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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
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.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
Relationship closeness
Quality of product
Delivery capabilities
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
Relationship closeness
Quality of product
Delivery capabilities
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
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 Moderately -
strongly
Quality of product 1
Delivery capabilities 1
Warranty level 1
Average price 1
Reputation 1
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 4
Quality of product 1
Delivery capabilities 1
Warranty level 1
Average price 1
Reputation 1
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 4
Quality of product 1 Very
strongly
Delivery capabilities 1 2.nd element
strongly
Warranty level 1 Equal
Average price 1 Moderately
Reputation 1
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 4
Quality of product 1 7
Delivery capabilities 1 1/5
Warranty level 1 1
Average price 1 3
Reputation 1
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 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
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 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
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 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
Comparison of criteria w.r.t. goal
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
Relationship closeness
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
+ +
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
Composition and synthesis Impact of suppliers on goal
+
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 .16 .33 .45 .77 .25 .69
B .59 .33 .09 .05 .50 .09
C .25 .33 .46 .17 .25 .22
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 .16 .33 .45 .77 .25 .69 .37
B .59 .33 .09 .05 .50 .09
C .25 .33 .46 .17 .25 .22
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 .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
Relationship closeness
1 1/5
Quality of product
1
Delivery capabilities
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
Relationship closeness
1 5
Quality of product
1
Delivery capabilities
1
Warranty level
1
Average price
1
Reputation
1
Group Decision Making
Combined Decision?
Rela
tion
shi
p cl
osen
ess
Qua
lity
of
prod
uct
Relationship closeness
1 5
Quality of product
1
Rela
tion
shi
p cl
osene
ss
Qua
lity
of
prod
uct
Relationship closeness
1 1/5
Quality of product
1
Rela
tion
shi
p cl
osene
ss
Qua
lity
of
prod
uct
Relationship closeness
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”
Group Decision Making
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
Group Decision Making
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
AHP Rating Evaluating Employees for Raises
Criteria Dependability Education Experience Attitude Leadership
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
AHP Rating Evaluating Employees for Raises
Criteria Dependability Education Experience Attitude Leadership
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
AHP Rating Evaluating Employees for Raises
Criteria Dependability Education Experience Attitude Leadership
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
AHP Rating Evaluating Employees for Raises
Criteria Dependability Education Experience Attitude Leadership
w 15.50% 24.00% 13.80% 17.20% 29.50%
Leadership
Good .66 1
Average .29 .44
Bad .05 .08
rating intensities
AHP Rating Evaluating Employees for Raises
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
AHP Rating Evaluating Employees for Raises
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
AHP Rating Evaluating Employees for Raises
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