How to do ahp analysis in excel
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This document provides instructions for how to perform Analytic Hierarchy Process (AHP) analysis in Excel. It discusses developing a hierarchy of decision criteria and alternatives, making pairwise comparisons between elements, normalizing the comparisons to generate weights, and checking consistency. The basic steps are outlined as developing pairwise comparison matrices, normalizing the matrices to obtain weights, and calculating a consistency ratio to validate the judgments.
![References
Saaty, T.L. (1980). The analytic hierarchy process. McGraw-Hill, New York.
Saaty, T.L.,Vargas, L.G. (1991). Prediction, Projection and Forecasting. Kluwer Academic
Publishers, Dordrecht, 251 pp.
+ Knowledges
Haas, R. and Meixner, N. (n.d.). An Illustrated Guide to the Anlytic Hierarchy Process. Institute
of Marketing & Innovation, University of Natural Resources and Applied Life Sciences,
Vienna [Available online] http://www.boku.ac.at/mi/
Multi-Attribute Decision Analysis Approach: Qualitative Approach Analytic Hierarchy Process
(AHP) – Expert Choice Exercise
www.satecs.com – Some words on the Analytic Hierarchy Process (AHP) and the provided
DECISION MODELING WITH MICROSOFT EXCEL: Multi-Objective Decision Making
21
www.satecs.com – Some words on the Analytic Hierarchy Process (AHP) and the provided
ArcGIS extension ‘ext_ahp’](https://image.slidesharecdn.com/howtodoahpanalysisinexcel-150908171045-lva1-app6891/85/How-to-do-ahp-analysis-in-excel-21-320.jpg)
How to do ahp analysis in excel
- 1. How to do AHP analysis in Excel Khwanruthai BUNRUAMKAEW (D3) Division of Spatial Information Science Graduate School of Life and Environmental Sciences University of Tsukuba ( March 1st, 2012)
- 2. The Analytical Hierarchy Process - AHP • AHP is one of the multiple criteria decision-making method that was originally developed by Prof. Thomas L. Saatymethod that was originally developed by Prof. Thomas L. Saaty (1977). • provides measures of judgement consistency • derives priorities among criteria and alternatives • simplifies preference ratings among decision criteria 2 • simplifies preference ratings among decision criteria using pair wise comparisons
- 3. Using AHP 1. Decompose the decision-making problem into a hierarchy 2. Make pair wise comparisons and establish priorities among the elements in the hierarchy 3. Synthesise judgments (to obtain the set of overall or weights for achieving your goal)or weights for achieving your goal) 4. Evaluate and check the consistency of judgements 3
- 4. The basic procedure is as follows: 1. Develop the ratings for each decision alternative for each criterion byfor each criterion by • developing a pair wise comparison matrix for each criterion • normalizing the resulting matrix • averaging the values in each row to get the corresponding rating • calculating and checking the consistency ratio 4
- 5. 2. Develop the weights for the criteria by • developing a pairwise comparison matrix for each criterion • normalizing the resulting matrix • averaging the values in each row to get the corresponding rating • calculating and checking the consistency ratio 3. Calculate the weighted average rating for each decision alternative. Choose the one with the highest score. 5
- 6. Structure the Hierarchy Decompose the decision-making problem into a hierarchy of criteria and alternatives. GoalGOAL Subfactor 11 Subfactor 12 Subfactor 13 Factor 1 Subfactor 21 Subfactor 22 Factor 2 Subfactor 31 Subfactor 32 Subfactor 33 Factor 3Criteria 1 Criteria 3Criteria 2 Criteria 11 Criteria 12 Criteria 13 Criteria 21 Criteria 33Criteria 32Criteria 31Criteria 22 Alt 1 Alt 2 Alt 3 6 Level 1 is the goal of the analysis. Level 2 is multi-criteria that consist of several criterions, You can also add several other levels of sub-criteria. The last level is the alternative choices
- 7. Scale Degree of preference The first step in the AHP procedure is to make pair wise comparisons between each criterion. The example scale for comparison (Saaty & Vargas, 1991). Scale Degree of preference 1 Equal importance 3 Moderate importance of one factor over another 5 Strong or essential importance 7 Very strong importance 9 Extreme importance 2,4,6,8 Values for inverse comparison 7 Results of the comparison (for each factors pair) were described in term of integer values from 1 (equal value) to 9 (extreme different) where higher number means the chosen factor is considered more important in greater degree than other factor being compared with.
