Hai V. Pham, PhD in Computer Intelligence and Information Science, Ritsumeikan University, JAPAN AHP example Decision Support System 2014 14 Hai V. Pham Learning resources for Bsc./ Eng. students Example of AHP application Basic Example For matching student’s major in Computer Science and Information Management (CSIM) Program, Asian Institute Of Technology ( AIT), we consider the situation in which you, as a new student with a different background, need to select three majors among of computer science (CS), information management (IM) and information communication technology (ICT) for your decision to enter the CSIM program. The goal is to focus on matching major that choosing the field of study is fit to your background. Looking over the among choices, you determine that there are three sets of choosing majors, CS, IM, ICT you want to consider. This presents in the relationship between your matching major and sets of choosing field of study in a two-level hierarchical diagram in Figure 2.15 below: Level 1: (Goal) Level 2: Alternatives Matching Major CS IM ICT Figure I.1 Structure of the AHP hierarchy example According to Thomas L. Saaty, the author of Analytic Hierarchy Process (AHP) has figured out that the decision model is based on structuring the problem elements in terms of how the alternative solutions (the results) influence decision criteria which helps the accomplishment of the decision problem’s main objective measuring effectiveness. For solving problems, we consider that using only the whole numbers 1 to 9 ( see comparison scales in table 2.10) with 1 indicating that the two criteria being compared are of equal importance and a 9 meaning that the first criteria is extremely more important than the second. For instance, if CS is strongly favored to ICT, then we give this comparison of CS to ICT a score of 4, which means that CS is more important than ICT factors as 4 times. In turn, the comparison score of ICT to CS must have reciprocal value of 1/4. To continue with the example, all comparisons are to present at the judgmental matrix of the assumption as follows: Major (M) CS CS IM ICT 1 2 4 IM 1/2 1 3 ICT 1/4 1/3 1 2 Hai V. Pham Learning resources for Bsc./ Eng. students The priorities are defined by the AHP eigenvector which means the largest eigenvalue to indicate the significance of each alternative in accomplishing the goal. Assume that a matrix with n rows and columns, we have n =3 in a case of example. For each row i of the matrix, calculate ∏i = CS x IM x ICT ( the product of the ratios) Calculate Bi meaning a geometric Bi = n ∏ i i =1 Bi so that we calculate Pi=Bi/B (Pi is the ith priority to the ith alternative of major Let B = n Mi. The calculation for the CSIM matching major judgment matrix is as follows: Matching Major (M) CS CS IM ICT 1 1/2 1/4 IM 2 1 1/3 ∏ ICT 4 3 1 i Bi = n ∏ Pi=Bi/B i i=1..3 i=1..3; n=3 i=1..3 8 1.5 0.08 2 1.14 0.43 3.57 0.56 0.32 0.12 The priorities for the matching major among of CS, IM, ICT are in order of the following: 0.56, 0.32, 0.12 . This information indicate that set of majors CS (0.56) affects the most to matching your major, followed by IM and finally ICT. Hence, the matching student’s major in Computer Science is the first choice of the CSIM program. Advanced Example Based on the basic example, an advanced example is to focus on the overall objective that is matching future job. The criteria deal with the various sets of matching future job, which consists of matching major, technological and practical skill and adaptive labor society factors. Now, how to select a major for your decision of the matching future job among of choices such as CS, IM and ICT in CSIM program? The solution of question can be pictured by the following three-level