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Analytic Hierarchy Process
(A.H.P.)
P.V.for all criteria
P.V. for
Criterion #1
P.V. for
Criterion #2
P.V. for
Criterion #3
P.V. for
Criterion #4
TOTAL SCORE
Design #1
Design #2
Design #3
Outline
- What is Analytic Hierarchy Process (A.H.P.)?
- What is the need that (A.H.P) can cover?
- How does (A.H.P.) fit into the design process?
- Methodology
- Example
- Conclusions / Wrapping up
School of Mechanical, Aerospace &
Automotive Engineering
What is Analytic Hierarchy Process (A.H.P.)?
5036MAA – Design and Sustainability
A.H.P.:
 is a multi-criteria decision making method
 can be used to rank a set of criteria (major design objectives)
 can be used to rate the criteria on a relative scale of importance
 can be used to rank & rate alternative designs
 allow some small inconsistency in judgment because (human
judgement is not always consistent)
Main idea:
 to introduce ratio scales for paired comparisons
 to form a normalised comparison matrix
 to derive a priority vector for each comparison matrix
 to use priority vectors to determine relative importance of designs
Analytic Hierarchy Process: used
to (a) rank criteria to be included
in our design; and (b)
rank alternative designs
according to their relative
importance
AHP: Priority Vector
Main task: to rank alternative designs according to their relative importance
Level 0: goal of the analysis
Level 1: multi-criteria to be used (can also add other levels of sub- criteria)
Level 2: alternative choices (alternative designs)
Example:
Factor A: Cost; Factor B: Quality; Factor C: Performance; Factor D: Manufacturability
Choice X: Design #1; Choice X: Design #2; Choice X: Design #3
CRITERI
A
Cost Quality Performance Manufacturability
Cost 1
Quality 1
Performance 1
Manufacturability 1
CRITERI
A
Cost Quality Performance Manufacturability
Cost 1 2 3 3
Quality 1 3 2
Performance 1 2
Manufacturability 1
Step 2: Use own judgement and complete upper-triangular part of matrix
CRITERI
A
Cost Quality Performance Manufacturability
Cost 1 2 3 3
Quality 1/2 1 3 2
Performance 1/3 1/3 1 2
Manufacturability 1/3 1/2 1/2 1
Step 3: Complete lower-triangular part of matrix (reciprocal of upper-triangular part)
CRITERIA Cost Quality Performance Manufacturability
Cost 1 2 3 3
Quality 1/2 1 3 2
Performance 1/3 1/3 1 2
Manufacturability 1/3 1/2 1/2 1
SUM 2.1667 3.8333 7.5000 8.0000
CRITERI
A
Cost Quality Performance Manufacturability
Cost = 1 / 2.1667 = 2 / 3.8333 = 3 / 7.5000 = 3 / 8.0000
Quality = (1/2) / 2.1667 = 1 / 3.8333 = 3 / 7.5000 = 2 / 8.0000
Performance = (1/3) / 2.1667 = (1/3) / 3.8333 = 1 / 7.500 = 2 / 8.0000
Manufacturability = (1/3) / 2.1667 = (1/2) / 3.8333 = (1/2) / 7.5000 = 1 / 8.0000
PRIORITY
VECTOR
Step 5: Normalize values (divide each entry by sum of respective column)
Step 6: Average values in each row
CRITERI
A
(
+Cost
Quality Performance
+
Manufacturability ROW
AVERAGE
Cost 0.4615 0.5217 0.4000 0.3750 / 4 0.4396
Quality ( 0.2308
+
0.2609 0.4000
+ 0.2500 / 4 0.2854
Performance
( 0.1538
(
+
0.0870 0.1333
+
0.2500 / 4 0.1560
Manufacturability 0.1538 0.1304 0.0667 0.1250 / 4 0.1190
CRITERI
A
Cost Quality Performance Manufacturability ROW AVERAGE
Cost 0.4615 0.5217 0.4000 0.3750 0.4396
Quality 0.2308 0.2609 0.4000 0.2500 0.2854
Performance 0.1538 0.0870 0.1333 0.2500 0.1560
Manufacturability 0.1538 0.1304 0.0667 0.1250 0.1190
CRITERI
A
Cost Quality Performance Manufacturability
Cost 0.4615 0.5217 0.4000 0.3750
Quality 0.2308 0.2609 0.4000 0.2500
Performance 0.1538 0.0870 0.1333 0.2500
Manufacturability 0.1538 0.1304 0.0667 0.1250
Step 6: Average normalized values row-wise& form “Priority Vector” for “CRITERIA”
PRIORITY VECTOR
Calculation of row averages:
First row: (0.4615 + 0.5217 + 0.4000 + 0.3750) / 4 = 0.4396
Second row: (0.2308 + 0.2609 + 0.4000 + 0.2500) / 4 = 0.2854
Third row:
Forth row:
(0.1538 + 0.0870 + 0.1333 + 0.2500) / 4 = 0.1560
(0.1538 + 0.1304 + 0.0667 + 0.1250) / 4 = 0.1190
Criterion: Cost Design #1 Design #2 Design #3 Priority Vector
Design #1 1.00 1.00 7.00 0.5105
Design #2 1.00 1.00 3.00 0.3893
Design #3 0.14 0.33 1.00 0.1001
Sum 2.14 2.33 11.00 1.00
Combine all Priority Vectors to calculate a “Total Score” for each Design. Select
the Design with the highest score.
