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PENGAMBILAN KEPUTUSAN DAN MODELING
Proses Hirarki Analitik (Analytical Hierarchy Process-AHP)
Marimin
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KOMPONEN KEPUTUSAN
AlternatifKeputusan
Kriteria Keputusan
Bobot Kriteria
ModelPenilaian
ModelPenghitungan
TipePengambil Keputusan
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Decision Making
We need to prioritize both tangible and intangible criteria:
j In most decisions, intangibles such as political factors and
social factors
take precedence over tangibles such as economic factors and
technical factorsj It is not the precision of measurement on a particular factor
that determines the validity of a decision, but the importance
we attach to the factors involved.
j How do we assign importance to all the factors and synthesize
this diverse information to make the best decision?
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Knowing Less, Understanding More
Youdontneedto knowevery-
thingtogettotheanswer.
Expertafterexpertmissedthe
revolutionarysignificanceof
what Darwinhadcollected.
Darwin,who knewless,
somehowunderstoodmore.
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Nonmonotonic Relative Nature of Absolute Scales
Good for
preserving food
Bad for
preserving food
Good for
preserving food
Bad forcomfort
Good for
comfort
Bad for
comfort
100
0
Temperature
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MCDMSEBAGAISALAHSATUMODEL DALAM
PENGAMBILAN KEPUTUSAN
Tujuanyangakandicapai
Masalahyangakandiselesaikan
Alternatives
alat/rencana/
Pengambil
Keputusan
Kriteria
Kinerja
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Linear Hierarchy
component,
cluster(Level)
element
A loop indicates that eachelement depends only on itself.
Goal
Subcriteria
Criteria
Alternatives
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PRINSIP KERJAAHP
Penentuan Komponen Keputusan
- Tujuan/Sasaran
- Kriteria
- Alternatif
Penyusunanhirarkidari komponen keputusan
PenilaianAlternatifdan Kriteria
Pemeriksaan KonsistensiPenilaian
PenentuanPrioritas KriteriadanAlternatif
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Comparison Matrix
Given: Three apples of different sizes.
Theimagecannotbedisplayed.Yourcomputer may nothaveenough memory
toopen theimage,ortheimagemay havebeen corrupted.Restartyourcomputer,and thenopen thefileagain. Ifthered x stillappea
Theimagecannotbe displayed.Your computer may nothaveenough memory toopen theimage,or the imagemay havebeen corrupted.Restartyour computer,and then open thefile
again.If thered x stillappears,you may havetodeletetheimageand then insertitagain.
Theimagecannotbe displayed.Yourcomputer may nothaveenough memory toopen theimage,or theimagemay havebeen corrupted.Restartyour computer,and then open thefileagain.If thered xstillappears,you may havetodeletetheimageand then insertitagain.
Size
ComparisonApple A Apple B Apple C
Apple A S1/S1 S1/S2 S1/S3
Apple B S2 /S1 S2 /S2 S2 /S3
Apple C S3 /S1 S3 /S2 S3 /S3
Apple A Apple B Apple C
We Assess Their Relative Sizes By Forming Ratios
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Pairwise ComparisonsSize
Apple A AppleB AppleC
Size
Comparison
Apple A Apple B Apple C
Apple A 1 2 6 6/10 A
Apple B 1/2 1 3 3/10 B
Apple C 1/6 1/3 1 1/10 C
When the judgments are consistent, as they are here, any normalized
column gives the priorities.
Resulting
Priority
Eigenvector
Relative Size
of AppleTheimagecannotbe displayed.Your computer may nothaveenough memory toopen theimage,or the imagemay havebeen corrupted.Restartyour computer,and then open thefileagain.Ifthe red x stillappears,you may haveto deletetheimageand then insertitagain.
Theimagecannotbe displayed.Yourcomputer may nothaveenough memory toopen theimage,or theimagemay havebeen corrupted.Restartyour computer,and then open thefileagain.If thered xstillappears,you may havetodeletetheimageand then insertitagain.
Theimagecannotbedisplayed.Yourcomputer may nothaveenough memorytoopen theimage,ortheimagemay havebeen corrupted.Restartyourcomputer,and thenopen thefileagain. Ifthered x still appea
Theimagecannotbe displayed.Your computer may nothaveenough memory toopen theimage,or the imagemay havebeen corrupted.Restartyour computer,and then open thefileagain.If thered x stillappears,you may havetodeletetheimageand then insertitagain.
Theimagecannotbe displayed.Yourcomputer may nothaveenough memory toopen theimage,or theimagemay havebeen corrupted.Restartyour computer,and then open thefileagain.If thered xstillappears,you may havetodeletetheimageand then insertitagain.
