Quantitative Techniques for Decision Making-4 (AHP)

1
Quantitative Techniques for Decision
Making-4(AHP)

• Narges Imanipour
• n.imanipour_at_ent.ut.ac.ir
• Fall 1387

2
Multi-Criteria Decision Making

• Multi-objective decision making (MODM)
• Multi-attribute decision making (MADM)
• Alternatives
• Multiple attributes
• Incommensurable units
• Attributes weights
• Decision matrix

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???? ???? 3 ????? ????? 12 A2
????? 30 ???? ???? ???? 20 A3
?? 1 ???? ???? ?? 30 A4
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• ?) ????????????? ???? ?? ??? ??? ?? ????? ?????
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• ??????? ????? ???????
• ???) ??? ???????
• ?) ??? ????? (Linmap)
• ?) ??? ??????? ??????? ?????
• ?) ??? ????? ????.

15
?????? ????? ????? ??????(Analytical Hierarchy
Analysis-AHP)

• ?????? ????? ????? ?????? ?? ????? ??? ???? ?????
  ????? ?? ??? ?? ???? ???? ? ???????? ????????
  ????? ???? ?? ????? ????? ??? ????? ??
  (MADM)???. ??? ??????
• ????? ??? ???? ????? ????? ?? ?? ???? ??????
  ????? ?????? ????? ?? ????.
• ????? ?????????? ???????? ??? ? ???? ?? ?? ???
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• ?? ????? ????? ??? ???????? ???.

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?????? ??? AHP

• ???? ????? ??????
• ????? ??????? ????
• ?????? ??? ???? ?????? ? ??? ??????
• ?????? ??? ???? ????? ??
• ?????? ??? ????? ????? ??
• ???? ???? ????? ??
• ????? ???????

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  ???? ?? ?? ?? ????? ????? ? ?????? ??? ???? ????
  ???? ?? ???. ????? ?????? ?? ?? ?? ??? ????? ??
  ????
• ????? ?????? ???????(structural hierarchies)
• ?? ??? ??? ????? ?????? ????? ????? ?? ????
  ?????? ?? ?? ???????? ?? ?????.
• ????? ?????? ????? ??(functional hierarchies)
• ?? ??? ??? ????? ?????? ?????? ????? ?? ????
  ??????? ? ????? ?? ?? ??????? ???.
• ?? ????? ?????? ????? ?? ???? ?? ??? ???? ??? ??
  ?? ???????? ??? ?? ??? ???? ????? ??? ? ?????? ??
  ??? ?? ??????? ??? ???
• ???- ???????- ??????????-????? ??
• ???- ???????- ??????????- ?????- ????????-?????
  ??

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Ref. Expert system with application,29,2005,889-89
9
Choice of a suitable KM tool
Cost
Functionality
Vendor
Operating expenditure
Document management
Management report
Workflow management
Capital expenditure
Support maintenance upgrade
collaborizzation
communication
scalability
Vendor reputation
training
implementation
KM consulting
know ledger
Sharpoint portal server
eroom
22
???? ????? ??????
??? ???
???????
??? ???????
??? ???
23
??????? ????

• ?? AHP ?? ???? ?? ????? ?????? ???? ?? ???? ??
  ????? ????? ?? ??? ?? ??? ?????? ?? ???? ????
  ?????? ?? ??? . ???? ?????? ?? ?? ???? ???? ?????
  ?? ???. ???? ???? ??? ??????? ??????? ?? ?? ????
  ?? ????? ????? ?????? ???? ????? ??????? A ?? B
  ??? ??????? A ?? C ? ?? ????? ??????? B ?? C
  ?????? ?? ???.
• ????? ?? ???? ?? ???? 1 ???.
• ??? ????? ???? A ?? ???? B ????? x ??? ??? ?????
  ????? B ?? A ????? 1/x ????? ???.

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• ?? ??? ?????? ?? ?? ???????? ????? ???????? ??
  ?????? ??????? ?? ???. ???? ?????? ???? i ???? ??
  ???? j ?? ???? ??? ??????? ?? ???.

