ahp procedure general

7/23/2019 AHP Procedure General

http://slidepdf.com/reader/full/ahp-procedure-general 1/26

Dr.P.Muralidhar

NICMAR CISC

Hyderabad



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



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 ,.-



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



*imple mathematics criteria , set by the decisionmaker -

preferences of that criteria , also set by the

decision maker-the standard preference table



"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

:

;

<



=ecause the standard preference tablehas been determined by e3perienced

researchers in A!" to be a reasonable basis for comparing t#o alternatives



*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



*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



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



"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 =



"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



"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



"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#



.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



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



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



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



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



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



%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



4he 2SDA used it or the selection obrid#e materials across the nation inse!eral states.



Not really as lon# as the decisionma*er has set criteria and setpreerences o that criteria AHP can be

used.



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<



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,.



4HAN3 82

ahp procedure general

Documents