P.V.for all criteria
P.V. for
Criterion #1
P.V. for
Criterion #2
P.V. for
Criterion #3
P.V. for
Criterion #4
TOTAL
SCORE
Design #1
Design #2
Design #3

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Chapter 2b.pptx

  • 1. Analytic Hierarchy Process (A.H.P.) P.V.for all criteria P.V. for Criterion #1 P.V. for Criterion #2 P.V. for Criterion #3 P.V. for Criterion #4 TOTAL SCORE Design #1 Design #2 Design #3
  • 2. Outline - What is Analytic Hierarchy Process (A.H.P.)? - What is the need that (A.H.P) can cover? - How does (A.H.P.) fit into the design process? - Methodology - Example - Conclusions / Wrapping up
  • 3. School of Mechanical, Aerospace & Automotive Engineering What is Analytic Hierarchy Process (A.H.P.)? 5036MAA – Design and Sustainability A.H.P.:  is a multi-criteria decision making method  can be used to rank a set of criteria (major design objectives)  can be used to rate the criteria on a relative scale of importance  can be used to rank & rate alternative designs  allow some small inconsistency in judgment because (human judgement is not always consistent) Main idea:  to introduce ratio scales for paired comparisons  to form a normalised comparison matrix  to derive a priority vector for each comparison matrix  to use priority vectors to determine relative importance of designs
  • 4. Analytic Hierarchy Process: used to (a) rank criteria to be included in our design; and (b) rank alternative designs according to their relative importance
  • 5. AHP: Priority Vector Main task: to rank alternative designs according to their relative importance Level 0: goal of the analysis Level 1: multi-criteria to be used (can also add other levels of sub- criteria) Level 2: alternative choices (alternative designs) Example: Factor A: Cost; Factor B: Quality; Factor C: Performance; Factor D: Manufacturability Choice X: Design #1; Choice X: Design #2; Choice X: Design #3
  • 6. CRITERI A Cost Quality Performance Manufacturability Cost 1 Quality 1 Performance 1 Manufacturability 1 CRITERI A Cost Quality Performance Manufacturability Cost 1 2 3 3 Quality 1 3 2 Performance 1 2 Manufacturability 1 Step 2: Use own judgement and complete upper-triangular part of matrix CRITERI A Cost Quality Performance Manufacturability Cost 1 2 3 3 Quality 1/2 1 3 2 Performance 1/3 1/3 1 2 Manufacturability 1/3 1/2 1/2 1 Step 3: Complete lower-triangular part of matrix (reciprocal of upper-triangular part)
  • 7. CRITERIA Cost Quality Performance Manufacturability Cost 1 2 3 3 Quality 1/2 1 3 2 Performance 1/3 1/3 1 2 Manufacturability 1/3 1/2 1/2 1 SUM 2.1667 3.8333 7.5000 8.0000 CRITERI A Cost Quality Performance Manufacturability Cost = 1 / 2.1667 = 2 / 3.8333 = 3 / 7.5000 = 3 / 8.0000 Quality = (1/2) / 2.1667 = 1 / 3.8333 = 3 / 7.5000 = 2 / 8.0000 Performance = (1/3) / 2.1667 = (1/3) / 3.8333 = 1 / 7.500 = 2 / 8.0000 Manufacturability = (1/3) / 2.1667 = (1/2) / 3.8333 = (1/2) / 7.5000 = 1 / 8.0000 PRIORITY VECTOR Step 5: Normalize values (divide each entry by sum of respective column) Step 6: Average values in each row CRITERI A ( +Cost Quality Performance + Manufacturability ROW AVERAGE Cost 0.4615 0.5217 0.4000 0.3750 / 4 0.4396 Quality ( 0.2308 + 0.2609 0.4000 + 0.2500 / 4 0.2854 Performance ( 0.1538 ( + 0.0870 0.1333 + 0.2500 / 4 0.1560 Manufacturability 0.1538 0.1304 0.0667 0.1250 / 4 0.1190
  • 8. CRITERI A Cost Quality Performance Manufacturability ROW AVERAGE Cost 0.4615 0.5217 0.4000 0.3750 0.4396 Quality 0.2308 0.2609 0.4000 0.2500 0.2854 Performance 0.1538 0.0870 0.1333 0.2500 0.1560 Manufacturability 0.1538 0.1304 0.0667 0.1250 0.1190 CRITERI A Cost Quality Performance Manufacturability Cost 0.4615 0.5217 0.4000 0.3750 Quality 0.2308 0.2609 0.4000 0.2500 Performance 0.1538 0.0870 0.1333 0.2500 Manufacturability 0.1538 0.1304 0.0667 0.1250 Step 6: Average normalized values row-wise& form “Priority Vector” for “CRITERIA” PRIORITY VECTOR Calculation of row averages: First row: (0.4615 + 0.5217 + 0.4000 + 0.3750) / 4 = 0.4396 Second row: (0.2308 + 0.2609 + 0.4000 + 0.2500) / 4 = 0.2854 Third row: Forth row: (0.1538 + 0.0870 + 0.1333 + 0.2500) / 4 = 0.1560 (0.1538 + 0.1304 + 0.0667 + 0.1250) / 4 = 0.1190
  • 9. Criterion: Cost Design #1 Design #2 Design #3 Priority Vector Design #1 1.00 1.00 7.00 0.5105 Design #2 1.00 1.00 3.00 0.3893 Design #3 0.14 0.33 1.00 0.1001 Sum 2.14 2.33 11.00 1.00 Combine all Priority Vectors to calculate a “Total Score” for each Design. Select the Design with the highest score. P.V.for all criteria P.V. for Criterion #1 P.V. for Criterion #2 P.V. for Criterion #3 P.V. for Criterion #4 TOTAL SCORE Design #1 Design #2 Design #3