a. wahyudi + 1 ahp analytical hierarchy process ahp analytical hierarchy process rediscussed by a....
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AHPAHPANALYTICAL HIERARCHY PROCESSANALYTICAL HIERARCHY PROCESS
Rediscussed byA. Wahyudi Atmoko
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Question when Using AHP?
1.1. What is the problem fitting for AHP?What is the problem fitting for AHP?
2.2. What is the AHP model?What is the AHP model?
3.3. How to collect & analysis data?How to collect & analysis data?
4.4. What’s the AHP result?What’s the AHP result?
5.5. Overview.Overview.
6.6. Case exercise.Case exercise.
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Thomas L. SaatyThomas L. Saaty
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Did you ever find these problem?
• Planning & Strategy DevelopmentPlanning & Strategy Development
• Resources AllocationResources Allocation
• Conflict ResolutionConflict Resolution
• Cost & Benefit AnalysisCost & Benefit Analysis
• Group Decision MakingGroup Decision Making
• ForecastingForecasting
• Etc. Etc.
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When you face those problems, what factors do you have to look before deciding a decision? How many alternatives are available in your decision making?
How do you choose an alternative among others?
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AHPSynthesis
Deductive & Inductive Thinking
Synthesis qualitative information & numerical processing using matrix manipulation from ordinal scale.
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AHPSynthesis
Deductive & Inductive Thinking
Synthesis qualitative information & numerical processing using matrix manipulation from ordinal scale.
and
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Case
XYZ University plans to develop organization strategy. Few factors are believed will affect the organization strategy, namely:
1) Purchasing power for post graduate declines.2) Skilled labors are more needed.3) The best of brand name & campus location.4) High competition in D3 program
Which strategy should be choose among these alternative, namely:1) Cost Leadership2) Focus3) Differentiation
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Hierarchy
Purchasing Power
0.29
Skilled Labors
0.55
Brand Name & Location
0.10
High Competition
0.06
Cost Lead.
0.43
Focus
0.33
Differentiation
0.24
XYZ UNIVERSITY STRATEGY DEV.FOCUS:
CRITERIA:
ALTERNATIVES:
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Focus:
Fakcor:
Akcor:
Goal:
Alternatives:
STRATEGI PENGEMBANGAN SDMMELALUI PELATIHAN
SDM teknologi manajemen
pemilik Tenaga kerja pimpinan depnaker
Peningkatanproduktivitas
Peningkatanomzet
Pengemb.karir
Agenpembangunan
materi metoda pelaksanaanTindaklanjut
konsultan
(Sumber: Syamsul Maarif, 2005)
Hierarchy
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Focus:
Scenario:
Factor:
Alternatives:
KEPUTUSAN KEUANGAN
Pesimistik Status Quo Optimistik
PeningkatanDiversivikasi
PotensiPertumbuhan
Posisi PasarYg Kuat
Kebebasan drEkonomi Internl
Proyek A Proyek B Proyek C Proyek D
Fiskal
Hierarchy
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Steps in AHP
Focus
System Identification
DeductiveInductive
Design Hierarchy
Survey:(Individual Matrix)
CRfit
CalculateAggregate Matrix
Vertical Calculation
Horizontal Calculation
Choose Priority
YesA
Revision
No
A
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Value Remarks
1
3
5
7
9
2, 4, 6, 8
reciprocal
A is as important as B
A is more important than B
A is clearly more important than B
A is almost absolutely more important than B
A is absolutely more important than B
Value in between
If i element has a value (one among values above) when compared with j element, so j element has the opposite values of i element.
Ordinal ScaleOrdinal Scale
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Individual Matrix
USD PP SL BL HC
PP 1 1/3 4 6
SL 3 1 5 7
BL 1/4 1/5 1 2
HC 1/6 1/7 1/2 1
Interpretation:PP = 4 x BL SL = 3 x PPPP = 6 x HC SL = 5 x BL, etc.
Questionnaire: Seberapa penting (kali lebih . . . ) Pk dibandingkan Pm dalam pengembangan universitas?
PP = Purchasing
Power
SL =Skilled Labors
BL =Brand Name & Location
HC =High
Competition
USD = XYZ UNIVERSITY
STRATEGY DEV.
