the analytic hierarchy process - İtÜ · 2012. 6. 4. · selecting the best material supplier to...

The Analytic Hierarchy Process

Özgür Kabak, Ph.D.

AHP

These slides are mostly taken from Prof. İlker TOPCU’s AHP/ANP Lecture notes on

http://web.itu.edu.tr/~topcuil/ya/AHP.htm



square

circle

triangle

diamond

rectangle

.05

.10

.15 .24

.47

Cognitive Psychology

has found that

people are poor at assimilating large quantities of information on problems

People cope with cognitive overload by employing heuristics that simplify the problem

This can lead to selection of suboptimal alternatives

George A. Miller, in his paper

" The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information”

indicated that

the capacity of human short term memory is seven separate items, plus or minus two.

The brain of a regular human can

simultaneously process,

differentiate, and deal with

at most 7 factors

for some people this limit can be decreased to 5, for some other people it can be increased to 9

(The Psychological Review, 1956, vol. 63, pp. 81-97)

Why Hierarchy?

when people faced with a complex problem

in order to understand the problem better

they must break down the problem into its smaller constituent parts

and construct a hierarchical model to represent it

Why Hierarchy?

Decision making problem should be depicted as thoroughly as possible:

The constructed hierarchy

arranging the factors in appropriate levels

must include enough relevant detail

cluster (level)

element

This loop indicates that each element depends only on itself

Goal

Subcriteria

Criteria

Alternatives

Hierarchy

Selecting the best material supplier to purchase key components for new products

Relationship closeness

Quality of product

Delivery capabilities

Warranty level

Average price

Reputation

Supplier A Supplier B Supplier C

Supplier Selection

Goal

Criteria

Sub-

Criteria

Ratings

(for each

Sub-

Criterion)

Regulatory Compliance

Development Cost

Prob. of Tech. Success

R&D and Eng. Resources

Development Time

Patent Position

Outstanding

Above Average

Average

Below Average

Capability to Market

Market Growth

Market Share

Market Potential

Customer Acceptance

Outstanding

Above Average

Average

Below Average

NPV

Capital Invest

ROI

Unit Cost

Outstanding

Above Average

Average

Below Average

Capability to Manufacture

Facility/Equp. Req.

Safety

Outstanding

Above Average

Average

Below Average

Future of the Firm

Technical Marketing Financial Manufacture

p1 p2 p99

R&D Project Selection

Case 1

Case 2

Communication

& Problem Solving

Family & Children

Temper

Security

Affection

Loyalty

Food

Shelter

Sex

Sociability

Finance

Understanding

World View

Theology

Housekeeping

Sense of Beauty

& Intelligence

Whom to marry - a compatible spouse

Independence Flexibity Growth Challenge Commitment Humor Intelligence

Psychological Physical Socio-cultural Philosophical Aesthetic

marry don’t marry

Campbell Graham McGuire Faucet

1. Sosyal dokuya yönelik hizmetlerin verilmesi (Kadınlar ve çocuklar için sosyal yaşam evleri; yaşlılar için bakım evleri; engelliler için özel yollar, alış veriş ve hizmet birimleri)

2. Gençlik merkezleri ve mekanları (sanat, kültür, bilişim, hobi ve eğlence) yapılması

3. Nikah salonu yapılması 4. Güzel sanatlar üniversitesi/fakültesi /

Sanat akademisi açılmasının teşvik edilmesi 5. Uluslararası düzeyde (dans, müzik, sinema,

tiyatro) festivalleri yapılması 6. Kültür ve kongre merkezi kurulması 7. Bakırköy müzesi kurulması 8. Tarihi eserlerin restore edilerek korunması 9. Yeşil alanların, oyun ve spor alanlarının

arttırılması 10. Yeşil alanların, oyun ve spor alanalarının

arttırılması 11. Ayamama çevresinde botanik bahçesi ve

sağlık vadisi oluşturulması 12. Ayamama çevresinde botanik bahçesi ve

sağlık vadisi oluşturulması 13. Bütün belediye hizmet birimlerinin toplu

halde bulunacağı tek bir bina yapılması 14. Bütün belediye hizmet birimlerinin toplu