- 8. Factor Factor weighting score Factor More importance than Equal Less importance than Table: Primary questionnaire design: effective criteria and pair wise comparison Example More importance than Equal Less importance than C1 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 C2 C2 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 C3 C3 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 C1 Table: Pair wise comparison matrix which holds the preference values Criteria C1 C2 C3 C1 1 4 5 If the criteria in the column is preferred to the criteria in 8 C1 1 4 5 C2 0.25 1 0.5 C3 0.2 2 1 This table shows a simple comparison matrix of order 3 where 3 criteria C1, C2 and C3 are compared against each other. =1/2 is preferred to the criteria in the row, then the inverse of the rating is given.
- 9. Consider the following example: Factor Factor weighting score Factor More importance than Equal Less importance than C1 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 C2 C2 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 C3 C3 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 C4 C4 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 C5 Factor C1 C2 C3 C4 C5 C1 1.00 7.00 3.00 1.00 1.00 C2 1.00 0.14 0.20 0.20 B C D E FA 1 2 3 C4 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 C5 C5 … … … … … … … … …… … ……… … …… … …… Start with the total cost criterion and generate the following data in a spreadsheet: C2 1.00 0.14 0.20 0.20 C3 1.00 1.00 1.00 C4 1.00 1.00 C5 1.00 4 5 6 9 How to fill up the upper triangular matrix is using the following rules: 1.If the judgment value is on the left side of 1, we put the actual judgment value. 2.If the judgment value is on the right side of 1, we put the reciprocal value.
- 10. B C D E FA To fill the lower triangular matrix, we use the reciprocal values of the upper diagonal. If aij is the element of row i column j of the matrix, then the lower diagonal is filled using this formula = Making Comparison Matrix (How to make reciprocal matrix?) Factor C1 C2 C3 C4 C5 C1 1.00 7.00 3.00 1.00 1.00 C2 =1/7 1.00 0.14 0.20 0.20 C3 =1/3 =1/0.14 1.00 1.00 1.00 C4 =1/1 =1/0.20 =1/1 1.00 1.00 1 4 5 2 3 ==11/E/E22 ==11/C/C22 ==11/D/D22 ==11/F/F22 C4 =1/1 =1/0.20 =1/1 1.00 1.00 C5 =1/1 =1/0.20 =1/1 =1/1 1.00 5 6 ==11/E/E33 ==11/F/F33 10 This slide shows how to analyze this paired comparisons
- 11. Factor C1 C2 C3 C4 C5 B C D E FA 1 The criteria in the row is being compared to the criteria in the column. PairwiseinputsPairwiseinputs Step 1: Pair wise comparison C1 1.00 7.00 3.00 1.00 1.00 C2 0.14 1.00 0.14 0.20 0.20 C3 0.33 7.00 1.00 1.00 1.00 C4 1.00 5.00 1.00 1.00 1.00 C5 1.00 5.00 1.00 1.00 1.00 Total 3.48 25.00 6.14 4.20 4.20 4 5 6 7 2 3 PairwiseinputsPairwiseinputs Total 3.48 25.00 6.14 4.20 4.207 • The next step is to normalize the matrix. This is done by totaling the numbers in each column. 11 PairwiseinputsPairwiseinputs =Sum (B=Sum (B22:B:B66)) • Thus now we have complete comparison matrix
- 12. Each entry in the column is then divided by the column sum to yield its normalized score. The sum of each column is 1. B C D E FA G H This step is to normalize the matrix by totaling the numbers in each column. Step 2: Normalization C5 1.00 5.00 1.00 1.00 1.00 Total 3.48 25.00 6.14 4.20 4.20 Factor C1 C2 C3 C4 C5 Total Average C1 0.29 0.28 0.49 0.24 0.24 1.53 0.31 C2 0.04 0.04 0.02 0.05 0.05 0.20 0.04 9 10 11 8 7 6 =Sum (B=Sum (B1010:F:F1010)) =AVERAGE(G10/5) Normalizedinputs (priorityvector) C2 0.04 0.04 0.02 0.05 0.05 0.20 0.04 C3 0.10 0.28 0.16 0.24 0.24 1.01 0.20 C4 0.29 0.20 0.16 0.24 0.24 1.13 0.23 C5 0.29 0.20 0.16 0.24 0.24 1.13 0.23 12 13 14 11 =(B=(B66/B/B77)) =(C=(C66/C/C77)) Highest average score 12 1= Normalizedinputs (priorityvector) =1
- 13. Now, calculate the consistency ratio and check its value. The purpose for doing this is to make sure that the original preference ratings were consistent. Step 3: Consistency analysis ratings were consistent. There are 3 steps to arrive at the consistency ratio: 1.Calculate the consistency measure. 2.Calculate the consistency index (CI). 3.Calculate the consistency ratio (CI/RI where RI is a random index). lmax - n . n - 1 CI = CR = CI / RI 13 CR = CI / RI To calculate the consistency measure, we can take advantage of Excel’s matrix multiplication function =MMULT().