????? ???? ??????? ???????
9 Extremely preferred ????? ????? ??? ?? ?? ???????
7 Very strongly preferred ????? ? ????? ?? ??????? ???? ???
5 Strongly preferred ????? ?? ??????? ?? ????? ???
3 moderately preferred ??? ???? ?? ??????? ?? ?????
1 Equally preferred ????? ? ??????? ?? ????? ?????
2?4?6?8 ??????? ??? ?????
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A B C
A 1 2 8
B 1/2 1 6
C 1/8 1/6 1
?????? ?????? ???? ??????? ?? ???? ?? ????? ????? ?????? ?????? ???? ??????? ?? ???? ?? ????? ????? ?????? ?????? ???? ??????? ?? ???? ?? ????? ????? ?????? ?????? ???? ??????? ?? ???? ?? ????? ?????
A B C
A 1 1/3 1/4
B 3 1 1/2
C 4 2 1
?????? ?????? ???? ??????? ?? ???? ?? ????? ???? ?????? ?????? ???? ??????? ?? ???? ?? ????? ???? ?????? ?????? ???? ??????? ?? ???? ?? ????? ???? ?????? ?????? ???? ??????? ?? ???? ?? ????? ????
A B C
A 1 4 4
B 1/4 1 7
C 1/4 1/7 1
?????? ?????? ???? ??????? ?? ???? ?? ????? ??? ?????? ?????? ???? ??????? ?? ???? ?? ????? ??? ?????? ?????? ???? ??????? ?? ???? ?? ????? ??? ?????? ?????? ???? ??????? ?? ???? ?? ????? ???
A B C
A 1 1/4 1/6
B 4 1 1/3
C 6 3 1
?????? ?????? ???? ??????? ?? ???? ?? ????? ???? ?????? ?????? ???? ??????? ?? ???? ?? ????? ???? ?????? ?????? ???? ??????? ?? ???? ?? ????? ???? ?????? ?????? ???? ??????? ?? ???? ?? ????? ????
26
???? ???? ????? ???
???? 1 3 2 2
???? 1/3 1 1/4 1/4
????? 1/2 4 1 1/2
??? 1/2 4 2 1
?????? ?????? ???? ??????? ?????? ?????? ???? ??????? ?????? ?????? ???? ??????? ?????? ?????? ???? ??????? ?????? ?????? ???? ???????
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??????? ?????

• ??? ?? ?????? AHP ????? ??????? ????? ??? ??
  ?????? ?? ???? ????? ??????? ????? ?? ?????? ????
  ? ???? ?? ????? ?? ?? ?? ????? ???.
• ????? ???????
• aij ????? i ?? j
• aik ????? i ?? k
• akj ????? k ?? j
• ??? ????? aikakjaij ?? ???? ?? i ? j ? k??????
  ???? ?????. ?????? ????? ?????? ???.

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A B C
A 1 2 8
B 1/2 1 6
C 1/8 1/6 1
?????? ?????? ???? ??????? ?? ???? ?? ????? ????? (????????) ?????? ?????? ???? ??????? ?? ???? ?? ????? ????? (????????) ?????? ?????? ???? ??????? ?? ???? ?? ????? ????? (????????) ?????? ?????? ???? ??????? ?? ???? ?? ????? ????? (????????)
A B C
A 1 2 6
B 1/2 1 3
C 1/6 1/3 1
?????? ?????? ???? ??????? ?? ???? ?? ????? ????? (??????) ?????? ?????? ???? ??????? ?? ???? ?? ????? ????? (??????) ?????? ?????? ???? ??????? ?? ???? ?? ????? ????? (??????) ?????? ?????? ???? ??????? ?? ???? ?? ????? ????? (??????)
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?????? ???

• ??? ????(local priority).
• ??? ???? ?? ???? ?? ????? ?? ???????? ? ??
  ??????? ?? ?????? ?????? ???? ???? ?? ???
• ??? ?????(overall priority)
• ?? ????? ?????? ???? ?? ???? ?? ????? ?????? ??
  ??? ? ?? ???? ?? ????? ?? ???? ???? ?? ????.

30
?????? ?????? ??? ????

• ?????? ?????? ???? ?????? ??? ???? ?? ??????? ??
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• ?????? ??????? ????
• ?????? ?????? ?? ???????? ???? ????? ?? ????
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• ??? ????? ??????
• ??? ????? ?????? ????????
• ??? ????? ????
• ?????? ?????? ????? ????- ????? ?????- ???????
  ?????-??????? ?????

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?????? ??? ???? ?? ????? ?????? ???????

• ??????? ?????
• ??? 1- ????? ?? ???? ?? ?? ?????? ???? ????????
  ????.
• ??? 2- ??????? ????? ?? ??? ?? ???? ?????.
• ??? 3- ?????? ??????? ????? ?????? ?? ?????? ????
  ???.

