1. 決策分析, Decision Analysis 講義 輔助資料 企業管理學系, 黃 興 錫 94. 10. 14.
決策分析, 
Decision Analysis 
講義 輔助資料
Kainan University
企業管理學系,   黃  興 錫

2. Contents 1. AHP /Fuzzy AHP Method and It’s Application Practices :
- Three-step Approach of Decision Alternative Analysis,
Project Risk Analysis Models
- Model Application to School Food Service System
- Summary and Conclusions
* Exercise AHP Application in real problem
2. Discussion for Term Project Topics
- Proposal form
- Suggest some Topics

3. 1. AHP and Fuzzy-AHP Method 要約
AHP : Analytic Hierarchy Process
1) AHP 紹介
     2) AHP Model的 適用
       ) 階層的 評價構造 設計
          2.2) 固有値 優先 順位 決定
          2.3) 雙比較 評價的 一貫性 檢證
     3) 爲意思決定評價  應用
     4) 爲意思決定評價 綜合優先順位決定模型
     5) Fuzzy set AHP Model
          5.1) Fuzzy set Model
          5.2)  應用 例題
     6) 結 論 -

4. - 意思結定分析 評價 時 全 階層的 意思決定 考慮
1) AHP 槪要
- 意思結定分析 評價 時 全 階層的 意思決定 考慮
- AHP技法 Saaty(1980) 創始
- AHP方法是 代案 評價分析 方法,
多目的(Multi-Object),
多 評價基準(Multi-criterion),
多 主體(Multi-Actor),
多 屬性(Multi-Attribute),
多 段階 (Multi-Level) 評價 方法
- 上位係層的 評價基準 使用
下位構造的 平家因子的 相對的 優位程度 算出,
雙比較 行列(Pair-wise Comparison Matrix) 算出,
傳遞階層的 複合比重 Vector 算出,
固有値(Eigen Value)問題 -

5. - AHP 方法是 使用上位階層的 平價基準, 下位構組
平家因子的 相對的 優位程度 算出,
雙比較(Pair-wise Comparison) 傳遞階層的 複合比重
Vector 算出; 固有値(Eigen Value)
-  爲 AHP技法 使用的 問題 解決, Saaty(1980) 3個 原理
提案(隨行節次 ) :
          ․ 分解(Decomposition)
          ․ 比較判斷(Comparative Judgment)
(雙比較 行列(Pair-wise Comparison Matrix) 算出
          ․ 優先 順位 決定(Comparative Priorities) -

6. AHP技法 實際 意思決定分析問題, 評價 適用 段階 (問題 定意, Problem Definition)
  2) AHP Model 適用
AHP技法 實際  意思決定分析問題, 評價 適用 段階
    段階 1: 意思決定要素的 階層的 評價構造 選定  
(問題 定意, Problem Definition)          
   段階 2: 意思決定要素的 雙比較 Matrix 作成       
  段階 3: 階層間 意思決定要素的 相對的 加重値算定
               意思決定代案的 優先順位 決定                    
   段階 4: 一貫性 檢證           -

7. (1) 階層的 構造 設計 係層 2 思決定屬性 係層 3 思決定對案 係層 4 係層 1 意思決定問題的 胞括 分析目標 意思決定屬性 n
(1) 階層的 構造 設計 2
意思決定問題的
胞括 分析目標
意思決定屬性 1
思決定屬性
思決定對案 n
係層 1
係層 2
係層 3
係層 4 -

8. ２．固有Value 優先順位(Eigen-value)
雙比較行列(Pair-wise Comparison Matrix) 作成
雙比較行列 Matrix :
A = (aij),   i = 1, 2, …, n
If 屬性 i is better than j , aij → 1 ~ 9
(Saaty’s 9 Garding Values) -

9. 3.3 Fuzzy -AHP Method
☞ The concepts and rules of fuzzy decision making provide us with
the necessary tools for structuring a decision from a kind of
information.
☞ From the Shannon's summed frequency matrix for complementary
cells,
☞ an additional fuzzy set matrix was made by considering = 1 –
for all cells. The fuzzy matrix complement cell values sum to 1 and
fuzzy set difference matrix is defined as follows :
= U(A, B)-U(B, A), if U(A, B) > U(B, A),
= otherwise
where, for U(A, B) quantifies, A is preferable to B. -

10. Five Steps Fuzzy AHP :
To obtain fuzzy preferences, the following five steps were considered:
Step 1 : Find the summed frequency matrix ( using Shannon method )
Step 2 : Find the fuzzy set matrix R which is the summed frequency
matrix divided by the total number of evaluators
Step 3 : Find the difference matrix
= U(A, B)-U(B, A), if U(A, B) > U(B, A),
= otherwise
where, for U(A, B) quantifies, A is preferable to B.
Step 4 : Determine the portion of each project that is not dominated
as follows :
= 1 - max( , , … , )
Step 5 : The priority of the fuzzy set is then the rank order of XND
values with a decreasing order.

