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83

Int. J. Services Sciences, Vol. 1, No. 1, 2008

Decision making with the analytic hierarchy

process

Thomas L. SaatyKatz Graduate School of Business,

University of Pittsburgh,

Pittsburgh, PA 1!"#, USA $%&ail'saaty()atz*+itt*edu

Abstract: ecisions involve &any intangibles that need to be traded off* -o do

that, they have to be &easured along side tangibles .hose &easure&ents &ust

also be evaluated as to, ho. .ell, they serve the ob/ectives of the decision

&a)er* -he Analytic 0ierarchy Process A0P2 is a theory of &easure&ent

through +air.ise co&+arisons and relies on the /udge&ents of e+erts to derive

+riority scales* 4t is these scales that &easure intangibles in relative ter&s* -he

co&+arisons are &ade using a scale of absolute /udge&ents that re+resents,

ho. &uch &ore, one ele&ent do&inates another .ith res+ect to a given

attribute* -he /udge&ents &ay be inconsistent, and ho. to &easure

inconsistency and i&+rove the /udge&ents, .hen +ossible to obtain better

consistency is a concern of the A0P* -he derived +riority scales are synthesised

by &ulti+lying the& by the +riority of their +arent nodes and adding for all

such nodes* An illustration is included*

Keywords: decision &a)ing5 intangibles5 /udge&ents5 +riorities Analytic 0ierarchy

Process5 A0P5 co&+arisons5 ratings5 synthesis*

Reference to this +a+er should be &ade as follo.s' Saaty, -*6* !##82

7ecision &a)ing .ith the analytic hierarchy +rocess, Int. J. Services

Sciences, 9ol* 1, :o* 1, ++*83;e&ber of the :ational Acade&y of

$ngineering, USA* 0e is internationally recognised for his decision%&a)ing

+rocess, the Analytic 0ierarchy Process A0P2 and its generalisation to

net.or) decisions, the Analytic :et.or) Process A:P2* 0e .on the Gold

>edal fro& the 4nternational Society for >ulticriteria ecision >a)ing for his

contributions to this field* 0is .or) is in decision &a)ing, +lanning, conflict

resolution and in neural synthesis*

1Introduction

?e are all funda&entally decision &a)ers* $verything .e do consciously or

unconsciously is the result of so&e decision* -he infor&ation .e gather is to hel+ us

understand occurrences, in order to develo+ good /udge&ents to &a)e decisions about

these occurrences* :ot all infor&ation is useful for i&+roving our understanding and

/udge&ents* 4f .e only &a)e decisions intuitively, .e are inclined to believe that all

)inds of infor&ation are useful and the larger the @uantity, the better* But that is not true*

-here are nu&erous ea&+les, .hich sho. that too &uch infor&ation is as bad as little

infor&ation* Kno.ing &ore does not guarantee that .e understand better as illustrated

by so&e authors .riting $+ert after e+ert &issed the revolutionary significance of

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Decision making with the AH 8

=o+yright C !##8 4nderscience $nter+rises 6td*

.hat ar.in had collected* ar.in, .ho )ne. less, so&eho. understood &oreD* -o

&a)e a decision .e need to )no. the +roble&, the need and +ur+ose of the decision, the

criteria of the decision, their subcriteria, sta)eholders and grou+s affected and thealternative actions to ta)e* ?e then try to deter&ine the best alternative, or in the case of

resource allocation, .e need +riorities for the alternatives to allocate their a++ro+riate

share of the resources*

!"ita sem#a $a%a %asarn&a $engam'il ke$#t#san. Segala ses#at# &ang kita lak#kan

secara sa%ar ata# ti%ak sa%ar a%alah hasil %ari 'e'era$a ke$#t#san. In(ormasi &ang

kami k#m$#lkan a%alah #nt#k mem'ant# kita memahami ke)a%ian, #nt#k

mengem'angkan $enilaian &ang 'aik #nt#k mem'#at ke$#t#san tentang ke)a%ian ini.