- 14. Factor C1 C2 C3 C4 C5 Total Average Consistancy Measure C1 0.29 0.28 0.49 0.24 0.24 1.53 0.31 5.37 B C D E FA G H I 9 10 Consistency Ratio (CR) C1 0.29 0.28 0.49 0.24 0.24 1.53 0.31 5.37 C2 0.04 0.04 0.02 0.05 0.05 0.20 0.04 5.08 C3 0.10 0.28 0.16 0.24 0.24 1.01 0.20 5.10 C4 0.29 0.20 0.16 0.24 0.24 1.13 0.23 5.15 C5 0.29 0.20 0.16 0.24 0.24 1.13 0.23 5.15 Total 1.00 1.00 1.00 1.00 1.00 CI= 0.04 12 13 14 10 11 15 RI= 1.12 C.Ratio 0.04 16 14 =MMULT(B2:F2,H10:H14)/H10 =MMULT(B3:F3,H10:H14)/H11 =(AVERAGE(H=(AVERAGE(H1010:H:H1414))--55)/)/44 =I=I1515/I/I1616)) RI is provided by AHP (see slide 16) CR = CI / RI
- 15. Approximation of the Consistency Index 1. Multiply each column of the pair wise comparison matrix by the corresponding weight.matrix by the corresponding weight. 2. Divide of sum of the row entries by the corresponding weight. 3. Compute the average of the values from step 2, denote it by lmax . 4. The approximate lmax - n .CI =4. The approximate 15 =(AVERAGE(H10:H14)-5)/4 lmax - n . n - 1 CI =
- 16. Consistency Ratio (CR) CR = CI / RI • In practice, a CR of 0.1 or below is considered acceptable. • Any higher value at any level indicate that the judgements warrant • reflects the consistency of one’s judgement lmax - n . n - 1 Random Index (RI) re-examination. CI = Consistency Index (CI) 16 Notes: n = order of matrix Random Index (RI) • the CI of a randomly-generated pair wise comparison matrix n 1 2 3 4 5 6 7 8 9 10 RI 0.00 0.00 0.58 0.9 1.12 1.24 1.32 1.41 1.46 1.49 Random inconsistency indices for n = 10 (Saaty, 1980)
- 17. If we are perfectly consistent, then the consistency measures will equal n and therefore, the CIs will be equal to zero and so With AHP, we can measure the degree of consistency; and if unacceptable, we can revise pair wise comparisons. Summary will equal n and therefore, the CIs will be equal to zero and so will the consistency ratio. If this ratio is very large (Saaty suggests > 0.10), then we are not consistent enough and the best thing to do is go back and revise the comparisons. All of this work concludes the first step in the procedure. The next step is to use similar pair wise comparisons to determine the Now, continue for the other sub-criteria. You can easily do this by copying this sheet into other sheets and then simply changing the pair wise comparisons. 17 next step is to use similar pair wise comparisons to determine the appropriate weights for each of the criteria.
- 18. Remark By now you have learned several introductory methods on Multi-Criteria Decision Making (MCDM) from the advantage of Excel’s simple cross tabulation, using rank, and weighted score until AHP. Widely Used AHP • Cost/Benefit Analysis • Strategic planning • R&D priority setting and selection • Technology choice • Investment priority • Priority for developing tourism • Evaluation of for new telecommunications services • Other evaluation of alternatives 18
- 19. ((11) Normalization: “Behind the scene”) Normalization: “Behind the scene” The mathematics of AHP 19
- 20. ((22) Consistency analysis : “Behind the scene”) Consistency analysis : “Behind the scene” 20 Source: Haas, R. and Meixner, N.
- 21. References Saaty, T.L. (1980). The analytic hierarchy process. McGraw-Hill, New York. Saaty, T.L.,Vargas, L.G. (1991). Prediction, Projection and Forecasting. Kluwer Academic Publishers, Dordrecht, 251 pp. + Knowledges Haas, R. and Meixner, N. (n.d.). An Illustrated Guide to the Anlytic Hierarchy Process. Institute of Marketing & Innovation, University of Natural Resources and Applied Life Sciences, Vienna [Available online] http://www.boku.ac.at/mi/ Multi-Attribute Decision Analysis Approach: Qualitative Approach Analytic Hierarchy Process (AHP) – Expert Choice Exercise www.satecs.com – Some words on the Analytic Hierarchy Process (AHP) and the provided DECISION MODELING WITH MICROSOFT EXCEL: Multi-Objective Decision Making 21 www.satecs.com – Some words on the Analytic Hierarchy Process (AHP) and the provided ArcGIS extension ‘ext_ahp’