11. An example is shown as follows := =

12. = 1 - Max(0.0) = = 1.0
= 1 - Max(1.0) = = 0.0
= 1 - Max(0.2) = = 0.8
The fuzzy set priority score : > 0.0 > 0.8 > 0.8
and the alternative priority : A > C > D > B.

13. ☞ For the integration of the results of individual evaluations,
3.3 Integration of Individual Evaluation
☞ For the integration of the results of individual evaluations,
prioritized sets, we used two Heuristic models 1, Model 2 and
Fuzzy set priority method
1) Heuristic Model 1 :
For example of the Heuristic Method 1, a sample result with
N = 5 evaluators and M = 3 alternatives is given as :
Evaluator 1 : B > A > C, Evaluator 2 : B > C > A,
Evaluator 3 : C > A > B, Evaluator 4 : C > B > A,
Evaluator 5 : C > B > A

14. ☞ Heuristic Method 1 rank order is given by
C(0.467) > B(0.400) > A(0.133).

15. 2) Heuristic Model 2 :
- The evaluator frequency matrices were added to form a summed
frequency matrix
- Then, the preference matrix was developed by a comparison of the
scores in the component cells(A, B versus B, A).
- If the A, B value equals B, A, then each component cell in the matrix
is given by 1/2. On the other hand if the A, B value is greater than the
B, A , then A, B is given by one and B, A cell of the preference matrix
is given by 0.
☞ By applying the Heuristic Model 2 to the same example of
Heuristic Method 1, the result is given by
C(0.450) > A(0.392) > B(0.158) .

16. 3) Fuzzy Set Priority Method
. The fuzzy matrix complement cell values sum to 1 and fuzzy
set difference matrix is defined as follows :
R-RT = U(A, B) - (B, A), if U(A, B) > U(B, A),
= 0, otherwise
To obtain fuzzy preferences, following five steps are considered :
Step 1 : Find the summed frequency matrix (using heuristic method 2)
Step 2 : Find the fuzzy set matrix R which is the summed frequency matrix
divided by the total number of evaluators
Step 3 : Find the difference matrix
R - RT = U(A, B) - U(B, A), if U(A, B) > U(B, A),
= 0, otherwise
where, for U(A, B) quantifies, A is preferable to B.
Step 4 : Determine the portion of each part
Step 5 : The priority of the fuzzy set is then the rank order of values in
decreasing.
The sample problem result by fuzzy set priority method is given by
C(0.492) > B(0.387) > A(0.121).

17. ☞ 3.4 In ternet /intranet Based Solution Builder
for Decision Support System -
Brainstorming
AHP,
Fuzzy
AHP
Aggregate
Priorities
3-step Algorithm for Optimal Solution
Figure 2. 3
step
approach o f
Decision Support System ☞
Developed a
solution builder using
GUI
type Simulation
Software.
Three steps of
this
solution builder . 6

18. Figure 4. Client and Server in Decision Support System

19. Fig 6. Schematic Flow Diagram of the Proposed Model

20. The GUI-type program of Solution Builder-2001

21. Figure 5. Main-program of Solution Builder 2001

22. ☞ We used a brainstorming method and developed a GUI-type program

23. School Food Service Sys.Performanc
☞ Sample Example 1 :
Sample Output of School Food Service System Problem
1) Step 1 : Brainstorming
Quality
Product
Flexibility
School Food Service Sys.Performanc
Cost

25. School Food Service Sys. Performance4
2) Step 2 : AHP
Level 1
School Food Service Sys. Performance4
Level 2
Cost
Quality
Product Flexibility
Level 3
Out Sourcing
Partial Ownership
Short Term Contract
Make