*i%ak sem#a in(ormasi 'erg#na #nt#k meningkatkan $emahaman %an $enilaian kita. Jika

kita han&a mem'#at ke$#t#san secara int#iti(, kita cen%er#ng #nt#k $erca&a 'ahwa

sem#a )enis in(ormasi &ang 'erg#na %an le'ih 'esar k#antitas, semakin 'aik. *a$i it#

ti%ak 'enar. A%a 'an&ak contoh, &ang men#n)#kkan 'ahwa terlal# 'an&ak in(ormasi

se'#r#k se%ikit in(ormasi.

+engetah#i le'ih ti%ak men)amin 'ahwa kita memahami le'ih 'aik se$erti &ang

%igam'arkan oleh 'e'era$a $en#lis men#lis Ahli setelah ahli merin%#kan makna

revol#sioner a$a &ang telah %ik#m$#lkan Darwin. Darwin, &ang tah# se%ikit, entah

'agaimana memahami le'ih . -nt#k mem'#at ke$#t#san &ang kita $erl# tah# masalah,

ke'#t#han %an t#)#an ke$#t#san, kriteria ke$#t#san, s#'kriteria mereka, $emangk#

ke$entingan %an kelom$okkelom$ok &ang terkena %am$ak %an tin%akan alternati( #nt#k

mengam'il. "ami kem#%ian menco'a #nt#k menent#kan alternati( ter'aik, ata# %alam

kas#s alokasi s#m'er %a&a, kita $erl# $rioritas alternati( #nt#k mengalokasikan saham

&ang ses#ai mereka %ari s#m'er %a&a.2

ecision &a)ing, for .hich .e gather &ost of our infor&ation, has beco&e a&athe&atical science today Eiguera et al*, !##2* 4t for&alises the thin)ing .e use so

that, .hat .e have to do to &a)e better decisions is trans+arent in all its as+ects* ?e need

to have so&e funda&ental understanding of this &ost valuable +rocess that nature

endo.ed us .ith, to &a)e it +ossible for us to &a)e choices that hel+ us survive*

ecision &a)ing involves &any criteria and subcriteria used to ran) the alternatives of a

decision* :ot only does one need to create +riorities for the alternatives .ith res+ect to

the criteria or subcriteria in ter&s of .hich they need to be evaluated, but also for the

criteria in ter&s of a higher goal, or if they de+end on the alternatives, then in ter&s of the

alternatives the&selves*-he criteria &ay be intangible, and have no &easure&ents to

serve as a guide to ran) the alternatives, and creating +riorities for the criteria the&selves

in order to .eigh the +riorities of the alternatives and add over all the criteria to obtain the

desired overall ran)s of the alternatives is a challenging tas)* 0o.F 4n the li&ited s+ace

.e have, .e can only cover so&e of the essentials of &ulticriteria decision &a)ing,

leaving it to the reader to learn &ore about it fro& the literature cited at the end of this

+a+er*

-he &easure&ent of intangible factors in decisions has for a long ti&e, defied hu&an

understanding* :u&ber and &easure&ent are the core of &athe&atics and &athe&atics is

essential to science* So far, &athe&atics has assu&ed that all things can be assigned

nu&bers fro& &inus infinity to +lus infinity in so&e .ay, and all &athe&atical &odelling

of reality has been described in this .ay by using aes and geo&etry* :aturally, all this is

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Decision making with the AH 8

+redicated on the assu&+tion that one has the essential factors and all these factors are&easurable* But there are &any &ore i&+ortant factors that .e do not )no. ho. to

&easure than there are ones that .e have &easure&ents for* Kno.ing ho. to &easure

such factors could conceivably lead to ne. and i&+ortant theories that rely on &any &ore

factors for their e+lanations* After all, in an interde+endent universe everything de+ends

on everything else* 4s this /ust a +latitude or is there so&e truth behind itF 4f .e )ne. ho.

to &easure intangibles, &uch .ider roo& .ould be o+en to inter+ret everything in ter&s

of &any &ore factors than .e have been able to do so far scientifically* ne thing is clear,

nu&erical &easure&ent &ust be inter+reted for &eaning and usefulness according to its