halde bulunacağı tek bir bina yapılması 15. Özgürlük meydanından kalkan metro ve

deniz otobüslerinin entegrasyonu 16. Otoparkların arttırılması ve yeraltı

otoparkları kurulması . . . . . . 34. Veri tabanı oluşturulması ve iletişim için

yararlanılması

1. Huzurlu, güvenli ve refah içinde model bir ilçe oluşturma

2. Sosyal ve kültürel yaşamı iyileştirme ve mozaiğini koruma

3. Ekonomik (hizmet iş kolları) ortamı iyileştirme

4. Fiziksel ortamı (ulaştırma, kent altyapısı) şehir plancılığı yaklaşımıyla iyileştirme

5. Doğal, çevresel ve tarihi güzellikleri koruma

6. Bakırköylülük bilincini geliştirme ve Bakırköy markasını oluşturma

7. Katılımlı, dinamik, çağdaş, sosyal belediyecilik anlayışına uygun bir yerinden yönetim oluşturma

“Sohbetli yaşamın

olduğu yer: Bakırköy”

1. Toplu Etkinlikler ve Kültür-Sanat Merkezi Projesi

2. Küçük El Sanatları Projesi

3. Spor Projesi 4. Dinlenme Alanları

Projesi 5. Bilim ve Teknoloji

Parkı / Mesleki Eğitim Projesi

“Yaşanabilir, katılımcı,

insan mutluluğuna önem veren

bir Eskişehir”

Dış ortam (Entegrasyon)

Katılım ortamı

Doğal ortam

Fiziki yapı ortamı

Ekonomik ortam

Sosyal ortam

•Eğitim •Kültür-Sanat •Sağlık •Eğlence Spor

•Ticaret •Hizmet •Sanayi •Turizm •Tarım •Yüksek Teknoloji

•İmar •Ulaşım •Altyapı •Şehir Görüntüsü

•Hava •Toprak •Su

•Bölgesel •Ulusal •Uluslararası

•Yerel Yönetim •Merkezi Yönetim •Sivil Toplum Kuruluşları •Özel Sektör

Üniversitelerle işb.

Hekimlerle işbirliği

Eczanelerle işbirliği

Dağ. kanallarıyla işb.

Devletle işbirliği

Sektör içi işbirliği

Yerli birleşme Ortak tanıtım(iç/dış) Sektör içi eğitimve kurumsallaşma İhracatta işbirliği Sözleşmeli AR-GE Co-marketing, Co-promotion

“Uluslararası ölçüde rekabet gücüne sahip,

yaşam kalitesini

arttırıcı ve ülke ihtiyacının büyük kısmını karşılayan ilaç

sanayinin bulunması”

İth.- ihr. dengesi

Ar-Ge ve yenilikçilik

Hammadde üretimi

Fon yaratılması

Tüketici bilinci

Üretimin sürekliliği

Yönlendirici devlet (yerli hammadde, Ar-Ge’ye teşvik , Üretim yatırımına (yab.ser.) teşvik , AB’ye uyu, Bioeşdeğerlilik)

Yeni Mevzuat (Geri Ödeme Sistemi, OTC Yönetmeliği, KDV'nin düşmesi, KKDF'nin kalkması, İDY, Fiyat kararnamesi)

Fiyatın piy.tar. belirlenmesi Bağımsız ilaç otoritesi Sosyal güvenlik reformunun

genişletilmesi

Dağıtım kanallarında kurumsallaşma Dağıtım kanallarında eğitim

AR-GE Eğitim

Etik kuralların uygulanması Eğitimle reçetelemenin

iyileştirilmesi Hekimin hastayla para ilişkisinin

bitmesi

Eczanelerarası network Eczacıların danışmanlık hizmeti

1. Organ nakli merkezlerinin oluşturulması (dedike merkezlerin belirlenmesi ve sayının sınırlanması)

2. Organ bandrolü uygulamasının başlatılması 3. Ülkenin tüm kurumlarının kabul ettiği

düzenleyici kurul/ üst kurul kurulması (bilimsel, dinamik, siyasetten bağımsız, devlete yakın, karar veren, hesap soran bir Profesyonel Transplantasyon Organizasyon kurulu, ulusal/bölgesel)

4. Donör bildirimi sonrasında ameliyat hastanesinin belirlenme mekanizmasının oluşturulması, sistematiğin belirlenmesi

5. Beyin ölümü sonrası organizasyonun düzenlenmesi, yoğun bakıma yönelik beyin ölümü tanımı sonrası donör bakım eğitimlerinin verilmesi

