Project: A Comprehensive Study on Decision-Making Methods | Môn Multi-Criteria Decision Making - Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh
AHP is a systematic decision-making method developed by Thomas L. Saaty in the late 1970s. It is designed to address complex decision problems by organizing criteria and alternatives into a hierarchical structure and facilitating pairwise comparisons to derive priorities. Tài liệu được sưu tầm gồm 9 trang, giúp bạn ôn tập tốt hơn. Mời các bạn đón xem.
Môn: Multi-Criteria Decision Making 10 tài liệu
Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh 1.1 K tài liệu
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lOMoAR cPSD| 58504431 I. AHP Method
Defination: AHP is a systematic decision-making method developed by Thomas L. Saaty in the
late 1970s. It is designed to address complex decision problems by organizing criteria and
alternatives into a hierarchical structure and facilitating pairwise comparisons to derive
priorities. AHP is particularly useful for multi-criteria decision analysis and is widely applied in
various fields to support rational decision-making.
• Pair – wise Comparison matrix:
Wij representstherelativeimportance∨preferenceof criterionicompared¿criterion j
• Normalization of Pairwise Comparison Matrix (Normalized W):
Normalize each column of W by dividing each element by the sum of its column
Weight Vector (Priority Vector):
Obtain the average of each row in the normalized matrix to get the weight vector Consistency Ratio (CR): CI= λmax−n n−1 CI CR= RI
• Synthesis of Criteria and Alternatives:
Multiply the weight vector (w) by the performance values of each alternative to obtain
overall scores for each alternative.
1. Pair – wise Comparison matrix Criteria Grade Price 5 MOQ 9 Distance 3 Design 7 Credit 3 terms Pair - wise Comparison matrix Price MO Distance Design Credit Q terms Price 1.00 0.20 3.00 0.33 3.00 MOQ 5.00 1.00 7.00 3.00 7.00 Distance 0.33 0.14 1.00 0.20 1.00 Design 3.00 0.33 5.00 1.00 5.00 Credit 0.33 0.14 1.00 0.20 1.00 terms SUM 9.67 1.82 17.00 4.73 17.00 Normalised Pair-wise matrix Price MO