+riority to serve our values in a +articular decision* 4t does not have the sa&e +riority for

all +roble&s* 4ts i&+ortance is relative*

-herefore, .e need to learn about ho. to derive relative +riorities in decision &a)ing*

engam'ilan ke$#t#san, &ang kami meng#m$#lkan se'agian 'esar in(ormasi kami, telah

men)a%i ilm# matematika hari ini !/ig#era et al., 200. Ini +eresmikan $emikiran kita

g#nakan sehingga, a$a &ang har#s kita lak#kan #nt#k mem'#at ke$#t#san &ang le'ih

'aik trans$aran %alam segala as$ekn&a. "ita $erl# memiliki 'e'era$a $emahaman %asar

$roses &ang $aling 'erharga ini 'ahwa alam %i'erkahi kita %engan, #nt#k

mem#ngkinkan 'agi kita #nt#k mem'#at $ilihan &ang mem'ant# kita 'ertahan hi%#$.

engam'ilan ke$#t#san meli'atkan 'an&ak kriteria %an s#'kriteria &ang %ig#nakan

#nt#k menent#kan $eringkat alternati( ke$#t#san. *i%ak han&a sat# $erl# mem'#at

$rioritas #nt#k alternati( seh#'#ngan %engan kriteria ata# s#'kriteria %alam hal mana

mereka $erl# %ieval#asi, teta$i )#ga #nt#k kriteria %alam hal t#)#an &ang le'ih tinggi,

ata# )ika mereka 'ergant#ng $a%a alternati(, maka %alam hal alternati(sen%iri. "riteria

m#ngkin ti%ak 'erw#)#%, %an ti%ak memiliki $eng#k#ran #nt#k mela&ani se'agai$an%#an #nt#k menent#kan $eringkat alternati(, %an menci$takan $rioritas #nt#k kriteria

sen%iri #nt#k mem$ertim'angkan $rioritas alternati( %an menam'ah le'ih %ari sem#a

kriteria #nt#k men%a$atkan )a)aran kesel#r#han &ang %iinginkan %ari alternati( a%alah

t#gas &ang menantang. agai +ana3 Dalam r#ang ter'atas &ang kita miliki, kita han&a

'isa men#t#$i se'agian $enting %ari $engam'ilan ke$#t#san m#ltikriteria,

meninggalkann&a ke$a%a $em'aca #nt#k mem$ela)ari le'ih lan)#t tentang hal it# %ari

literat#r %ik#ti$ $a%a akhir t#lisan ini.

eng#k#ran (aktor 'erw#)#% %alam ke$#t#san memiliki #nt#k wakt# &ang lama,menantang $emahaman man#sia. J#mlah %an $eng#k#ran a%alah inti %ari matematika

%an matematika sangat $enting #nt#k ilm# $engetah#an. Se)a#h ini, matematika telah%ias#msikan 'ahwa segala ses#at# %a$at %i'erikan nomor %ari min#s tak terhingga ke$l#s tak terhingga %alam 'e'era$a cara, %an sem#a $emo%elan matematika realitastelah %igam'arkan %engan cara ini %engan mengg#nakan ka$ak %an geometri. *ent#,sem#a ini %i%asarkan $a%a as#msi 'ahwa seseorang memiliki (aktor $enting %an sem#a(aktor ini %a$at %i#k#r. *a$i a%a 'an&ak (aktor &ang le'ih $enting 'ahwa kita ti%ak tah#

'agaimana meng#k#r %ari a%a orangorang &ang kita miliki $eng#k#ran #nt#k.+engetah#i 'agaimana meng#k#r (aktor(aktor se$erti %i'a&angkan 'isa men&e'a'kanteoriteori 'ar# %an $enting &ang 'ergant#ng $a%a 'an&ak (aktor #nt#k $en)elasanmereka. Setelah sem#a, %alam saling tergant#ng semesta sem#an&a tergant#ng $a%asegala ses#at# &ang lain. A$akah ini han&a 'asa'asi ata# a$akah a%a ke'enaran %i'alik it#3 Jika kita tah# 'agaimana meng#k#r 'erw#)#%, r#ang &ang le'ih l#as akan

ter'#ka #nt#k mena(sirkan segala ses#at# %alam hal &ang le'ih 'an&ak (aktor %ari$a%a

kita telah mam$# melak#kan se)a#h ilmiah. Sat# hal &ang )elas, $eng#k#ran n#merikhar#s %ita(sirkan makna %an keg#naan ses#ai %engan $rioritas #nt#k mela&ani nilainilai kita %alam ke$#t#san tertent#. *i%ak memiliki $rioritas &ang sama #nt#k sem#amasalah. Arti $entingn&a relati(.4leh karena it#, kita $erl# 'ela)ar tentang 'agaimana #nt#k mem$eroleh $rioritas relati(

%alam $engam'ilan ke$#t#san.

