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Kainan University 企業管理學系 , 黃 興 錫

決策分析 , Decision Analysis 講義 輔助資料. 94. 10. 14. Kainan University 企業管理學系 , 黃 興 錫. Contents 1. AHP /Fuzzy AHP Method and It ’ s Application Practices : - Three-step Approach of Decision Alternative Analysis, Project Risk Analysis Models

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Kainan University 企業管理學系 , 黃 興 錫

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  1. 決策分析, Decision Analysis 講義 輔助資料 94. 10. 14. 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 2.1) 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. 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. 2) AHP Model 適用 AHP技法 實際  意思決定分析問題, 評價 適用段階 -

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

  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 ☞ Theconcepts 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), = 0 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 thesummed 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), = 0 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 - 0.0 = 1.0 = 1 - Max(1.0) = 1 - 1.0 = 0.0 = 1 - Max(0.2) = 1 - 0.2 = 0.8 = 1 - Max(0.2) = 1 - 0.2 = 0.8 The fuzzy set priority score : 1.0 > 0.0 > 0.8 > 0.8 and the alternative priority :A > C > D > B.

  13. 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 ☞ Developed a solution builder using GUI - type Simulation Software. ☞ Three steps of this solution builder . 3-step Algorithm for Optimal Solution Aggregate Aggregate AHP, AHP, Brainstorming Brainstorming Fuzzy Fuzzy - - AHP AHP Priorities Priorities - - - - Figure 2. 3 - step approach o f Decision Support System 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 Cost Product Flexibility Quality ☞ Sample Example 1 : Sample Output of School Food Service System Problem 1) Step 1 : Brainstorming

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

  25. Title Level School Food Service problem Del OK PM

  26. Table 4. Sample Output of Pair-wise Matrix A B1 B2 B3 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

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

  28. 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 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

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

  30. - Alternative Evaluation Using AHP

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

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

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

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

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

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

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

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

  39. Figure 3. Project Risk in Life Cycle

  40. 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.

  41. Figure 4. Project Risk Structure

  42. Figure 5. Risk Identification

  43. 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

  44. -2 -1 0 1 2 Base Case Post-research .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 PF· PT · PE · PI=PE PF · PT · PE · PI=PE 0.93×0.85×0.93×0.93=0.70 0.94×0.89×0.94×0.94=0.74

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

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

  47. 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

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

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