6. Beyin ölümü yasal karar sisteminin düzenlenmesi, yönetmelik çıkarılması

7. Beyin ölümü- Sigorta (Kamu-Özel Sektör) ilişkisinin düzenlenmesi

8. Yoğun bakım standartlarının belirlenmesi için yönetmeliğin hazırlanması ve bir an önce çıkarılması

. . . . . . 25. Organ naklinde tek adres, tek telefon

sistemi/ Alo Sağlık 184 telefon hattı bu konuda test edilmesi

1. Beyin ölümü tespit ve bildirim sürecini iyileştirme

2. Yoğun bakım standartlarını iyileştirme

3. Yasal boşlukları giderme (yasa, yönetmelik)

4. Organ nakli koordinasyon sistemini iyileştirme

5. Organ nakli ekonomisini güçlendirme

6. Sağlık hizmet zincirinin tüm halkalarını bilgilendirme-bilinçlendirme

7. Toplumsal iletişimi etkinleştirme

“İhtiyacı karşılamak için sisteme karşı güven oluşturarak

kadavra donör sayısını

arttırmak”

The Analytic Hierarchy Process is

a powerful and understandable methodology that allows groups or individuals to combine qualitative and quantitative factors in decision making process.

a Multi Criteria Decision Making method for complicated and unstructured problems.

an approach that uses a hierarchical model having levels of goal, criteria, possible sub-criteria, and alternatives.

Priorities: Importance - Preference

AHP captures priorities from paired comparison judgments of the elements of the decision with respect to each of their parent criteria:

– Paired comparison judgments are arranged in a matrix

– Priorities are derived from the matrix as its principal eigenvector

– It also allows for the measurement of inconsistency in judgment

Importance of elements are equal Decision maker is indifferent between elements

9 8 7 6 5 4 3 2 1

9 8 7 6 5 4 3 2 1

First element is moderately more important than second one First element is moderately preferred to second one

9 8 7 6 5 4 3 2 1

First element is strongly more important than second one First element is strongly preferred to second one

9 8 7 6 5 4 3 2 1

First element is very strongly more important than second one First element is very strongly preferred to second one

9 8 7 6 5 4 3 2 1

First element is extremely more important than second one First element is strongly preferred to second one