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8" *.5. Saat&

2Background

-here are t.o +ossible .ays to learn about anything ; an ob/ect, a feeling or an idea* -he

first is to ea&ine and study it in itself to the etent that it has various +ro+erties,

synthesize the findings and dra. conclusions fro& such observations about it* -he second

is to study that entity relative to other si&ilar entities and relate it to the& by &a)ing

co&+arisons*

-he cognitive +sychologist Blu&enthal 1

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Decision making with the AH 8H

3The analytic hierarchy process

-o &a)e a decision in an organised .ay to generate +riorities .e need to deco&+ose the

decision into the follo.ing ste+s*

1 efine the +roble& and deter&ine the )ind of )no.ledge sought*

! Structure the decision hierarchy fro& the to+ .ith the goal of the decision, thenthe ob/ectives fro& a broad +ers+ective, through the inter&ediate levels criteriaon .hich subse@uent ele&ents de+end2 to the lo.est level .hich usually is aset of the alternatives2*

3 =onstruct a set of +air.ise co&+arison &atrices* $ach ele&ent in an u++er levelis used to co&+are the ele&ents in the level i&&ediately belo. .ith res+ect to

it* Use the +riorities obtained fro& the co&+arisons to .eigh the +riorities in the

level i&&ediately belo.* o this for every ele&ent* -hen for each ele&ent inthe level belo. add its .eighed values and obtain its overall or global +riority*=ontinue this +rocess of .eighing and adding until the final +riorities of thealternatives in the botto& &ost level are obtained*

-o &a)e co&+arisons, .e need a scale of nu&bers that indicates ho. &any ti&es &ore

i&+ortant or do&inant one ele&ent is over another ele&ent .ith res+ect to the criterion or

+ro+erty .ith res+ect to .hich they are co&+ared* -able 1 ehibits the scale* -able !

ehibits an ea&+le in .hich the scale is used to co&+are the relative consu&+tion of

drin)s in the USA* ne co&+ares a drin) indicated on the left .ith another indicated at

the to+ and ans.ers the @uestion' 0o. &any ti&es &ore, or ho. strongly &ore is that

drin) consu&ed in the US than the one at the to+F ne then enters the nu&ber fro& thescale that is a++ro+riate for the /udge&ent' for ea&+le enter < in the coffee, .ine2

+osition &eaning that coffee consu&+tion is < ti&es .ine consu&+tion* 4t is auto&atic

that 1I< is .hat one needs to use in the .ine, coffee2 +osition* :ote that .ater is

consu&ed &ore than coffee, so one enters ! in the .ater, coffee2 +osition, and J in the

coffee, .ater2 +osition* ne al.ays enters the .hole nu&ber in its a++ro+riate +osition

and auto&atically enters its reci+rocal in the trans+ose +osition*

-nt#k mem'#at ke$#t#san %engan cara &ang terorganisir #nt#k menghasilkan $rioritas

kita $erl# meng#raikan ke$#t#san %alam langkahlangkah 'erik#t.

1 *ent#kan masalah %an menent#kan )enis $engetah#an &ang %icari.

2 Str#kt#r hirarki ke$#t#san %ari atas %engan t#)#an ke$#t#san, maka t#)#an %ari

$ers$ekti( &ang l#as, melal#i tingkat menengah !kriteria &ang elemen 'erik#tn&a

tergant#ng ke level teren%ah !&ang 'iasan&a a%alah sat# set alternati(.

9 #atlah sat# set matriks $er'an%ingan 'er$asangan. Setia$ elemen %alam tingkat atas

%ig#nakan #nt#k mem'an%ingkan #ns#r#ns#r %i tingkat langs#ng %i 'awah seh#'#ngan

%engan it#.

