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Kainan University 企業管理學系 , 黃 興 錫
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Transcript of Kainan University 企業管理學系 , 黃 興 錫
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Kainan University,
, Decision Analysis
94. 10. 14.
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Contents 1. AHP /Fuzzy AHP Method and Its 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
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1. AHP and Fuzzy-AHP Method AHP : Analytic Hierarchy Process 1) AHP 2) AHP Model 2.1) 2.2) 2.3) 3) 4) 5) Fuzzy set AHP Model5.1) Fuzzy set Model 5.2) 6)
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1) AHP
- - AHP Saaty(1980) - AHP , (Multi-Object), (Multi-criterion), (Multi-Actor), (Multi-Attribute), (Multi-Level) - , (Pair-wise Comparison Matrix) , Vector , (Eigen Value) -
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- AHP , , (Pair-wise Comparison) Vector ; (Eigen Value) - AHP , Saaty(1980) 3 ( ) : (Decomposition) (Comparative Judgment) ( (Pair-wise Comparison Matrix) (Comparative Priorities) -
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- 2) AHP Model AHP ,
1: ( , Problem Definition) 2: Matrix 3: 4:
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- (1)
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Value (Eigen-value) (Pair-wise Comparison Matrix) Matrix : A = (aij), i = 1, 2, , n If i is better than j , aij 1 ~ 9 (Saatys 9 Garding Values)
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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), = 0 otherwise where, for U(A, B) quantifies, A is preferable to B. -
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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 evaluatorsStep 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.
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An example is shown as follows :
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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
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Heuristic Method 1 rank order is given by C(0.467) > B(0.400) > A(0.133).
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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) .
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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).
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Figure 4. Client and Server in Decision Support System
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Fig 6. Schematic Flow Diagram of the Proposed Model
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The GUI-type program of Solution Builder-2001
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Figure 5. Main-program of Solution Builder 2001
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We used a brainstorming method and developed a GUI-type program
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Sample Example 1 : Sample Output of School Food Service System Problem1) Step 1 : Brainstorming
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School Food Service Sys. Performance4 Cost Quality Product FlexibilityOut Sourcing Partial Ownership Make Short Term ContractLevel 1Level 3Level 22) Step 2 : AHP
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Table 4. Sample Output of Pair-wise Matrix
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Final Weighted Value of Each Alternative :
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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 3) Step 3 : Integration of Individual Evaluations :
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Sample Example 2 : Sample Output of New School Selection Problem
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- Alternative Evaluation Using AHP
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A sample output pair-wise matrix of sample problem Table 1. Pair-wise Comparison Matrix
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the final result of school selection AHP which is given by School B(0.378) > School A(0.367) > School C(0.254).
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Figure 9. The AHP Result of School Selection Problem The AHP Result of School Selection Problem
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Heuristic Method 1 rank order is given by C(0.467) > B(0.400) > A(0.133).
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A sample output pair-wise matrix of sample problem Table 1. Pair-wise Comparison Matrix
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the final result of school selection AHP which is given by School B(0.378) > School A(0.367) > School C(0.254).
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Figure 9. The AHP Result of School Selection Problem The AHP Result of School Selection Problem
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Figure 2. Three Steps of Risk Analysis1) Project Risk Facets 2. Project Risk Analysis
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Figure 3. Project Risk in Life Cycle
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2) PROJECT RISK ANALYSIS MODELS . Normally project risk can be assessed by following factors : Contribution to project performance, Technical validity, Economic effect, Systematic validity.
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Figure 4. Project Risk Structure
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Figure 5. Risk Identification
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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
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4) Stochastic Network Simulation Method Figure 6. Schematic Structure of Stochastic Network Simulation Model
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Figure 7. Sample Output for Time/Cost.
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5) MODEL APPLICATIONA 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.
Four sub-systems ; new-CNC, Auto-assembler, main-body, and sensers. - The detail network flow of this system is shown in Figure 9 Figure 8. Project Block Diagram
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Figure 9. The detail Network Flow Diagram of Sample System
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Figure 10. Cost/Time Diagram
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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.
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Exercise AHP Application
* Ref : Software : SB2003 - Brainstorming , - AHP, - Integration
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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
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1. Personal Purposes 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)
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Fig : Brainstorming Main Menu of Solution Builder Main Manu of School Selection Problem Brainstorming Menu
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- Click Obj Node - School Selection Then select Criteria for School Selection
Fig. Problem Define
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- Connect Six Criteria to Main Node ( School Selection)
Fig. Select Criteria
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- Result of Selection Criteria And an Alternative Fig. Alternative Derived
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- 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
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Fig. Result of data Read from Brainstorming File
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- Select Each Node of Each Level and Input the Data for the WeightedValues as Fig. Data Input Frame
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- Data input by each Node Index of Consistency CR = 0.229 Fig. Data Input Frame
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Software : SB2003 - Brainstorming , - AHP, - Integration )
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Thank YouKainan University
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