26. School Food Service problem
Del OK PM
Level
Title

27. Table 4. Sample Output of Pair-wise Matrix
Eigen Val. B1
1.00
2.00
4.00
0.71
=3.09 B2
0.50
1.00
5.00
0.21
Cl=0.0815 B3
0.25
0.20
1.00
0.08
CR=0.14 B1 C1 C2 C3 C4
Eigen Val C1
1.00
0.33
0.50
0.50
0.17 C2
3.00
1.00
1.00
2.00
0.34
=5.760 C3
2.00
1.00
1.00
1.00
0.26
Cl=0.190 C4
2.00
0.50
1.00
1.00
0.23
CR=0.170 B2 C1 C2 C3 C4
Eigen Val C1
1.00
2.00
4.00
5.00
0.44 C2
0.50
1.00
3.00
7.00
0.30
=5.107 C3
0.25
0.33
1.00
5.00
0.19
Cl=0.0275 C4
0.20
0.14
0.20
1.00
0.07
CR=0.024 B3 C1 C2 C3 C4
Eigen Val C1
1.00
3.00
9.00
4.00
0.53 C2
0.33
1.00
1.00
1.00
0.19
=5.760 C3
0.11
1.00
1.00
3.00
0.17
Cl=0.190 C4
0.25
1.00
0.33
1.00
0.11
CR=0.170

28. ☞ Final Weighted Value of Each Alternative :
Cost
Make B 1 2 3 C 4
Product
Flexibility
0.17
0.44
0.53
0.34
0.30
0.19
0.26
0.23
0.07
0.11 B1 B2
0.14
School Food Service
Sys. Performance
Quality
Out Sourcing
Partial
Ownership A
0.71
0.21
0.08
0.38
0.27
Short Term
Contract
☞ Final Weighted Value of Each Alternative :
(0.38)
(0.27)
(0.21)
(0.14)
>

29. 3) Step 3 : Integration of Individual Evaluations :
☞ In this step, we integrated the results of the reviewers by
the majority rule. The individual results of 4 reviewers are given by
Reviewer 1 : C1 > C3 > C2 > C4
Reviewer 2 : C2 > C1 > C3 > C4
Reviewer 3 : C2 > C1 > C3 > C4
Reviewer 4 : C1 > C2 > C4 > C3
☞ Using the Heuristic 1, Heuristic 2 and Fuzzy Set Ranking
Method, We integrated as following :
Table 5. Results of Integrated Priority
Majority Rule used
Priority by Alternative
1. Heuristic model 1
C2 > C1> C3 > C4
2. Heuristic model 2
C1 > C2> C4 > C3
3. Fuzzy Set Ranking Method
C1 > C2> C3 > C4

30. ☞ Sample Example 2 :
Sample Output of New School Selection Problem

31. - Alternative Evaluation Using AHP

32. ☞ A sample output pair-wise matrix of sample problem
Table 1. Pair-wise Comparison Matrix

33. ☞ the final result of school selection AHP which is given by
School B(0.378) > School A(0.367) > School C(0.254).

34. The AHP Result of School Selection Problem
Figure 9. The AHP Result of School Selection Problem
The AHP Result of School Selection Problem

35. ☞ Heuristic Method 1 rank order is given by
C(0.467) > B(0.400) > A(0.133).

36. ☞ A sample output pair-wise matrix of sample problem
Table 1. Pair-wise Comparison Matrix

37. ☞ the final result of school selection AHP which is given by
School B(0.378) > School A(0.367) > School C(0.254).

38. The AHP Result of School Selection Problem
Figure 9. The AHP Result of School Selection Problem
The AHP Result of School Selection Problem

39. 2. Project Risk Analysis 1) Project Risk Facets
Figure 2. Three Steps of Risk Analysis

40. Figure 3. Project Risk in Life Cycle

41. 2) PROJECT RISK ANALYSIS MODELS
. Normally project risk can be assessed by
following factors :
①  Contribution to project performance,
②  Technical validity,
③  Economic effect,
④  Systematic validity.