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Horizontal Calculation
PriorityValue
USD PP SL BL HC VE VP VA VB
PP 1 0.33 4 6 1.68 0.29 1.21 4.15
SL 3 1 5 7 3.20 0.55 2.32 4.18
BL 0.25 0.2 1 2 0.56 0.10 0.40 4.06
HC 0.17 0.14 0.5 1 0.33 0.06 0.23 4.08
5.78 16.47
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Step:
VE1 = √ ∏ aij
n
J=1
n
VE1 = √(1 x 1/3 x 4 x 6) = 1.684
1. Row calculation (VE):
Exp.:
VP1 = 1.68/5.78 = 0.29
Exp.:
2. Priority Vector calculation (VP):
VP =VE
∑VE
Horizontal Calculation
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Find CI & CR
3. Calculate maximum eigen value:
Exp.:
Exp.:
VA & VB = Intermediary Vector
VA = aij x VP
VA1 = 1(0.29) + 1/3(0.55) + 4(0.10) + 6(0.06) = 1.21
VB =
VB1 = 1.21/0.29 = 4.15
VA
VP ð max =
a)
b)
Horizontal Calculation
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ð max =∑VB
n
c)
ð max = 16.47/4 = 4.12 Exp.:
4. Calculate Consistency Index (CI)
CI =ð max - n n-1
Exp.:
CI = (4.12-4)/(4-1) = 0.04
a)
Horizontal Calculation
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TABLE RI (THOMAS L. SAATY)n RI n RI12345678
0.000.000.580.901.121.241.321.41
9101112131415
1.451.491.511.481.561.561.59
CR =CI
RI
b)
CR = 0.04/0.90 = 0.04Exp.: Formulation
CR > 10% = Not Consistent
Horizontal Calculation
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How if CR ‘s not consistent
Exp. : Sa Si Su
Sa 1 8 6 0.75 W1matrix X = Si 1/8 1 1/4 0.07 W2 Su 1/6 4 1 0.18 W3
CR = 11.69 % matrix x needs revision
CR > 10% = Not Consistent
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a12
Sa Si Su Sa 1 8 6 0.75 W1
matrix X = Si 1/8 1 1/4 0.07 W2 Su 1/6 4 1 0.18 W3
Vector Priority (W1, W2, W3) = (0.75, 0.07, 0.18)
Difference between two absolute values a12 & w1/w2 aij wi/wj
a12 w1/w2 = 0.75 = 12 0.07
How if CR ‘s not consistent
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a12
Sa Si Su Sa 1 12 6 0.78
Si 1/12 1 1/4 0.05 Su 1/6 4 1 0.16
Revision
CR = 5% Consistent
How if CR ‘s not consistent
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Vertical Calculation
PP CL FC DF VE VP VA VB dMax CI RI CR
CL 1 0.25 2 0.79 0.19 0.58
3.01
3.01 0.005 3 0.01
FC 4 1 6 2.88 0.70 2.11
3.01 0.58
Consistent
DF 0.5 0.17 1 0.44 0.11 0.32
3.01
4.11 9.03
SL CL FC DF VE VP VA VB dMax CI RI CR
CL 1 5 3 2.47 0.65 1.95
3.00
3.00 0.002 3 0.00
FC 0.2 1 0.5 0.46 0.12 0.37
3.00 0.58
Consistent
DF 0.33 2 1 0.87 0.23 0.69
3.00
3.80 9.01
PrioritasLokal
CL = Cost Leadership; FC = Focus; DF = Differentiation
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BL CL FC DF VE VP VA VB dMax CI RI CR
CL 1 0.33 0.13 0.35 0.08 0.24
3.02
3.02 0.009 3 0.02
FC 3 1 0.25 0.91 0.21 0.62
3.02 0.58
Consistent
DF 8 4 1 3.17 0.72 2.16
3.02
4.43 9.05
HC CL FC DF VE VP VA VB dMax CI RI CR
CL 1 0.17 0.25 0.35 0.09 0.26
3.05
3.05 0.027 3 0.05
FC 6 1 3 2.62 0.64 1.97
3.05 0.58
Consistent
DF 4 0.33 1 1.10 0.27 0.83
3.05
4.07 9.16
Local Priority
CL = Cost Leadership; FC = Focus; DF = Differentiation
Vertical Calculation
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PP SL BL HC
CL 0.19 0.65 0.08 0.09 PP 0.29 CL 0.43
FC 0.70 0.12 0.21 0.64 SL 0.55 FC 0.33
DF 0.11 0.23 0.72 0.27 BL 0.10 DF 0.24
HC 0.06Local Priority
Global Priority
XX ==
Vertical Calculation
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Calculate Aggregate Matrix
Respondent 1 Respondent 3
X1 Na Ni Nu X1 Na Ni Nu
Na 1 0.25 2 Na 1 0.33 0.13
Ni 4 1 6 Ni 3 1 0.25
Nu 0.5 0.17 1 Nu 8 4 1
Respondent 2 Respondent 4
X1 Na Ni Nu X1 Na Ni Nu
Na 1 5 3 Ni 1 0.17 0.25
Ni 0.2 1 0.5 Nu 6 1 3
Nu 0.33 2 1 CSR 4 0.33 1
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Aggregate Matrix
X1 Na Ni Nu
Na 1 0.51 0.66
Ni 1.95 1 1.22
Nu 1.52 0.82 1
Aggregate Matrix Formulation:
gij = √ ∏ aij
Remarks: Before calculating aggregate matrix, be sure that individual matrix per respondent
is consistent.
gij = √ (0.25 x 0.33 x 5 x 0.17) = 0.51
Exp.:
n
4
Calculate Aggregate Matrix
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