A Detailed Analytical Hierarchy Process (AHP) Application Example

1. A Detailed Analytical Hierarchy Process (AHP) Application Example

2. AHP Steps • Determine the selection criteria. • Determine the criteria weightings. • Identify and rate alternatives relative to the criteria. • Compute scores for the alternatives. • Review the decision.

3. Step 1: Determine Criteria • When selecting from a list of alternatives for an electrical engineering senior project, we usually consider the following criteria (reduced for simplicity as an example): • Project complexity • Project marketability • Time estimation (since the project must be completed before graduation) • The total estimated cost for the project team

4. For this project, we assume that the alternatives are • To design a car audio system • To design a robotic arm picking up an object • To design an interactive war game (software) • To design a temperature measurement system

5. Based on the above discussions, there are four criteria: • Complexity • Marketability • Time • Cost

6. And there are four project ideas (alternatives): • Audio system • Robotic arm • War game • Temperature system

7. Our Purpose is to complete the following AHP matrix to assist the decision making:

8. Step 2: Determine Weightings • This step is to determine the weightings of criteria (relative importance) using semi-quantitative, pair-wise comparison method: The above quantitative ratings are decided based on the recommended qualitative rating convention (which involves subjectivity but could be collective decision among team members): 1 = equal, 3 = moderate, 5 = strong, 7 = very strong, 9 = extreme.

9. Further Explanations regarding Weightings • Since this is an engineering school senior design project, the complexity is considered moderately more important than marketability • But the marketability is considered strongly more important than cost (school projects are usually less costly) • Because the project must be completed before graduation, the time is considered very strongly more important than cost • The matrix must have the relationship about the diagonal: Aij = 1/Aji (take a close look at the above example)

10. After the comparisons of the criteria are completed, the geometric means should be calculated for each row using the following formula:

11. Therefore, the geometric means equal to:

12. To perform the normalization of the weightings, we first add all geometric means: • Sum(Means) = 1.3+1.5+1.6+0.3 = 4.7 • The specific weighting is: W= Wi/Sum(Means).

13. Therefore, for complexity, the normalized weighting is: • Geometric Mean of Complexity/Sum(Means) = 1.3/4.7 = 0.28; • Similarly, the normalized weighting for marketability is 1.5/4.7 = 0.32 • The normalized weighting for time is 1.6/4.7 = 0.34 • And the normalized weighting for cost is 0.3/4.7 = 0.06 • Checking the accuracy of the calculations for the weightings, add all weightings, and they should be equal to one (0.28+0.32+0.34+0.06=1).

14. The weighting calculations of criteria are summarized in the following table:

15. Step 3: Identify and rate alternatives relative to the criteria • When rating the alternatives relative to criteria, if quantitative data are available, we should use it • Otherwise, we must use semi-qualitative approach, such as paired comparisons, or use assessment ratings

16. For Complexity… • We consider 10 is the most complex, and 1 is the least complex • Also we use the following judgment: 1) 9-10: very complicated; 6-8: reasonably complicated; 3-5: less complicated; 1-2: not complicated at all • We also consider that the higher the level of complexity, the more likely the project will be favorably accepted

17. The following table shows the ratings of the complexity for different project alternatives:

18. For Marketability… • We consider 10 is the most marketable, and 1 is the least • Again we use the following judgment: 1) 9-10: very marketable; 6-8: reasonably marketable; 3-5: less marketable; 1-2: not marketable at all • We consider that the higher the level of marketability, the more likely the project will be favorably accepted

19. The following table shows the ratings of the marketability for different project alternatives:

20. For Time… • Since the quantitative data are estimated, we use the estimations directly • However, because the longer the time that the project will take, the less likely the project will be considered favorably, we use the following formula to calculate the ratings: • Transitional Variable = min{time}/Time

21. In this example… • if the team hours estimated for Audio project is 140, and the minimum time estimated is the estimated team hours for Temperature project (100 hours) • The transitional time variable for Audio is 100/140=0.71 • Then the transitional variables are normalized to obtain the weightings

22. The following table shows the ratings of the time for different project alternatives:

23. For Cost… • Again since the quantitative data are estimated, we use the estimations directly • Also because the higher the cost that the project will need, the less likely the project will be considered favorably, we use the following formula to calculate: • Transitional Variable = min{cost}/Cost • If the cost estimated for Audio project is $300, and the minimum cost is the estimated cost for the Game project ($200), the transitional cost variable for Audio is 200/300=0.67 • Then the transitional variables are normalized to obtain the weightings

24. The following table shows the ratings of the cost for different project alternatives:

25. Step 4: Compute scores for the alternatives • The weightings of the criteria and the ratings of the alternative are filled in the following table (next slide) • The scores S1, S2, S3, and S4 are calculated using the formula (the calculation can be easily done using excel spreadsheet):

26. The weightings of the criteria and the ratings of the alternative

27. Step 5: Review and Make decision • The final decision or selection can be made by comparing the results summarized in the table • The composite ratings indicate that the Interactive War Game design project could be the most favorable choice, followed by the Temperature Measurement design project • It appears that the Car Audio system project is the least favorable choice