9 8 7 6 5 4 3 2 1

Intermediate values

Use reciprocals for inverse comparisons

1 9

1 2

1 4

1 6

1 8

1 7

1 5

1 3

1

Selecting the best material supplier to purchase key components for new products


Quality of product


Warranty level

Average price

Reputation

Supplier A Supplier B Supplier C

Supplier Selection

Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y

leve

l

Ave

rage

pr

ice

Repu

tation

Priorities


Quality of product


Warranty level

Average price

Reputation

Comparison of criteria w.r.t. goal

Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y

leve

l

Ave

rage

pr

ice

Repu

tation

Priorities

Relationship closeness 1

Quality of product 1

Delivery capabilities 1

Warranty level 1

Average price 1

Reputation 1


Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y

leve

l

Ave

rage

pr

ice

Repu

tation

Priorities

Relationship closeness 1 Moderately -

strongly



Warranty level 1

Average price 1

Reputation 1


Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y

leve

l

Ave

rage

pr

ice

Repu

tation

Priorities

Relationship closeness 1 4



Warranty level 1

Average price 1

Reputation 1


Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y

leve

l

Ave

rage

pr

ice

Repu

tation

Priorities


Quality of product 1 Very

strongly

Delivery capabilities 1 2.nd element

strongly

Warranty level 1 Equal

Average price 1 Moderately

Reputation 1


Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y

leve

l

Ave

rage

pr

ice

Repu

tation

Priorities


Quality of product 1 7

Delivery capabilities 1 1/5

Warranty level 1 1

Average price 1 3

Reputation 1


Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y

leve

l

Ave

rage

pr

ice

Repu

tation

Priorities

Relationship closeness 1 4 3 1 3 4

Quality of product 1 7 3 1/5 1

Delivery capabilities 1 1/5 1/5 1/6

Warranty level 1 1 1/3

Average price 1 3

Reputation 1


Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y

leve

l

Ave

rage

pr

ice

Repu

tation

Priorities

Relationship closeness 1 4 3 1 3 4

Quality of product 1/4 1 7 3 1/5 1

Delivery capabilities 1/3 1/7 1 1/5 1/5 1/6

Warranty level 1 1/3 5 1 1 1/3

Average price 1/3 5 5 1 1 3

Reputation 1/4 1 6 3 1/3 1


Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y

leve

l

Ave

rage

pr

ice

Repu

tation

Priorities

Relationship closeness 1 4 3 1 3 4 .32

Quality of product 1/4 1 7 3 1/5 1 .14

Delivery capabilities 1/3 1/7 1 1/5 1/5 1/6 .03

Warranty level 1 1/3 5 1 1 1/3 .13

Average price 1/3 5 5 1 1 3 .24

Reputation 4 1 6 3 1/3 1 .14


A B C Priorities

A 1 9 7 .77

B 1/9 1 1/5 .05

C 1/7 5 1 .17

Warranty level

Prices $ Priorities

A 10 .25

B 5 .50

C 10 .25

A B C Priorities

A 1 6 4 .69

B 1/6 1 1/3 .09

C 1/4 3 1 .22

Average price Reputation

A B C Priorities

A 1 1/3 1/2 .16

B 3 1 3 .59

C 2 1/3 1 .25


A B C Priorities

A 1 1 1 .33

B 1 1 1 .33

C 1 1 1 .33

A B C Priorities

A 1 5 1 .45

B 1/5 1 1/5 .09

C 1 5 1 .46

Quality of product Delivery capabilities

Comparison of suppliers w.r.t. criteria

Composition and synthesis Impact of suppliers on goal

+ +


Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y leve

l

Ave

rage

price

Repu

tation

Composite impact of suppliers

.32 .14 .03 .13 .24 .14

A

B

C


+


Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y leve

l

Ave

rage

price

Repu

tation


.32 .14 .03 .13 .24 .14

A .16 .33 .45 .77 .25 .69

B .59 .33 .09 .05 .50 .09

C .25 .33 .46 .17 .25 .22


Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y leve

l

Ave

rage

price

Repu

tation


.32 .14 .03 .13 .24 .14

A .16 .33 .45 .77 .25 .69 .37

B .59 .33 .09 .05 .50 .09

C .25 .33 .46 .17 .25 .22


Relation

ship

clos

ene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilities

Warr

ant

y leve

l

Ave

rage

price

Repu

tation


.32 .14 .03 .13 .24 .14

A .16 .33 .45 .77 .25 .69 .37

B .59 .33 .09 .05 .50 .09 .38

C .25 .33 .46 .17 .25 .22 .25

Eigenvector solution

A a b c

a 1 0.5 3

b 2 1 4

c 0.33 0.25 1

x/sum a b c

a 0.3 0.286 0.38

b 0.6 0.571 0.50

c 0.1 0.143 0.13

1 1 1

Column normalization

Row average

Sum 3.33 1.75 8.00

w

0.3202

0.5571

0.1226

Normalisation when scores of the alternatives are know

Prices $

A 10

B 5

C 10

Number of deliveries on time

Get the inverse for cost attributes

1/price

A 1/10

B 1/5

C 1/10

sum 0.4

Normalise w.r.t. sum of the column

Priorities

A 0.25

B 0.5

C 0.25

#

A 8

B 7

C 5

sum 20

#

A 8

B 7

C 5

Priorities

A 0.4

B 0.35

C 0.25

Consistency index

λmax

Consistency

0.97

1.69

0.37

3.0186

3.0300

3.0065

3.0183

Aw Aw w

average

CI=

λmax - n

n - 1

Random consistency index

RI=

Consistency ratio

CR = RI

CI

SEE TABLE

n RI

3 0.52

4 0.89

5 1.11

6 1.25

7 1.35

8 1.40

9 1.45

RI

=0.0092

=0.52

=1.76%

.3202

.5571

.1226

w

Group Decision Making

Rela

tion

shi

p cl

osene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilit

ies

War

rant

y le

vel

Ave

rage

pr

ice

Repu

tati

on

Priorities


1 1/5

Quality of product

1


1

Warranty level

1

Average price

1

Reputation

1

Sourcing Manager: “Relationship closeness” is strongly more important than “Quality of product”

Production Manager: Quality of product” is strongly more important than “Relationship closeness”

Rela

tion

shi

p cl

osene

ss

Qua

lity

of

prod

uct

Delive

ry

capa

bilit

ies

War

rant

y le

vel

Ave

rage

pr

ice

Repu

tati

on

Priorities


1 5

Quality of product

1


1

Warranty level

1

Average price

1

Reputation

1


Combined Decision?

Rela

tion

shi

p cl

osen

ess

Qua

lity

of

prod

uct


1 5

Quality of product

1

Rela

tion

shi

p cl

osene

ss

Qua

lity

of

prod

uct


1 1/5

Quality of product

1

Rela

tion

shi

p cl

osene

ss

Qua

lity

of

prod

uct


1 ?