: ;#nakan $rioritas &ang %i$eroleh %ari $er'an%ingan #nt#k menim'ang $rioritas %i

tingkat %i 'awahn&a. 5ak#kan ini #nt#k setia$ elemen. "em#%ian #nt#k setia$ elemen

%alam level %i 'awah nilai tam'ah &ang %itim'ang %an mem$eroleh $rioritas secara

kesel#r#han ata# glo'al. 5an)#tkan $roses ini 'erat %an menam'ahkan hingga akhir

$rioritas alternati( %i 'awah tingkat $aling %i$eroleh

-nt#k mem'#at $er'an%ingan, kita $erl# skala angka &ang men#n)#kkan 'era$a kali

le'ih $enting ata# %ominan sat# elemen le'ih elemen lain seh#'#ngan %engan kriteria

ata# $ro$erti seh#'#ngan %engan mana mereka %i'an%ingkan. *a'el 1 men#n)#kkan

skala. *a'el 2 men#n)#kkan contoh %i mana skala %ig#nakan #nt#k mem'an%ingkan

kons#msi relati( min#man %i Amerika Serikat. Sat# mem'an%ingkan min#man &ang

%it#n)#kkan %i se'elah kiri %engan &ang lain %it#n)#kkan %i 'agian atas %an men)awa'

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2Cofee 5 11 9 1 1/2

11 /9 /91/3 /9Wine /91/9 111

1 1/4 /91/5 /31/3 1Tea 2 1

1/2 1 1Beer 1/3/29 31

Soda 1/291 14 2 2

31 1/2 /31 19Milk 1

9 123Water 9 32

88 *.5. Saat&

$ertan&aan< era$a kali lagi, ata# se'era$a k#at le'ih 'an&ak min#man &ang

%ikons#msi %i AS %ari$a%a &ang %i atas3 Sat# kem#%ian memas#ki nomor %ari skala

&ang ses#ai #nt#k $enghakiman< misaln&a mas#k 7 %i !ko$i, angg#r $osisi &ang 'erarti

'ahwa kons#msi ko$i a%alah 7 kali kons#msi angg#r. Hal ini otomatis &ang 1=7 a%alah

a$a &ang $erl# %ig#nakan %alam !angg#r, ko$i $osisi. erhatikan air &ang %ikons#msi

le'ih %ari ko$i, sehingga seseorang memas#ki 2 %alam !air, ko$i $osisi, %an > %i !ko$i,

air $osisi. Sat# selal# memas#ki sel#r#h nomor %i $osisi &ang ses#ai %an secara

otomatis mas#k tim'al 'alik %alam $osisi trans$ose.

Table 1 -he funda&ental scale of absolute nu&bers

Intensit&

o(

Im$ortance

De(inition ?@$lanation

1 $@ual 4&+ortance -.o activities contribute e@ually to the ob/ective

! ?ea) or slight

3 >oderate i&+ortance $+erience and /udge&ent slightly favour

one activity over another

>oderate +lus

Strong i&+ortance $+erience and /udge&ent strongly favour

one activity over another

" Strong +lus

H 9ery strong or

de&onstrated i&+ortance

An activity is favoured very strongly over

another5 its do&inance de&onstrated in +ractice

8 9ery, very strong

< $tre&e i&+ortance -he evidence favouring one activity over anotheris of the highest +ossible order of affir&ation

eci+rocal

s of above

4f activity ihas one of theabove non%zero nu&bersassigned to it .henco&+ared .ith activity),then)has the reci+rocalvalue .hen co&+ared

.ith i

A reasonable assu&+tion

1*1;1*< 4f the activities are very

close

>ay be difficult to assign the best value but

.hen co&+ared .ith other contrasting

activities the size of the s&all nu&bers .ould

not be too noticeable, yet they can still indicate

the relative i&+ortance of the activities*

Table 2 elative consu&+tion of drin)s

hich %rink is cons#me% more in the -SA3

An e@am$le o( e@amination #sing )#%gements

Drink cons#m$tion in -S Bo((ee ine *ea eer So%as +ilk ater

Note'-he derived scale based on the /udge&ents in the &atri is'

#*1HH #*#1< #*#! #*11" #*1

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Decision making with the AH 8