Theimagecannotbedisplayed.Yourcomputer may nothaveenough memorytoopen theimage,ortheimagemay havebeen corrupted.Restartyourcomputer,and thenopen thefileagain.I fthered x stillappea
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Goal
SatisfactionwithSchool
Learning Friends School Vocational College Music
Life Training Prep. Classes
SchoolA
SchoolC
SchoolB
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1 Equal importance
3 Moderate importance of one over another
5 Strong or essential importance
7 Very strong or demonstrated importance
9 Extreme importance
2,4,6,8 Intermediate values
Use Reciprocals forInverse Comparisons
Fundamental Scale of Absolute Numbers
for PairwiseC
omparisons
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School Selection
L F SL VT CP MC
Learning 1 4 3 1 3 4 .32
Friends 1/4 1 7 3 1/5 1 .14
SchoolLife 1/3 1/7 1 1/5 1/5 1/6 .03
VocationalTrng. 1 1/3 5 1 1 1/3 .13
CollegePrep. 1/3 5 5 1 1 3 .24
MusicClasses 1/4 1 6 3 1/3 1 .14
Weights
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Memilih Komputer
Kompatabilita
s
Unjuk kerja Purnajual
IBM
ACER
Hp Compaq
Sasaran
Kriteria
IBM
ACER
Hp Compaq
IBM
ACER
Hp Compaq
Alternatif
Gambar : Hubungansasaran, kriteriadanalternatifdalamAHP
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Nilai Keterangan
1 Samapenting (Equal)3 Sedikitlebihpenting (Moderate)
5 Jelaslebihpenting (Strong)
7 Sangatjelaspenting (Very Strong)
9 Mutlak lebihpenting (Extreme)
2,4,6,8 Apabilaragu-raguantara2nilaiyangberdekatan
1/(1-9) Kebalikannilaitingkat kepentingandariskala1-9
Misalnyahasilperbandinganberpasanganuntuk contohdiatasadalah:
E1 Kompatibilitas Unjuk kerja PurnajualKompatibilitas 1/1 3/1
Unjuk kerja 2/1 1/1 4/1
Purna jual 1/3 1/1
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Penyelesaianuntuk contohdiatas (misalnyadengansyaratnilaieigensudah
tidak berubahsampai 4 angkadibelakang koma):
Ubahmatrik menjadibilangandesimal:
1.000
2.000
0.333
0.500
1.000
0.250
3.000
4.000
1.000
Iterasi keI :
Kuadratkanmatrik diatas
1.000
2.000
0.333
0.500
1.000
0.250
3.000
4.000
1.000
1.000
2.000
0.333
0.500
1.000
0.250
3.000
4.000
1.000
X
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3.0000
5.3333
1.1666
1.7500
3.0000
0.6667
8.0000
14.0000
3.0000
=
Jumlahkannilaisetiapbarismatrik danhitungnilaihasilnormalisasinya:
JmlBaris Hasil Normalisasi
3.0000
5.3333
1.1666
1.7500
3.0000
0.6667
8.0000
14.0000
3.0000
12.7500
22.3333
4.8333
12.7500/39.9166=0.3194
22.3333/39.9166=0.5595
4.8333/39.9166=0.1211Jumlah 39.9166 1.0000
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Iterasi keII :
Kuadratkan kembalimatrik diatas
3.0000
5.3333
1.1666
1.7500
3.0000
0.6667
8.0000
14.0000
3.0000
3.0000
5.3333
1.1666
1.7500
3.0000
0.6667
8.0000
14.0000
3.0000
X
27.6658
48.3311
10.5547
15.8330
27.6662
6.0414
72.4984
126.6642
24.6653
=
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Jumlahkannilaisetiapbarismatrik danhitungnilaihasilnormalisasinya:
JmlBaris Hasil Normalisasi
27.6658
48.3311
10.5547
15.8330
27.6662
6.0414
72.4984
126.6642
24.6653
115.9967
202.6615
44.2614
0.3196
0.5584
0.1210
Jumlah 362.9196 1.0000
HitungPerbedaannilaieigensebelumdansesudahnilaieigensekarang:
0.3196
0.5584
0.1210
0.3194
0.5595
0.1211
-
-
-
=
=
=
- 0.0002
0.0011
- 0.0009
Terlihatbahwaperbedaantersebuttidak terlalubesarsampaidengan 4 desimal
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Iterasi keIII :
Bila kitamelakukaniterasisatu kalilagi,makasyaratakanterpenuhi (nilaieigensudahtidak berbedasampai 4 desimal)
Jadinilaieigenyangdiperolehadalah : 0.3196,0.5584,0.1220
Apakahmaknadarinilaieigendiatas?
