66 16.52 15.17

27. 27
Steps of TOPSIS
Step 1 (b): divide each column by (Σx2
ij)1/2
to
get rij
Style Rel. Fuel
Saturn
Ford
0.46 0.61 0.54 0.53
0.53 0.48 0.48 0.46
0.59 0.41 0.48 0.59
Civic
Mazda 0.40 0.48 0.48 0.40
Cost

28. 28
Steps of TOPSIS
Step 2 (b): multiply each column by wj to
get vij.
Style Rel. Fuel
Saturn
Ford
0.046 0.244 0.162 0.106
0.053 0.192 0.144 0.092
0.059 0.164 0.144 0.118
Civic
Mazda 0.040 0.192 0.144 0.080
Cost

29. 29
Steps of TOPSIS
Step 3 (a): determine ideal solution A*.
A* = {0.059, 0.244, 0.162, 0.080}
Style Rel. Fuel
Saturn
Ford
0.046 0.244 0.162 0.106
0.053 0.192 0.144 0.092
0.059 0.164 0.144 0.118
Civic
Mazda 0.040 0.192 0.144 0.080
Cost

30. 30
Steps of TOPSIS
Step 3 (a): find negative ideal solution A'.
A' = {0.040, 0.164, 0.144, 0.118}
Style Rel. Fuel
Saturn
Ford
0.046 0.244 0.162 0.106
0.053 0.192 0.144 0.092
0.059 0.164 0.144 0.118
Civic
Mazda 0.040 0.192 0.144 0.080
Cost

31. 31
Steps of TOPSIS
Step 4 (a): determine separation from ideal
solution A* = {0.059, 0.244, 0.162, 0.080}
Si
*
= [ Σ (vj
*
– vij)2
] ½
for each row
j
Style Rel. Fuel
Saturn
Ford
(.046-.059)2
(.244-.244)2
(0)2
(.026)2Civic
Mazda
Cost
(.053-.059)2
(.192-.244)2
(-.018)2
(.012)2
(.053-.059)2
(.164-.244)2
(-.018)2
(.038)2
(.053-.059)2
(.192-.244)2
(-.018)2
(.0)2

32. 32
Steps of TOPSIS
Step 4 (a): determine separation from ideal
solution Si
*
Σ(vj
*
–vij)2
Si
*
= [ Σ (vj
*
– vij)2
] ½
Saturn
Ford
0.000845 0.029
0.003208 0.057
0.008186 0.090
Civic
Mazda 0.003389 0.058

33. 33
Steps of TOPSIS
Step 4 (b): find separation from negative ideal
solution A' = {0.040, 0.164, 0.144, 0.118}
Si' = [ Σ (vj'– vij)2
] ½
for each row
j
Style Rel. Fuel
Saturn
Ford
(.046-.040)2
(.244-.164)2
(.018)2
(-.012)2Civic
Mazda
Cost
(.053-.040)2
(.192-.164)2
(0)2
(-.026)2
(.053-.040)2
(.164-.164)2
(0)2
(0)2
(.053-.040)2
(.192-.164)2
(0)2
(-.038)2

34. 34
Steps of TOPSIS
Step 4 (b): determine separation from
negative ideal solution Si'
Σ(vj'–vij)2 Si' = [ Σ (vj'– vij)2
] ½
Saturn
Ford
0.006904 0.083
0.001629 0.040
0.000361 0.019
Civic
Mazda 0.002228 0.047

35. 35
Steps of TOPSIS
Step 5: Calculate the relative closeness to
the ideal solution Ci
*
= S'i / (Si
*
+S'i )
S'i /(Si
*
+S'i) Ci
*
Saturn
Ford
0.083/0.112 0.74 ← BEST
0.040/0.097 0.41
0.019/0.109 0.17
Civic
Mazda 0.047/0.105 0.45