Kainan University,

, Decision Analysis

94. 10. 14.

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

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) -

- AHP , , (Pair-wise Comparison) Vector ; (Eigen Value) - AHP , Saaty(1980) 3 ( ) : (Decomposition) (Comparative Judgment) ( (Pair-wise Comparison Matrix) (Comparative Priorities) -

- 2) AHP Model AHP ,

1: ( , Problem Definition) 2: Matrix 3: 4:

- (1)

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. -

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.

An example is shown as follows :

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

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

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) .

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

Fig 6. Schematic Flow Diagram of the Proposed Model

The GUI-type program of Solution Builder-2001

Figure 5. Main-program of Solution Builder 2001

We used a brainstorming method and developed a GUI-type program

Sample Example 1 : Sample Output of School Food Service System Problem1) Step 1 : Brainstorming

School Food Service Sys. Performance4 Cost Quality Product FlexibilityOut Sourcing Partial Ownership Make Short Term ContractLevel 1Level 3Level 22) Step 2 : AHP

Table 4. Sample Output of Pair-wise Matrix

Final Weighted Value of Each Alternative :

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 :

Sample Example 2 : Sample Output of New School Selection Problem

- Alternative Evaluation Using AHP

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

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

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

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

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

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

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

Figure 2. Three Steps of Risk Analysis1) Project Risk Facets 2. Project Risk Analysis

Figure 3. Project Risk in Life Cycle

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

Figure 4. Project Risk Structure

Figure 5. Risk Identification

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

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

Figure 7. Sample Output for Time/Cost.

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

Figure 9. The detail Network Flow Diagram of Sample System

Figure 10. Cost/Time Diagram

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.

Exercise AHP Application

* Ref : Software : SB2003 - Brainstorming , - AHP, - Integration

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

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)

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

- Click Obj Node - School Selection Then select Criteria for School Selection

Fig. Problem Define

- Connect Six Criteria to Main Node ( School Selection)

Fig. Select Criteria

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

- 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

Fig. Result of data Read from Brainstorming File

- Select Each Node of Each Level and Input the Data for the WeightedValues as Fig. Data Input Frame

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

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

Thank YouKainan University

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