Berikutiniadalahmatrik berpasanganbersertadengannilaieigennya:
Komatibilitas Unjuk kerja Purnajual Nilai Eigen
Kompatibilitas 1.000 0.500 3.000 0.3196
Unjuk kerja 2.000 1.000 4.000 0.5584
Purna jual 0.333 0.250 1.000 0.1220
Berdasarkannilaieigenmaka kitatahubahwa kriteriayangpalingpenting
adalahUnjuk kerja, kemudian KompatibilitasdanterakhirPurnajual
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Memilih Komputer1.00
Kompatibil.
0.3196
Unjuk kerja
0.5584
Purnajual
0.1220
IBM
ACER
Hp Compaq
Sasaran
Kriteria
IBM
ACER
Hp Compaq
IBM
ACER
Hp Compaq
Gambar : HasilPerhitunganBobot Kriteria
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PEMBOBOTANALTERNATIF
Susunlahmatrik berpasanganuntuk alternatif-alternatifbagisetiap kriteria,
misalnyauntuk kriteria Kompatibilitasadalah :
Kompatibilitas IBM ACER Hp Compacq
IBM 1/1 1/4 4/1 1/6
ACER 4/1 1/1 4/1 1/4
Hp 1/4 1/4 1/1 1/5
Compaq 6/1 4/1 5/1 1/1
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Unjuk Kerja IBM ACER Hp Compaq
IBM 1/1 2/1 5/1 1/1
ACER 1/2 1/1 3/1 2/1
Hp 1/5 1/3 1/1 1/4
Compaq 1/1 1/2 4/1 1/1
Misalnyauntuk kriteriaUnjuk kerjaadalah :
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Memilih Komputer1.00
Kompatibil
0.3196
Unjuk kerja
0.5584
Purnajual0.1220
IBM (0.1160)
ACER (0.2470)
Hp (0.0600)
Compaq (0.5700)
IBM (0.3790)
ACER (0.2900)
Hp (0.0740)
Compaq (0.2570)
IBM (0.3010)
ACER (0.2390)
HP (0.2120)
Compaq (0.2480)
Gambar: HasilAkhirSeluruhBobot
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Darihasilanalisadiatas,makajawabandapat kitaperolehdenganjalan
mengalikanmatrik nilaieigendarialternatifdenganmatrik bobotmatrik:
Kompatibilitas Unjuk kerja Purnajual Bobot Kriteria
IBM 0.1160 0.3790 0.3010 0.3196
ACER 0.2470 0.2900 0.2390 0.5584
Hp 0.0600 0.0740 0.2120 0.1220
Compac 0.5770 0.2570 0.2480
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Hasilnya :
IBM
Acer
Hp
Compaq
: 0.3060
: 0.2720
: 0.0940
: 0.3280
Jadirangkingyangdiperoleh :
Compaq : 0.3280
IBM : 0.3060
Acer : 0.2720
Hp : 0.0940
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ConsistencyRatio (CR)
ConsistencyRatiomerupakanparameteryangdigunakanuntuk memeriksaapakahperbandinganberpasangantelahdilakukandengan kosekwenatau
tidak.
CR
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ConsistencyRation (CR)
ConsistencyRatiomerupakanparameteryangdigunakanuntuk memeriksaapakahperbaikanberpasangantelahdilakukandengan kosekwenatau
tidak.Sebagaimisaluntuk Kriteria Kompatibilitas
Kompatibilitas IBM ACER Hp Compaq
IBM 1/1 1/4 4/1 1/6
ACER 4/1 1/1 4/1 1/4
Hp 1/4 1/4 1/1 1/5
Compaq 6/1 4/1 5/1 1/1
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Darinilaifaktor(nilaieigen)dari kriteria kompatibilitasadalah:
IBM
Acer
Hp
Compaq
: 0.1160
: 0.2470
: 0.0600
: 0.5770
Kitadapat WeightedSum Vectordenganjalanmengalikan keduamatrik tsb.