Distance Design Credit Criteria Q terms Weight Price 0.10 0.11 0.18 0.07 0.18 0.13 lOMoAR cPSD| 58504431 MOQ 0.52 0.55 0.41 0.63 0.41 0.50 Distance 0.03 0.08 0.06 0.04 0.06 0.05 Design 0.31 0.18 0.29 0.21 0.29 0.26 Credit 0.03 0.08 0.06 0.04 0.06 0.05 terms 2. Consistency Calculation Weight 0.13 0.50 0.05 0.26 0.05 Pair - wise Comparison matrix Price MOQ Distance Design Credit terms Price 1.00 0.20 3.00 0.33 3.00 MOQ 5.00 1.00 7.00 3.00 7.00 Distance 0.33 0.14 1.00 0.20 1.00 Design 3.00 0.33 5.00 1.00 5.00 Credit 0.33 0.14 1.00 0.20 1.00 terms Credit Criteria Consistency Price MOQ Distance Design terms SUM Weight vector Price 0.13 0.10 0.16 0.09 0.16 0.64 0.13 5.041396039 MOQ 0.64 0.50 0.38 0.78 0.38 2.68 0.50 5.31163956 Distance 0.04 0.07 0.05 0.05 0.05 0.28 0.05 5.046665539 Design 0.38 0.17 0.27 0.26 0.27 1.35 0.26 5.238586457 Credit 0.04 0.07 0.05 0.05 0.05 0.28 0.05 5.046665539 terms Conclusion Lamda max 5.13699 1 CI 0.03424 8 CR 0.03057 8 RI 1.12 3. Criteria Data Unit Price 1 2 3 4 5 6 1 1.00 0.14 1.00 1.00 3.00 3.00 2 7.00 1.00 7.00 7.00 9.00 9.00 3 1.00 0.14 1.00 1.00 3.00 3.00 4 1.00 0.14 1.00 1.00 3.00 3.00 5 0.33 0.11 0.33 0.33 1.00 1.00 6 0.33 0.11 0.33 0.33 1.00 1.00 Distance 1 2 3 4 5 6 1 1.00 1.00 0.11 0.11 0.11 0.14 lOMoAR cPSD| 58504431 MOQ 1 2 3 4 5 6 1 1.00 5.00 3.00 1.00 5.00 5.00 2 0.20 1.00 0.33 0.20 1.00 1.00 3 0.33 3.00 1.00 0.33 3.00 3.00 4 1.00 5.00 3.00 1.00 5.00 5.00 5 0.20 1.00 0.33 0.20 1.00 1.00 6 0.20 1.00 0.33 0.20 1.00 1.00 2 1.00 1.00 0.11 0.11 0.11 0.14 3 9.00 9.00 1.00 1.00 1.00 3.00 4 9.00 9.00 1.00 1.00 1.00 3.00 5 9.00 9.00 1.00 1.00 1.00 3.00 6 7.00 7.00 0.33 0.33 0.33 1.00 Design 1 2 3 4 5 6 1 1.00 3.00 7.00 7.00 7.00 7.00 2 0.33 1.00 5.00 5.00 5.00 5.00 3 0.14 0.20 1.00 1.00 1.00 1.00 4 0.14 0.20 1.00 1.00 1.00 1.00 5 0.14 0.20 1.00 1.00 1.00 1.00 6 0.14 0.20 1.00 1.00 1.00 1.00 Credit Terms 1 2 3 4 5 6 1 1.00 9.00 3.00 9.00 5.00 9.00 2 0.11 1.00 0.14 1.00 0.20 1.00 3 0.33 7.00 1.00 7.00 5.00 7.00 4 0.11 1.00 0.14 1.00 0.20 1.00 5 0.20 5.00 0.20 5.00 1.00 5.00 6 0.11 1.00 0.14 1.00 0.20 1.00 W 0.12 0.02 0.12 0.12 0.31 0.31 lOMoAR cPSD| 58504431 Unit 1 2 3 4 5 6 SUM W Consistancy Vector 4. AHP calculation 4.1. Unit Price Unit 1 2 3 4 5 6 Price 1 1.00 0.14 1.00 1.00 3.00 3.00 2 7.00 1.00 7.00 7.00 9.00 9.00 3 1.00 0.14 1.00 1.00 3.00 3.00 4 1.00 0.14 1.00 1.00 3.00 3.00 5 0.33 0.11 0.33 0.33 1.00 1.00 6 0.33 0.11 0.33 0.33 1.00 1.00 SUM 10.67 1.65 10.67 10.67 20.00 20.00 Unit 1 2 3 4 5 6 W Price 1 0.09 0.09 0.09 0.09 0.15 0.15 0.11 2 0.66 0.61 0.66 0.66 0.45 0.45 0.58 3 0.09 0.09 0.09 0.09 0.15 0.15 0.11 4 0.09 0.09 0.09 0.09 0.15 0.15 0.11 5 0.03 0.07 0.03 0.03 0.05 0.05 0.04 6 0.03 0.07 0.03 0.03 0.05 0.05 0.04 Price 1 0.11 0.08 0.11
0.11 0.13 0.13 0.68 0.11 6.088861463 2 0.78 0.58 0.78
0.78 0.39 0.39 3.70 0.58 6.388542964 3 0.11 0.08 0.11
