ahp procedure general
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7/23/2019 AHP Procedure General
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Dr.P.Muralidhar
NICMAR CISC
Hyderabad
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According to Operations Management 4thEdition by Russell and Taylor III it is aquantitative method for ranking decision
alternatives and selection the one givenmultiple criteria A!" is a process fordeveloping a numerical score to rank eachdecision alternative based on ho# #ell eachalternative meets the decision maker$s criteria
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Pair wise comparison matrix or all criteriaand alternati!es with respect to each criteria
"indin# Priority wei#hts rom the
synthesi$in# matrix
"indin# a %i#en !alue &A!era#e wei#ht' % max(rom wei#hted a!era#e matrix
DetermineConsistency
Accept decision matrix and use
priority wei#ht or urther calculation
Product o criteria and alternati!eswei#hts is called Normali$ed matrix
Discard decisionmatrix Consistency
)i!en another chanceto rechec* attheir ratin#s
Maximum !alue in normali$ed matrix is
the best amon# selected alternati!es
C.R+ ,.-,.-/C.R0 ,.-
C.R0 ,.-
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The question &'hich one do #e choose()or &'hich one is best () by selecting the best alternative that matches all of thedecision maker$s criteria
Eg *election of car+ vendor+ cricket playeretc
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*imple mathematics criteria , set by the decisionmaker -
preferences of that criteria , also set by the
decision maker-the standard preference table
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"RE.ERE/0E 1E2E1
Equally preferred
Equally to moderately preferred
Moderately preferred
Moderately to strongly pr eferred
*trongly preferred
*trongly to very strongly preferred
2ery strongly preferred
2ery strongly to e3tremely preferred
E3tremely preferred
/MERI0A1 2A1E
5
6
7
4
8
9
:
;
<
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=ecause the standard preference tablehas been determined by e3perienced
researchers in A!" to be a reasonable basis for comparing t#o alternatives
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*ay you have t#o criteria 0ost and quality for product A > = The cost for A? @9 and the qualityis above average The cost for =?@58 and the
quality is right at average 'hich do you choose(=y making a matri3 the price of = is very strongly preferred to A and A is only moderately preferred to= The matrices of these preferences #ould look like
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*ince price = is verystrongly preferred tothe price of A The
score of = to = is :and A to = is thereciprocal or inverse of5B:
0O*T
A =
A 5 :
= 5B: 5
0O*T
A =
A 5 :
= 5B: 5
CA1ITD
A =
A 5 5B7
= 7 5
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illey =ean 0o is selecting a ne# location to
e3pand its operations The company #ant to use
A!" to help it decide #hich location to build its
ne# plant illey =ean 0o has four criteria they#ill base their decision on these are the
follo#ingF property price+ distance from
suppliers+ the quality of the labor pool+ and thecost of labor They have three locations to decide
from
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"RI0E
A = 0
A 5 7 6
= 5B7 5 5B8
0 5B6 8 5
"RI0E
A = 0
A 5 7 6
= 5B7 5 5B8
0 5B6 8 5
GI*TA/0E
A = 0
A 5 9 5B7
= 5B9 5 5B<
0 7 < 5
1A=OR
A = 0
A 5 5B7 5
= 7 5 :
0 5 5B: 5
'AHE*
A = 0
A 5 5B7 5B6
= 7 5 4
0 6 5B4 5
*ho#ing that in preference in priceA and 0 are the equally preferred but
are preferred over =
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"RI0E
A = 0
A 5 7 6
= 5B7 5 5B8
0 5B6 8 5
? 55B9 < 59B8
.irst sum Jadd upK all
the values in each
column