42. Figure 4. Project Risk Structure

43. Figure 5. Risk Identification

44. 3) Risk Factor Analysis Method
In this study, we proposed two practical risk analysis models :
1) risk factor analysis model, and
2) network simulation model[6] are given as following.
A Deterministic model based on risk factor analysis method using a scoring
method, such as AHP(Analytic Hierarchy Process)[4] weighted value.
Four steps of this method is given by :
Step 1 : construct the evaluation items and evaluate each items
in the evaluating form using -2∼+2 scoring scale,
Step 2 : compute the AHP weighted value of each evaluation items and
compute the weighted score of each evaluation item,
Step 3 : compute the total evaluation score of each major evaluating items
considering following items(in this study, we used for items as following)
- industrial improvement feasibility,
- technical feasibility,
- economical feasibility,
- institutional feasibility
Step 4 : compute the risk using probability scale

46. PF· PT · PE · PI=PE PF · PT · PE · PI=PE
Base Case
Post-research
PF· PT · PE · PI=PE PF · PT · PE · PI=PE
0.93×0.85×0.93×0.93= ×0.89×0.94×0.94=0.74

47. 4) Stochastic Network Simulation Method
Figure 6. Schematic Structure of Stochastic Network Simulation Model

48. Figure 7. Sample Output for Time/Cost.

49. Figure 8. Project Block Diagram
5) MODEL APPLICATION
A new manufacturing system development :
- In the advanced development step after successful completion of its 3
years basic research.
- The system consisted of a main body and three sub-systems(A, B, C).
- The main body is planned to develop in house, and three censers will be
imported. The project block diagram is given as Figure 8.
Figure 8. Project Block Diagram
Four sub-systems ;
new-CNC, Auto-assembler, main-body, and sensers.
- The detail network flow of this system is shown in Figure 9

50. Figure 9. The detail Network Flow Diagram of Sample System

51. Figure 10. Cost/Time Diagram

53. 5. CONCLUSION
☞ In this research, developed a three-step approach based on
web-based make-or-buy decision model for multi-structured
decision support systems
☞ Those steps are :
1) brainstorming to define the alternatives and performance
evaluation factors,
2) individual evaluation the alternatives using fuzzy-AHP, heuristic
and fuzzy set reasoning methods, and
3) integration the individual evaluations using majority rule method.
☞ Developed a Risk Analysis Model considering (1) the schedule,
(2) cost and (3) performance risks.
☞ For a simple and efficient computation, we developed a systematic
and practical web-based program to calculate all the algorithms.
☞ The model was applied to a school food service system problem by
comparative computations for various multi-structured decision
support examples.

54. Exercise AHP Application
* Ref : Software : SB2003
- Brainstorming ,
- AHP,
- Integration

55. Exercise AHP Application
AHP Applications :
    ▪ Personal Purposes
    ▪ Business Strategic Planning
    ▪ Public Strategic Planning
    ▪ Military Policies Analysis
    ▪ Busyness Project Selections
    ▪ R&D Project Selections
    ▪ Cost/Eff. Analysis
    ▪ Internet-based Brain storming
       - Group Decision Analysis System
       - Internet Connection
       - Encoding Decoding Method Analysis

56. 1. Personal Purposes - How to select School for his environments
1.1 School Selection Problem
 -  How to select School for his environments
      Select one Alternative :  A univ,  B univ,  C univ,  D univ,
      Select Criteria :  Education System, 
                       Friendship, Campus Life,
                       School fee,
                       Career Management (Job Application Schedule),
                       Transportation
-  For the Best Alternative :
                    Brainstorming Method Used : Alternative Derive
                    AHP Method : Analysis Alternatives (Compute
Weighted Value)

57. Fig : Brainstorming Main Menu of Solution Builder
Main Manu of School Selection Problem –
Brainstorming Menu

58. - Click “Obj” Node -  “School Selection ” Then select Criteria
for School Selection
Fig.  Problem Define

59. - Connect Six Criteria to Main Node ( School Selection)
Fig.  Select Criteria

60. - Result of Selection Criteria And an Alternative
Fig.  Alternative Derived

61. Then read the Brainstorming Data in the Mauin
- Save the Results of Brainstorming
Then read the Brainstorming Data in the Mauin      
Solution Builder Yuo can see AHP Structure
(Automatically Converted)
   
 This Alternative - Model 3
      In Level 1 :  Problem Final Objective
      In Level 2 :  6 Criteria
      In Level 3 : School Alternative

62. Fig. Result of data Read from Brainstorming File

63. - Select Each Node of Each Level and Input the Data for
the Weighted Values as
Fig. Data Input Frame

64. - Data input by each Node
  Index of Consistency CR = 0.229
Fig. Data Input Frame

67. Software : SB2003
- Brainstorming ,
- AHP,
- Integration )

68. Thank You
Kainan University
企業管理學系,
敎授  黃  興 錫