0.11 0.13 0.13 0.68 0.11 6.088861463 4 0.11 0.08 0.11
0.11 0.13 0.13 0.68 0.11 6.088861463 5 0.04 0.06 0.04
0.04 0.04 0.04 0.26 0.04 6.036832413 6 0.04 0.06 0.04
0.04 0.04 0.04 0.26 0.04 6.036832413 Conclusion Lamda 6.121465 max CI 0.024293 RI 1.24 CR 0.019591 Conclusion 6.05835 Lamda max 7 lOMoAR cPSD| 58504431 CI 0.01167 4.2. MOQ MO 1 2 3 4 5 6 Q 1 1.00 5.0 3.0 1.0 5.0 5.0 0 0 0 0 0 2 0.20 1.0 0.3 0.2 1.0 1.0 0 3 0 0 0 3 0.33 3.0 1.0 0.3 3.0 3.0 0 0 3 0 0 4 1.00 5.0 3.0 1.0 5.0 5.0 0 0 0 0 0 5 0.20 1.0 0.3 0.2 1.0 1.0 0 3 0 0 0 6 0.20 1.0 0.3 0.2 1.0 1.0 0 3 0 0 0 SU 2.93 16. 8.0 2.9 16. 16. M 00 0 3 00 00 MO 1 2 3 4 5 6 W Q 1 0.3 0.3 0. 0. 0.3 0. 0.3 4 1 38 34 1 31 3 2 0.0 0.0 0. 0. 0.0 0. 0.0 7 6 04 07 6 06 6 3 0.1 0.1 0. 0. 0.1 0. 0.1 1 9 13 11 9 19 5 4 0.3 0.3 0. 0. 0.3 0. 0.3 4 1 38 34 1 31 3 5 0.0 0.0 0. 0. 0.0 0. 0.0 7 6 04 07 6 06 6 6 0.0 0.0 0. 0. 0.0 0. 0.0 7 6 04 07 6 06 6 W 0.33 0.06 0.15 0.33 0.06 0.06 MO 1 2 3 4 5 6 SUM W Consist Q ancy Vector 1 0.33 0.30 0.46 0.33 0.30 0.30 2.04 0. 6.1253 3 56125 3 2 0.07 0.06 0.05 0.07 0.06 0.06 0.37 0. 6.0165 0 80311 6 3 0.11 0.18 0.15 0.11 0.18 0.18 0.92 0. 6.0496 1 89441 5 lOMoAR cPSD| 58504431 4 0.33 0.30 0.46 0.33 0.30 0.30 2.04 0. 6.1253 3 56125 3 5 0.07 0.06 0.05 0.07 0.06 0.06 0.37 0. 6.0165 0 80311 6 6 0.07 0.06 0.05 0.07 0.06 0.06 0.37 0. 6.0165 0 80311 6 1 RI 1.24 0.00941 CR 2 4.3. Distance Distanc 1 2 3 4 5 6 e 1 1.00 1.00 0.11 0.11 0.11 0.14 2 1.00 1.00 0.11 0.11 0.11 0.14 3 9.00 9.00 1.00 1.00 1.00 3.00 4 9.00 9.00 1.00 1.00 1.00 3.00 5 9.00 9.00 1.00 1.00 1.00 3.00 6 7.00 7.00 0.33 0.33 0.33 1.00 SUM 36.00 36.0 3.56 3.56 3.56 10.29 0 Distanc 1 2 3 4 5 6 W e 1 0.03 0.03 0.0 0.0 0.0 0.01 0.03 3 3 3 2 0.03 0.03 0.0 0.0 0.0 0.01 0.03 3 3 3 3 0.25 0.25 0.2 0.2 0.2 0.29 0.27 8 8 8 4 0.25 0.25 0.2 0.2 0.2 0.29 0.27 8 8 8 5 0.25 0.25 0.2 0.2 0.2 0.29 0.27 8 8 8 6 0.19 0.19 0.0 0.0 0.0 0.10 0.13 9 9 9 W 0.03 0.03 0.27 0.27 0.27 0.13 Distanc 1 2 3 4 5 6 SU W Consistanc e M y Vector 1 0.03 0.03 0.03 0.03 0.03 0.02 0.16 0.0 6.0121580 3 55 lOMoAR cPSD| 58504431 2 0.03 0.03 0.03 0.03 0.03 0.02 0.16 0.0 6.0121580 3 55 3 0.24 0.24 0.27 0.27 0.27 0.38 1.69 0.2 6.2038216 7 56 4 0.24 0.24 0.27 0.27 0.27 0.38 1.69 0.2 6.2038216 7 56 5 0.24 0.24 0.27 0.27 0.27 0.38 1.69 0.2 6.2038216 7 56 6 0.19 0.19 0.09 0.09 0.09 0.13 0.78 0.1 6.1085972 3 85 Conclusion Lamda 6.1240 max 6 3 0.0248 CI 1 3 RI 1.2 4 CR 0.0200 1 4.4. Design Design 1 2 3 4 5 6 1 1.00 3.00 7.00 7.00 7.00 