Quality of product

1/? 1

Sourcing Manager: “Relationship closeness” is strongly more important than “Quality of product”

Production Manager: Quality of product” is strongly more important than “Relationship closeness”


DM1

very strongly (7) DM2

moderately (3)

Use arithmetic mean to combine decisions?

A B

A 1 X

B 1/X 1

X = (7+3)/2 = 5 1/X = (1/7+1/3)/2 = 0.24 ≠ 1/5

Use geometric mean to combine decisions?

X = √(7*3) = 4.58 1/X = √(1/7*1/3) = 0.22 = 1/4.58


a b c

a 1 0.5 3

b 2 1 4

c 0.33 0.25 1

a b c

a 1 1 0.25

b 1 1 3

c 4 0.33 1

a b c

a 1 0.707 0.866

b 1.414 1 3.464

c 1.155 0.289 1

Combine preferences

DM1 DM2

DM1&DM2

AHP Rating Evaluating Employees for Raises

Criteria Dependability Education Experience Attitude Leadership

w 15.50% 24.00% 13.80% 17.20% 29.50%

Dependability

Outstanding .48 1

Very good .28 .58

Good .16 .33

Average .05 .10

Unsatisfactory .03 .06

rating intensities



w 15.50% 24.00% 13.80% 17.20% 29.50%

Education

Doctorate .59 1

Masters .25 .42

Bachelors .11 .19

High school .05 .08

rating intensities



w 15.50% 24.00% 13.80% 17.20% 29.50%

Experience

> 15 years .61 1

6 – 15 years .25 .41

3 – 5 years .10 .16

< 3 years .04 .07

rating intensities



w 15.50% 24.00% 13.80% 17.20% 29.50%

Attitude

Enthused .49 1

Very good .26 .53

Good .14 .29

Average .08 .16

Bad .03 .06

rating intensities



w 15.50% 24.00% 13.80% 17.20% 29.50%

Leadership

Good .66 1

Average .29 .44

Bad .05 .08

rating intensities


Candidate Dependability

15.50% Education 24.00%

Experience 13.80%

Attitude 17.20%

Leadership 29.50%

1 Outstanding Doctorate > 15 years Enthused Good

2 Average Masters < 3 years Enthused Good

3 Good Bachelors > 15 years Very good Bad

4 Good Masters 3 - 5 years Very good Good

5 Average Bachelors 3 – 5 years Good Average

6 Outstanding Masters < 3 years Very good Average

7 Outstanding Bachelors 6 – 15 years Good Average

8 Very good Masters 6 – 15 years Average Good

9 Outstanding Masters 3 – 5 years Very good Average

10 Very good Doctorate 6 – 15 years Good Average

11 Unsatisfactory Bachelors 6 – 15 years Good Average

12 Very good Bachelors 3 – 5 years Enthused Good

13 Good Doctorate > 15 years Enthused Good

14 Good High school 3 – 5 years Very good Average

15 Outstanding Doctorate < 3 years Very good Average


Candidate Dependability

15.50% Education

24.00% Experience

13.80% Attitude

17.20% Leadership

29.50% Total Points

1 1 1 1 1 1 1

2 .10 .42 .07 1 1 .59

3 .33 .19 1 .53 .08 .35

4 .33 .42 .16 .53 1 .56

5 .10 .19 .16 .29 .44 .26

6 1 .42 .07 .53 .44 .49

7 1 .19 .41 .29 .44 .44

8 .58 .42 .41 .16 1 .57

9 1 .42 .16 .53 .44 .50

10 .58 1 .41 .29 .44 .57

11 .06 .19 .41 .29 .44 .29

12 .58 .19 .16 1 1 .62

13 .33 1 1 1 1 .90

14 .33 .08 .16 .53 .44 .32

15 1 1 .07 .53 .44 .62


Candidate Total Points

1 1

13 .90

12, 15 .62

2 .59

8, 10 .57

4 .56

9 .50

6 .49

7 .44

3 .35

14 .32

11 .29

5 .26

Softwares

Super Decisions www.superdecisions.com

Expert Choice www.expertchoice.com

Decision Lens www.decisionlens.com

Next Class

• Tomorrow!!

• Topic: Location Strategy

the analytic hierarchy process - İtÜ · 2012. 6. 4. · selecting the best material supplier to...

Documents