1/1 1/4 4/1 1/6 0.1160 0.5139
4/1 1/1 4/1 1/4 0.2470 1.0953
1/4 1/4 1/1 1/5 * 0.0600 = 0.2662
6/1 4/1 5/1 1/1 0.5770 2.5610
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Kemudian kitamenghitungConsistency Vectordenganmenentukannilai
rata-ratadariweightedsumvector:
0.5139/0.1160 4.4303
1.0953/0.2470 4.4342
0.2662/0.0600 = 4.4358
2.5610/0.5770 4.4385
Nilairata-ratadariConsistency Vectoradalah :
T = (4.4303 + 4.4342 + 4.4358 + 4.4385)/ 4 = 4.4347
NilaiConsistencyIndex dapatdihitungdenganmenggunakanrumus :
CI = (T - n)/ (n 1) ; n : banyak alternatif
= (4.4347 4)/ (4 1)
=0.1449
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Untuk menghitungConsistencyRatio,dibutuhkannilaiRI,yaituindeks
randomyangdidapatdaritabelberikut:
n RI
2 0.00
3 0.58
4 0.90
5 1.12
6 1.24
7 1.32
8 1.41
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PENYELESAIANAHP DENGAN
CRITERIUM DECISION PLUS
1. JalankanprogramCriterium DecisionPlus : Start/Programs/Criterium
DecisionPlus
2. Buatfilebrainstorming,denganperintah File/New
3. Buatstrukturhirarkidenganperintah View/GenerateHierarchy
4. TentukanmodelAHPdenganperintahModel/Technique/AHP
5. Lakukanpenilaianterhadap kriteriadenganperintah :
a. Klik kotak Goal
b.Lakukanperintah : Block/Ratesubcriteria
c.Penilaian kroteriadilakukandenganjalanmelakukanperintah:
Methods/FullPairwise
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d.Lakukanpenilaianperbandinganantaraduaalternatifuntuk
setiap kriteriayangtersedia
e.Setelahselesai kliklahtombol OK
6. Untuk melihathasilakhir,gunakanperintahResult/ DecisionScores
7. Untuk melihathasilakhirdalambentuk tabeldata,gunakanperintah
View/Result Data
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METODE PENILAIAN DENGANAHP
PerbandinganAlternatifA,B,C, D
Misalnyapada kasus
AlternatifA :
AlternatifB :
AlternatifC :
AlternatifD :
A B C D
1 3 5 1/7
- 1 4 7
- - 1 3
- - - 1
A
B
C
D
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FOKUS
FAKTOR
AKTOR
TUJUAN
ALTERNATIF
PENGEMBANGAN INDUSTRI
SumberdayaManusia
(28,79 %)
SumberdayaAlam
(16,52 %)
Modal
(16,13 %)Pemasaran
(12,13 %)
SaranadanPrasarana(6,28 %)
KebijakanPemerintah(20,15 %)
Pemerintah
(17,62 %)
Petani
(20,21 %)
Pengusaha
(16,94 %)
Koperasi
(18,23 %)
Perbankan
(13,00 %)
Pedagang
(13,99 %)
PerluasanLapanganPekerjaan(20,48 %)
PerluasanPasar(28,09 %)
PeningkatanDayaSaing(14,14 %)
PeningkatanPendapatan(25,44 %)
PembangunanDaerah
(11,85 %)
MempertahankandanMemperkuatindustriyangtelahada
(45,90 %)
MenciptakansuasanayangmedukungtumbuhnyaindustriBaru
(54,10 %)
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Level 0 : Fokus
Level 2 :
Tujuan
Level 3 :
Strategi
Penanggulangan Krisis Ekonomi
Nilai
Tukar
Rupiah
10.7 %
HargaMinyak
Dunia
6.4 %
Hutang
Pemerintah
9.9 %
Kebijakan
Pemerintah
17.7%
Kepemimpinan
Nasional
22.3 %
Ketahanan Ekonomi Nasional
70.6%
CitradanKredibilitas
Internasional
29.4%
Privatisasi
BUMN
13.8 %
Liberalisasi
Perdagangan
19.3 %
Rekapitalisasi
PerbankanJilid Dua
15.8 %
Penegakan
Hukum
33 %
Pemberdayaan
EkonomiRakyat/
SektorRiil
51.1%
Level 1 : Faktor
A. Struktur Hierarki dan Prioritas Penanggulangan Krisis Ekonomi
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Level 0 : Fokus
Level 1 : Faktor
Level 2 :
Tujuan
Level 3 :
Strategi
Penanggulangan Ledakan
Pengangguran
Pasar
Tenaga
Kerja
14.4 %
UMR
10.5%
Pendidikan &
KeterampilanTenaga
Kerja
24.3 %
Regulasi
Ketenagakerjaan
& Indag
10.7 %
Sumberdaya
Alam
10.6 %
Sumberdaya
Finansial
13.9 %
Pertumbuhan
Ekonomi
39.9 %
Pemerataan
Sumberdaya Ekonomi
60.1 %
Pembangunan
Infrastruktur
28.6 %
Pemberdayaan
UsahaMikro & Kecil
51.3 %
Investasi
Swasta &
PMA
20.1 %
Penegakan
Hukum
15.6%
B.Struktur Hierarki dan Prioritas Manajemen Krisis Pengangguran