7.00 2 0.33 1.00 5.00 5.00 5.00 5.00 3 0.14 0.20 1.00 1.00 1.00 1.00 4 0.14 0.20 1.00 1.00 1.00 1.00 5 0.14 0.20 1.00 1.00 1.00 1.00 6 0.14 0.20 1.00 1.00 1.00 1.00 SUM 1.90 4.80 16.00 16.00 16.00 16.00 Desi 1 2 3 4 5 6 W gn 1 0.53 0.6 0.4 0.4 0.4 0.4 0.4 3 4 4 4 4 8 2 0.18 0.2 0.3 0.3 0.3 0.3 0.2 1 1 1 1 1 7 3 0.08 0.0 0.0 0.0 0.0 0.0 0.0 4 6 6 6 6 6 4 0.08 0.0 0.0 0.0 0.0 0.0 0.0 4 6 6 6 6 6 5 0.08 0.0 0.0 0.0 0.0 0.0 0.0 4 6 6 6 6 6 6 0.08 0.0 0.0 0.0 0.0 0.0 0.0 4 6 6 6 6 6 W 0.48 0.27 0.06 0.06 0.06 0.06 lOMoAR cPSD| 58504431 Desig 1 2 3 4 5 6 SU W Consista n M ncy Vector 1 0.48 0.82 0.43 0.43 0.43 0.43 3.01 0. 6.22988 48 5057 2 0.16 0.27 0.31 0.31 0.31 0.31 1.66 0. 6.08163 27 2653 3 0.07 0.05 0.06 0.06 0.06 0.06 0.37 0. 6.02077 06 9221 4 0.07 0.05 0.06 0.06 0.06 0.06 0.37 0. 6.02077 06 9221 5 0.07 0.05 0.06 0.06 0.06 0.06 0.37 0. 6.02077 06 9221 6 0.07 0.05 0.06 0.06 0.06 0.06 0.37 0. 6.02077 06 9221 Conclusion Lamda 6.06577 max 2 0.01315 CI 4 RI 1.2 4 0.01060 CR 8 4.5. 4.6. Credit Terms Credit 1 2 3 4 5 6 Terms 1 1.00 9.00 3.00 9.00 5.00 9.00 2 0.11 1.00 0.14 1.00 0.20 1.00 3 0.33 7.00 1.00 7.00 5.00 7.00 4 0.11 1.00 0.14 1.00 0.20 1.00 5 0.20 5.00 0.20 5.00 1.00 5.00 6 0.11 1.00 0.14 1.00 0.20 1.00 SUM 1.87 24.00 4.63 24.00 11.60 24.00 Credit 1 2 3 4 5 6 W Terms 1 0.54 0.38 0.65 0.38 0.43 0.38 0.46 2 0.06 0.04 0.03 0.04 0.02 0.04 0.04 3 0.18 0.29 0.22 0.29 0.43 0.29 0.28 4 0.06 0.04 0.03 0.04 0.02 0.04 0.04 5 0.11 0.21 0.04 0.21 0.09 0.21 0.14 6 0.06 0.04 0.03 0.04 0.02 0.04 0.04 W 0.46 0.04 0.28 0.04 0.14 0.04 lOMoAR cPSD| 58504431 Credit Consistancy Terms 1 2 3 4 5 6 SUM W Vector 1 0.46 0.35 0.85 0.35 0.72 0.35 3.07 0.46 6.72676927 2 0.05 0.04 0.04 0.04 0.03 0.04 0.24 0.04 6.093743591 3 0.15 0.27 0.28 0.27 0.72 0.27 1.97 0.28 6.942600051 4 0.05 0.04 0.04 0.04 0.03 0.04 0.24 0.04 6.093743591 5 0.09 0.19 0.06 0.19 0.14 0.19 0.87 0.14 6.080961415 6 0.05 0.04 0.04 0.04 0.03 0.04 0.24 0.04 6.093743591 Conclusion Lamda 6.33859 max 4 CI 0.06771 9 RI 1.24 CR 0.05461 2 5. AHP Conclusion Credit Price MOQ Distance Design Terms Supplier 1 0.11 0.33 0.03 0.48 0.46 Supplier 2 0.58 0.06 0.03 0.27 0.04 Supplier 3 0.11 0.15 0.27 0.06 0.28 Supplier 4 0.11 0.33 0.27 0.06 0.04 Supplier 5 0.04 0.06 0.27 0.06 0.14 Supplier 6 0.04 0.06 0.13 0.06 0.04 Criteria W Price 0.13 MOQ 0.50 Distance 0.05 Design 0.26 Credit terms 0.05 SOLUTION Supplier 1 0.3334 Supplier 2 0.1785 Supplier 3 0.1373 Supplier 4 0.2148 Supplier 5 0.0748 Supplier 6 0.0612