hierarchical structure in Figure 2.16: Level 1: Goal Level 2: Criteria Level 3: Alternatives Matching Future Job Matching Major Technological & Practical Skills Adaptive Labor Society 3 CS IM ICT Hai V. Pham Learning resources for Bsc./ Eng. students Figure I.2 Structure of the AHP hierarchy in Advanced example Based on the pairwise comparison scale above, all assumed comparisons are to present at the judgmental matrix of the following: Comparison criteria factors focuses on Matching Future Job Matching Major Technological & Practical Skills Adaptive Labor Society Matching Major 1 2 1/3 Technological & Practical Skills Adaptive Labor Society 1/2 1 1/2 3 2 1 For example, if Adaptive Labor Society is strongly favored to Matching Major, then we give this comparison of Adaptive Labor Society to Matching Major a score of 3, which means that Adaptive Labor Society is more important than Matching Major factors as 3 times. In turn, the comparison score of Matching Major to Adaptive Labor Society must have reciprocal value of 1/3. The calculation for the matching Future Job judgment matrix is as follows: Comparison criteria factors focuses on Matching Future Job Matching Major Matching Major Technological & Practical Skills Adaptive Labor Society Pi=Bi/B Technological & Practical Skills Adaptive Labor Society I=1..3 i=1..3; n=3 i=1..3 1 2 1/3 0.67 0.88 0.26 1/2 1 1/2 0.25 0.63 0.19 3 2 1 6 1.82 0.55 ∏ i Bi = n ∏ i 3.33 According to calculating of the table, The Adaptive Labor Society criterion has the highest priority (0.55), then the second is Matching Major (0.26) and the third one is Technological and Practical Skills (0.19). To carry out the analysis of the third level of the hierarchy, the three judgment matrices are as follows: 4 Hai V. Pham Learning resources for Bsc./ Eng. students Matching Major judgment matrix: Matching Major (M) CS CS IM ICT 1 1/2 1/4 IM ∏ ICT i 2 1 1/3 4 3 1 Bi = n ∏ Pi=Bi/B i i=1..3 i=1..3; n=3 i=1..3 8 1.5 0.08 2 1.14 0.43 3.57 0.56 0.32 0.12 Technological and Practical Skills judgment matrix: Technological & Practical Skills CS CS IM ICT 1 1/2 1/3 IM ∏ ICT i 2 1 1/2 3 2 1 Bi = n ∏ Pi=Bi/B i i=1..3 i=1..3; n=3 i=1..3 6 1 0.17 1.82 1.00 0.56 3.38 0.54 0.30 0.17 Adaptive Labor Society judgment matrix: Adaptive Labor Society CS CS IM ICT 1 2 1/2 IM ∏ ICT i 1/2 1 1/3 2 3 1 Bi = n ∏ Pi=Bi/B i i=1..3 i=1..3; n=3 i=1..3 1 6 0.17 1.00 1.82 0.56 3.38 0.30 0.54 0.17 Focus on overall objective of the Matching Future Job To obtain the calculation of hierarchical priority for the major among of CS, IM, ICT, it multiplies each of its level 3 priorities by the corresponding level 2 priority and sum the products of the following: P1 = (0.26)(0.56) + (0.19)(0.54) + (0.55)(0.30) = 0.41 P2 = (0.26)(0.32) + (0.19)(0.30) + (0.55)(0.54) = 0.44 P3 = (0.26)(0.12) + (0.19)(0.17) + (0.55)(0.17) = 0.16 5 Hai V. Pham Learning resources for Bsc./ Eng. students The result is of the following table: Criteria Matching Major Technological & (MM) Practical Skills Adaptive Labor Calculating Hierarchical Society Priorities (Pi) (ALS) (TPS) Level 2 0.26 0.19 0.55 0.56 0.54 0.30 0.41 IM 0.32 0.30 0.54 0.44 priorities ICT 0.12 0.17 0.17 0.16 Priorities Alternatives CS Level 3 For the outcomes of this table above, the alternative of IM (0.41) is the highest priority, then CS (0.41) is the second and the lowest priority of ICT (0.16). Conclusion: In a case of the example, Information Technology (IM) is the first decision of study because of matching future job in CSIM program of AIT. The second choice is Computer Science (CS) and the third choice is Information Communication Technology (ICT). Therefore, AHP is a good technique for solving a problem in DSS application 6 

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