Analytic Hierarchy Process (AHP) fundamentals

introduction to analytic hierarchy process

1. Analytic Hierarchy Process (AHP) Nimantha Tharuka

2. Multi Criteria Decision Making Analysis (MCDMA) Involves Individuals subjectively and intuitively considering various factors prior to making a decision.

3. Multifactor Evaluation Process Factor Importance (Weight) IFS MAS KPMG Salary Career Advancement Location

4. Evaluation of IFS   Factor Name Factor Weight Factor Evaluation Weighed Evaluation Salary Career Advancement Location Total

5. Comparison of Results Factor IFS MAS KPMG Salary Career Advancement Location Weighted Evaluation

6. Founded by Dr. Thomas L. Saaty in 1980 Allows the use of qualitative, as well as quantitative criteria in evaluation Wide range of applications exist: Selecting a car for Purchasing Deciding upon a place to visit for vacation Deciding upon the importance of the factors impact to the global supply chains Analytic Hierarchy Process (AHP)

7. Steps of AHP Step 1 – Construction of the Hierarchy Structure (Goal, Criteria, Sub Criteria, Alternatives) Step 2 – Calculation of Factor Weight 1.Pairwise Comparison Matrix 2.Eigenvalue and Eigenvector 3.Consistency test Consistency Index Consistency ratio Step 3 – Calculation of the Level Weight Step 4 – Calculation of overall Ranking

8. Hierarchy Tree

9. Pairwise Comparison Semantic Differential Scale

10. Rating Scale Intensity of importance Definition 1 Equal importance 3 Weak importance of one over the other 5 Essential or strong importance 7 Demonstrated importance 9 Absolute importance 2, 4, 6, 8 Intermediate values between the two adjacent judgements

11. Select the Best Transport Mode Select the Best Transport mode Cost Travel Time Convenience & Safety Bus Train Car Goal Criteria Alternatives

12. Pairwise Comparison Basic Consistency Consider the factors A , B , & C IF, A is important than B, B is important the C, It implies that, A is important then C

13. Pairwise Comparison Criteria Comparison Cost Travel Time Convenience & Safety Cost 1 5 1/7 Travel Time 1/5 1 1/5 Convenience & Safety 7 5 1 Cost Travel Time Cost Convenience & Safety Travel Time Convenience & Safety

14. Ranking the Criteria   A = 1.45 14 5.125   Normalized Pairwise Comp. Matrix Normalized Pairwise Comp. Matrix Row Average   X = Priority Vector ( x) Column Sum

15. Weights of the Criteria Cost Travel Time Convenience & Safety Criteria Weights Select the Best Transport mode Cost Travel Time Convenience & Safety Goal Criteria

16. Checking for Consistency Consistency Ration (CR) – measure how consistent the judgements have been relative to large samples of purely random judgements AHP evaluation assume that the decision maker is rational. If the CR greater than 0.1 the judgements are untrustworthy because they are too close for comfort to randomness and the exercise is valueless or must be repeated

17.     The next stage is to calculate λ , Consistency Index (CI) and the Consistency Ration (CR). Consider [AX= λX] where X is the Eigenvector.         A X = = AX X λ   λ =  

18. RI = 0.58    

19. Ranking Alternatives Cost Bus Train Car Bus 1 1/3 5 Train 3 1 7 Car 1/5 1/7 1 Travel (T) Bus Train Car Bus 1 3 1/3 Train 1/3 1 1/5 Car 3 5 1 Con. & Safe. Bus Train Car Bus 1 1/3 3 Train 3 1 6 Car 1/5 1/6 1      

20. 1 0.33 5 3 1 7 0.2 0.14 1 4.2 1.47 13 0.24 0.22 0.38 0.71 0.68 0.54 0.05 0.10 0.08 0.28 0.64 0.08 3.050043 3.11072 3.002286   0.05536   0.0954 Cost 1 3 0.33 0.33 1 0.2 3 5 1 4.33 9 1.53 0.23 0.33 0.22 0.08 0.11 0.13 0.69 0.56 0.65 0.26 0.11 0.63 3.028016 3.005352 3.066315   0.033157   0.0571 Travel (T) 1 0.33 3 3 1 6 0.33 0.17 1 4.33 1.5 10 0.23 0.22 0.30 0.69 0.67 0.60 0.08 0.11 0.10 0.25 0.65 0.10 3.017819 3.036285 3.006345   0.018142   0.0312 Con. & Safe. Normalized Row AVG Priority Vector λ Normalized Row AVG Priority Vector λ Normalized Row AVG Priority Vector λ

21. Select the Best Transport mode Cost () Travel Time () Convenience & Safety () Bus (0.28) Train (0.64) Car (0.08) Goal Criteria Alternatives Bus (0.26) Train (0.11) Car (0.63) Bus (0.25) Train (0.65) Car (0.10)

22. Identify the Best Transport mode Mode Cost () Travel (T) () Con. & Safe. () Total Bus 0.28 0.26 0.25 Train 0.64 0.11 0.65 Car 0.08 0.63 0.10

23. Multiple Response IOS IOS IOS IOS IOS IOS Android Android Android Android Android Android 1 2 3 4 5 6 Name

24. Geometric Mean Method IOS Android Answer =  

25. Select the Best Transport Mode Select the Best Transport mode Cost Travel Time Convenience & Safety Ticket Price Maintenance Costs Fuel Costs Parking Fees Toll Costs Total Travel Time Waiting Time Time Flexibility Delays Safety Features Traffic Conditions Availability of Routes Luggage Handling Comfort Bus Train Car Goal Criteria Sub Criteria Alternatives

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