35
1 Multi-Criteria Decision Making MCDM Approaches Membuat Keputusan Menggunakan Pelbagai Kriteria

Multi criteria decision making

Embed Size (px)

Citation preview

Page 1: Multi criteria decision making

1

Multi-Criteria Decision Making

MCDM Approaches

Membuat Keputusan Menggunakan Pelbagai Kriteria

Page 2: Multi criteria decision making

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.

Page 3: Multi criteria decision making

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

Page 4: Multi criteria decision making

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.

Page 5: Multi criteria decision making

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

Page 6: Multi criteria decision making

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

Page 7: Multi criteria decision making

7

Dalam penilaian projek pun melibatkan proses yang sama:

1. “Problem Tree”2. “Objective Tree”3. Strategi4. Kenalpasti projek/ program5. Penilaian setiap projek/program6. Membuat keputusan - MCDM

Contoh Masalah-masalah Pelbagai Kriteria

Page 8: Multi criteria decision making

8

Contoh Matrik Keputusan Pelbagai Kriteria

Contoh MCDM

Page 9: Multi criteria decision making

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 ?

Page 10: Multi criteria decision making

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 .

Page 11: Multi criteria decision making

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

Page 12: Multi criteria decision making

12

Weighted score method

Let Sij score of option i using criterion j wj weight for criterion j Si score of option i is given as:

Si = wj Sij

j

The option with the best score is selected.

Page 13: Multi criteria decision making

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) = wj U(Sij)U(Si) U( wj Sij)

Page 14: Multi criteria decision making

14

Example Using Weighted Scoring Method

Objective• Selecting a car

Criteria• Style, Reliability, Fuel-economy

Alternatives• Civic Coupe, Saturn Coupe, Ford Escort,

Mazda Miata

Page 15: Multi criteria decision making

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

Page 16: Multi criteria decision making

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

Page 17: Multi criteria decision making

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.

Page 18: Multi criteria decision making

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) mn 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)

Page 19: Multi criteria decision making

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/ (x2ij) for i = 1, …, m; j = 1, …, ni

Page 20: Multi criteria decision making

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

Page 21: Multi criteria decision making

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' }, wherev' = { min (vij) if j J ; max (vij) if j J' }

i i

Page 22: Multi criteria decision making

22

Steps of TOPSIS

Step 4: Calculate the separation measures for each alternative.

The separation from the ideal alternative is: Si

* = [ (vj

*– vij)2 ] ½ i = 1, …, m j

Similarly, the separation from the negative ideal alternative is:

S'i = [ (vj' – vij)2 ] ½ i = 1, …, m j

Page 23: Multi criteria decision making

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 ?

Page 24: Multi criteria decision making

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

Page 25: Multi criteria decision making

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} 44 score matrix. J = set of benefit attributes: style, reliability, fuel

economy (more is better) J' = set of negative attributes: cost (less is better)

Page 26: Multi criteria decision making

26

Steps of TOPSIS

Step 1(a): calculate (x2ij )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

xij2i

(x2)1/2

36 49 64 36

230 215 273 230

15.17 14.66 16.52 15.17

Page 27: Multi criteria decision making

27

Steps of TOPSIS

Step 1 (b): divide each column by (x2ij )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

Page 28: Multi criteria decision making

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

Page 29: Multi criteria decision making

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

Page 30: Multi criteria decision making

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

Page 31: Multi criteria decision making

31

Steps of TOPSIS

Step 4 (a): determine separation from ideal solution A* = {0.059, 0.244, 0.162, 0.080} Si

* = [ (vj

*– vij)2 ] ½ for each row j

Style Rel. Fuel

Saturn

Ford

(.046-.059)2 (.244-.244)2 (0)2 (.026)2 Civic

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

Page 32: Multi criteria decision making

32

Steps of TOPSIS

Step 4 (a): determine separation from ideal solution Si

*

(vj

*–vij)2 Si* = [ (vj

*– vij)2 ] ½

Saturn

Ford

0.000845 0.029

0.003208 0.057

0.008186 0.090

Civic

Mazda 0.003389 0.058

Page 33: Multi criteria decision making

33

Steps of TOPSIS Step 4 (b): find separation from negative ideal

solution A' = {0.040, 0.164, 0.144, 0.118} Si' = [ (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

Page 34: Multi criteria decision making

34

Steps of TOPSIS

Step 4 (b): determine separation from negative ideal solution Si'

(vj'–vij)2 Si' = [ (vj'– vij)2 ] ½

Saturn

Ford

0.006904 0.083

0.001629 0.040

0.000361 0.019

Civic

Mazda 0.002228 0.047

Page 35: Multi criteria decision making

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