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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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