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A B C
A 1 2 8
B 1/2 1 6
C 1/8 1/6 1
?????? ?????? ???? ??????? ?? ???? ?? ????? ????? ?????? ?????? ???? ??????? ?? ???? ?? ????? ????? ?????? ?????? ???? ??????? ?? ???? ?? ????? ????? ?????? ?????? ???? ??????? ?? ???? ?? ????? ?????
A B C
A 1 2 8
B 1/2 1 6
C 1/8 1/6 1
??? 13/8 19/6 15
A B C
A 8/13 12/19 8/15
B 4/13 6/19 6/15
C 1/13 1/19 1/15
A B C ???????
A 8/13 12/19 8/15 0.593
B 4/13 6/19 6/15 0.341
C 1/13 1/19 1/15 0.066
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???? ???? ????? ???
A 0.123 0.087 0.593 0.265
B 0.320 0.274 0.341 0.655
C 0.557 0.639 0.066 0.080
??? ????????? ?????? ???????? ???? ???? ????? ? ??? ??? ????????? ?????? ???????? ???? ???? ????? ? ??? ??? ????????? ?????? ???????? ???? ???? ????? ? ??? ??? ????????? ?????? ???????? ???? ???? ????? ? ??? ??? ????????? ?????? ???????? ???? ???? ????? ? ???
34
???? ???? ????? ???
???? 1 3 2 2
???? 1/3 1 1/4 1/4
????? 1/2 4 1 1/2
??? 1/2 4 2 1
?????? ?????? ???? ??????? ?????? ?????? ???? ??????? ?????? ?????? ???? ??????? ?????? ?????? ???? ??????? ?????? ?????? ???? ???????
???? ???? ????? ???
0.398 0.085 0.218 0.299
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?????? ??? ????? ????????? ??? ????? ?? ?????
?? ????? ??? ?? ????? ??????? ??? ???? ??????? ??
??? ???? ?? ?????
????? ??? ?????
A 0.3980.1230.0850.0870.2180.5930.2990.2650.265
B 0.3980.3200.0850.2740.2180.3410.2990.6550.421
C 0.3980.5570.0850.6390.2180.0660.2990.0800.314

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???? ???? ????? ??
??? ????? ??????? ??????
0.421 B 1
0.314 C 2
0.265 A 3
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• Jilley Bean Co. is selecting a new location to
  expand its operations. The company want to use
  AHP to help it decide which location to build its
  new plant. Jilley Bean Co. has four criteria they
  will base their decision on these are the
  following
• property price,
• distance from suppliers,
• the quality of the labor pool, and
• the cost of labor.
• They have three locations to decide from.

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The best location
Price
Distance
Labor
Wage
A
B
C
39
??????? ???? ?????? ???? ?? ???
Rank the criteria in order of importance use the
same method used in ranking each criterion.
Criteria Price Distance
Labor Wages Price 1
1/5 3
4 Distance 5
1 9 7
Labor 1/3 1/9
1 2 Wages
1/4 1/7 1/2
1
40
??????? ???? ????? ?? ???? ?? ??????
PRICE A B C A
1 3 2 B 1/3 1
1/5 C 1/2 5 1
DISTANCE A B C A
1 6 1/3 B 1/6 1
1/9 C 3 9 1
LABOR A B C A
1 1/3 1 B 3
1 7 C 1 1/7 1
WAGES A B C A
1 1/3 1/2 B 3
1 4 C 2 1/4 1
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?????? ??? ???? ????? ?? ?? ???? ????( ???????
?????)
PRICE A B
C A 1 3 2
B 1/3 1 1/5
C 1/2 5
1 11/6 9 16/5
PRICE A B
C A 1 3 2
B 1/3 1 1/5
C 1/2 5
1 11/6 9 16/5

• First sum (add up) all the values in
  each column.

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?????? ??? ???? ????? ?? ?? ???? ????( ???????
?????)
PRICE A B
C A 111/6 6/11 39 3/9
216/5 5/8
B 1/311/6 2/11
19 9 1/516/5 1/16
C
1/211/6 3/11 59 5/9 116/5
5/16 1 1
1

• Next the values in each column are divided by
  the corresponding column sums.

NOTICE the values in each column sum to 1.
43
?????? ??? ???? ????? ?? ?? ???? ????( ???????
?????)
PRICE
A B
C Row
Average A 6/11 .5455 3/9.3333
5/8 .6250 1.5038 3 .0512 B
2/11.1818 1/9.1111
1/16.0625 .3544 3 .1185 C
3/11.2727 5/9.5556
5/16.3803 1.2086 3 .3803


1.000

• Next find the average of each row.

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??? ???? ????? ?? ?? ???? ??????
Location Price Distance
Labor Wages A .5012
.2819 .1790 .1561
B .1185 .0598
.6850 .6196 C
.3803 .6583 .1360
.2243
45
??? ???? ?????? ?? ???
Criteria Price Distance Labor
Wage Row Average Price
.1519 .1375 .2222 .2857
.1933 Distance .7595
.6878 .6667 .5000
.6535 Labor .0506 .0764
.0741 .1429
.0860 Wage .0380 .0983
.0370 .0714
.0612 1.000
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?????? ??? ????? ????? ??

CRITERIA Price .1993 Distance
.6535 Labor .0860 Wage .0612
Location Price Distance
Labor Wages A .5012
.2819 .1790 .1561 B
.1185 .0598
.6850 .6196 C .3803
.6583 .1360 .2243
X
Location A score .1993(.0512) .6535(.2819)
.0860(.1790) .0621(.1561) .3091 Location B
score .1993(.1185) .6535(.0598)
.0860(.6850) .0612(.6196) .1595 Location C
score .1993(.3803) .6535(.6583)
.0860(.1360) .0612(.2243) .5314
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???? ???? ????? ??
LOCATION Score A

.3091 B .1595 C

.5314 1.0000
Ranking CgtAgtB