1. Supplement S7
Supplier Selection

2. Analytical Hierarchy Process
Ranks decision alternatives and selects the best one
Allows consideration of multiple criteria
Establish preferences for each alternative for each criteria
Assign importance scores to each criteria
Preferences and importance scores are combined for final selection

3. Supplier Selection Example
Suppliers: A, B, and C
Criteria: product cost, product quality, service, and delivery
NUMERICAL
PREFERENCE LEVEL VALUE
Equally preferred 1
Equally to moderately preferred 2
Moderately preferred 3
Moderately to strongly preferred 4
Strongly preferred 5
Strongly to very strongly preferred 6
Very strongly preferred 7
Very strongly to extremely preferred 8
Extremely preferred 9
Table S7.1

4. Southcorp Company Pairwise comparison Pairwise ranking of importance
COST QUALITY SERVICE DELIVERY
A B C
A 1 3 2
B 1/3 1 1/5
C 1/2 5 1
A 1 6 1/3
B 1/6 1 1/9
C 3 9 1
A 1 1/3 1
B 3 1 7
C 1 1/7 1
A 1 1/3 1/2
B 3 1 4
C 2 1/4 1
Pairwise ranking of importance
CRITERIA COST QUALITY SERVICE DELIVERY
Cost 1 1/5 3 4
Quality
Service 1/3 1/9 1 2
Delivery 1/4 1/7 1/2 1
Example S7.1

5. Southcorp Company 1. Find column sums for each criterion:
Pairwise comparison
COST QUALITY SERVICE DELIVERY
A B C
A 1 3 2
B 1/3 1 1/5
C 1/2 5 1
A 1 6 1/3
B 1/6 1 1/9
C 3 9 1
A 1 1/3 1
B 3 1 7
C 1 1/7 1
A 1 1/3 1/2
B 3 1 4
C 2 1/4 1
1. Find column sums for each criterion:
COST
SUPPLIER A B C
A 1 3 2
B 1/3 1 1/5
C 1/2 5 1
11/6 9 16/5
Example S7.1

6. Southcorp Company 2. Divide the values by corresponding column sums:
Pairwise comparison
COST QUALITY SERVICE DELIVERY
A B C
A 1 3 2
B 1/3 1 1/5
C 1/2 5 1
A 1 6 1/3
B 1/6 1 1/9
C 3 9 1
A 1 1/3 1
B 3 1 7
C 1 1/7 1
A 1 1/3 1/2
B 3 1 4
C 2 1/4 1
2. Divide the values by corresponding column sums:
COST
SUPPLIER A B C
A 1/(6/11) = 6/11 3/9 2/(16/5) = 5/8
B (1/3)/(6/11) = 2/11 1/9 (1/5)/(16/5) = 1/16
C (1/2)/(6/11) =3/11 5/9 1/(16/5) = 5/16
Example S7.1

7. Southcorp Company 3. Convert the divided values to decimals:
Pairwise comparison
COST QUALITY SERVICE DELIVERY
A B C
A 1 3 2
B 1/3 1 1/5
C 1/2 5 1
A 1 6 1/3
B 1/6 1 1/9
C 3 9 1
A 1 1/3 1
B 3 1 7
C 1 1/7 1
A 1 1/3 1/2
B 3 1 4
C 2 1/4 1
3. Convert the divided values to decimals:
COST
SUPPLIER A B C A B C
Example S7.1

8. Southcorp Company 4. Find row averages: Pairwise comparison COST Row
COST QUALITY SERVICE DELIVERY
A B C
A 1 3 2
B 1/3 1 1/5
C 1/2 5 1
A 1 6 1/3
B 1/6 1 1/9
C 3 9 1
A 1 1/3 1
B 3 1 7
C 1 1/7 1
A 1 1/3 1/2
B 3 1 4
C 2 1/4 1
4. Find row averages:
COST Row
SUPPLIER A B C Average A B C
1.0000
Example S7.1

9. Southcorp Company 5. Do Steps 1-4 for each criterion, and find:
Summarized preferences
CRITERIA
SUPPLIER Cost Quality Service Delivery A B C
Example S7.1

10. Southcorp Company 6. Do Steps 1-5 for the following table also:
Pairwise ranking of importance
CRITERIA COST QUALITY SERVICE DELIVERY
Cost 1 1/5 3 4
Quality
Service 1/3 1/9 1 2
Delivery 1/4 1/7 1/2 1
Example S7.1

11. Southcorp Company 6. Do Steps 1-5 for the following table also:
Pairwise ranking of importance
CRITERIA COST QUALITY SERVICE DELIVERY
Cost 1 1/5 3 4
Quality
Service 1/3 1/9 1 2
Delivery 1/4 1/7 1/2 1
Col. sums
Example S7.1

12. Southcorp Company Summarized preferences Preference vector
ROW
CRITERIA COST QUALITY SERVICE DELIVERY AVERAGES
Cost
Quality
Service
Delivery
1.0000
CRITERIA
Cost
Quality
Service
Delivery
Preference vector
= 1 /
Example S7.1

13. Southcorp Company Select Supplier C Overall score
CRITERIA
Cost
Quality
Service
Delivery
Cost Quality Service Delivery A B C
Supplier A score = (0.5012) (0.1819) +
0.0860(0.1790) (0.1561) =
Supplier B score =
Supplier C score =
Select Supplier C
Example S7.1