"RI0E
A = 0
A 5 7 6
= 5B7 5 5B8
0 5B6 8 5
? 55B9 < 59B8
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"RI0E
A = 0
A 555B9 ? 9B55 7< ? 7B< 659B8 ? 8B;
= 5B755B9 ? 6B55 5< ? 5B< 5B859B8 5B59
0 5B655B9 ? 7B55 8< ? 8B< 559B8 ? 8B59
? 5 5 5
/e3t the valuesin each column are
divided by the
corresponding
column sums
/OTI0EF the values in each column sum to 5
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"RI0E
A = 0 Ro#
Average
A 9B55 L8488 7B<L7777 8B;L 968 ? 587; 7 ? 856
= 6B55L5;5; 5B<L5555 5B59L968 ? 7844 7 ? 55;8
0 7B55L6:6: 8B<L8889 8B59L7;7 ? 56;9 7 ? 7;7
5
/e3t convert fractions to decimals and find the
average of each ro#
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.ind the average for all the criterion by doing steps 57
on all the criteria Arriving at the follo#ing
1ocation "rice Gistance 1abor 'ages
A 856 6;5< 5:< 5895
= 55;8 8<; 9;8 95<9
0 7;7 98;7 579 6647
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Rank the criteria in order of importance Luse the same method
used in ranking each criterion
0riteria "rice Gistance 1abor 'ages
"rice 5 5B8 7 4
Gistance 8 5 < :
1abor 5B7 5B< 5 6
'ages 5B4 5B: 5B6 5
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Repeat steps 54 #ith the ne# matrices Dou should arrive at thefollo#ing F
0riteria "rice Gistance 1abor 'age Ro# Average
"rice 585< 57:8 6666 6;8: 5<77
Gistance :8<8 9;:; 999: 8 9878
1abor 89 :94 :45 546< ;9
'age 7; <;7 7: :54 956
5
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CRITERIA
Price 5<<7
Distance 9878
Labor ;9
Wage 956
0learly the distance of
the land is N5+ follo#ed by
price to suppliers+ labor
pool quality+ and last cost
of #ages
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1ocation "rice Gistance 1abor 'ages
A 856 6;5< 5:< 5895
= 55;8 8<; 9;8 95<9
0 7;7 98;7 579 6647
CRITERIA
Price 5<<7
Distance 9878
Labor ;9
Wage 956
Take the criteria matri3 and multiple it by the preference vector
1ocation A score ? 5<<7J856K 9878J6;5<K ;9J5:<K 965J5895K ? 7<5
1ocation = score ? 5<<7J55;8K 9878J8<;K ;9J9;8K 956J95<9K ? 58<8
1ocation 0 score ? 5<<7J7;7K 9878J98;7K ;9J579K 956J6647K ? 8754
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LOCATION Score
A .3091
B .19
C .31!
1.0000
=ased on the scored 1ocation 0 should be chosen for illey
=ean 0o to built a plant
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%xpert Choice a company that speciali$esin AHP desi#n sotware and perormsser!ices with it. Some o their clientele
are1 "ord Motor Company
Sprint PCS
Department o A#riculture &2SDA(
Na!y National Health Ser!ice o the 2nited 3in#dom
"errari SpA in Italy
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4he 2SDA used it or the selection obrid#e materials across the nation inse!eral states.
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Not really as lon# as the decisionma*er has set criteria and setpreerences o that criteria AHP can be
used.
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Random inde3 JRIK is the consistency inde3 of arandomly generated pair#ise comparison matri3 RI depends on the number of elements being compared
Jie+ siPe of pair#ise comparison matri3K and takes onthe follo#ing valuesF
n 5 6 7 4 8 9 : ; < 5
RI 8; < 556 564 576 545 548 54<
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Russell5 Roberta S. and 4aylor III5 6ernard 7.8perations Mana#ement 9th edition. 2pperSaddle ri!er5 New :ersey1 Prentice Hall5 ;,,<.
%xpert Choice Client =ist /http1>>expertchoice.com>customers>client list.htm
Smith5 6ush and Schmoldt. 4he Selection o6rid#e Materials 2tili$in# the Analytical
Hierarchy Process. March ;,,<./http1>>www>srs9?,;.orprod.!t.edu>pubsub@>abstract>ab?B,.
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4HAN3 82
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