9 Pengambilan Keputusan-AHP-Ilkom 2
of 39
Transcript of 9 Pengambilan Keputusan-AHP-Ilkom 2
PENGAMBILAN KEPUTUSAN DAN MODELING Proses Hirarki Analitik (Analytical Hierarchy Process-AHP)
Marimin [email protected]
KOMPONEN KEPUTUSAN Alternatif Keputusan Kriteria Keputusan Bobot Kriteria Model Penilaian Model Penghitungan Tipe Pengambil Keputusan
2
Decision MakingWe 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 factors j 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?3
Knowing Less, Understanding More You dont need to know everything to get to the answer. Expert after expert missed the revolutionary significance of what Darwin had collected. Darwin, who knew less, somehow understood more.4
Nonmonotonic Relative Nature of Absolute ScalesGood for preserving food100
Bad for comfort
Bad for preserving food
Good for comfort
Good for preserving food
0
Bad for comfort
Temperature5
MCDM SEBAGAI SALAH SATU MODEL DALAM PENGAMBILAN KEPUTUSAN
Tujuan yang akan dicapai Masalah yang akan diselesaikan
Kriteria Kinerja
Pengambil Keputusan
Alternatives alat/rencana/6
Linear HierarchyGoal Criteria component, cluster (Level) element AlternativesA loop indicates that each element depends only on itself.7
Subcriteria
PRINSIP KERJA AHP Penentuan Komponen Keputusan - Tujuan/Sasaran - Kriteria - Alternatif Penyusunan hirarki dari komponen keputusan Penilaian Alternatif dan Kriteria Pemeriksaan Konsistensi Penilaian Penentuan Prioritas Kriteria dan Alternatif
8
Comparison MatrixGiven: Three apples of different sizes.The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appea
Apple A
Apple B
Apple C
We Assess Their Relative Sizes By Forming RatiosSize Comparison Apple A Apple B Apple C Apple A S1/S1 S2 / S1 S3 / S1 Apple B S1/S2 S2 / S2 S3 / S2 Apple C S1/S3 S2 / S3 S3 / S39
Pairwise ComparisonsSize Apple ASize ComparisonThe image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
Apple BApple BThe image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
Apple CApple CResulting Priority Eigenvector Relative Size of Apple
Apple A
The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appea
Apple AThe image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
1
2
6
6/10
A
Apple BThe image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appea
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.10
Goal Satisfaction with School
Learning
Friends
School Life
Vocational Training
College Prep.
Music Classes
School A
School B
School C
11
Fundamental Scale of Absolute Numbers for Pairwise Comparisons1 3 5 7 9 Equal importance Moderate importance of one over another Strong or essential importance Very strong or demonstrated importance Extreme importance
2,4,6,8 Intermediate values Use Reciprocals for Inverse Comparisons12
School SelectionL Learning Friends School Life Vocational Trng. College Prep. Music Classes 1 1/4 4 1 F SL 3 7 1 5 5 6 VT 1 3 1/5 1 1 3 CP 3 1/5 1/5 1 1 1/3 MC 4 1 1/6 1/3 3 1 Weights .32 .14 .03 .13 .24 .1413
1/3 1/7 1 1/3 1/4 1/3 5 1
Comparison of Schools with Respect to the Six CharacteristicsLearning A B C A B C 1 3 2 1/3 1/2 1 1/3 3 1Priorities
Friends A B C A B C 1 1 1 1 1 1 1 1 1
Priorities
School Life A B C A B C 1 1/5 1 5 1 5 1 1/5 1
Priorities
.16 .59 .25Priorities
.33 .33 .33Priorities
.45 .09 .46Priorities
Vocational Trng.
A A B C 1 1/9 1/7
B 9 1 5
C 7 1/5 1 .77 .05 .17 A B C
College Prep. A B C 1 2 1 1/2 1 1/2 1 2 1
Music Classes
A .25 .50 .25 A B C 1 1/6 1/4
B 6 1 3
C 4 1/3 1 .69 .09 .22
14
Memilih Komputer Kriteria
Sasaran
Kompatabilita s Alternatif
Unjuk kerja
Purna jual
IBM ACER Hp Compaq
IBM ACER Hp Compaq
IBM ACER Hp Compaq
Gambar : Hubungan sasaran, kriteria dan alternatif dalam AHP15
Nilai 1 3 5 7 9 2,4,6,8 1/(1-9)
Keterangan Sama penting (Equal) Sedikit lebih penting (Moderate) Jelas lebih penting (Strong) Sangat jelas penting (Very Strong) Mutlak lebih penting (Extreme) Apabila ragu-ragu antara 2 nilai yang berdekatan Kebalikan nilai tingkat kepentingan dari skala 1-9
Misalnya hasil perbandingan berpasangan untuk contoh diatas adalah:E1 Kompatibilitas Unjuk kerja Purna jual Kompatibilitas 1/1 2/1 1/3 Unjuk kerja Purna jual 3/1 4/1 1/116
1/1
Penyelesaian untuk contoh diatas (misalnya dengan syarat nilai eigen sudah tidak berubah sampai 4 angka dibelakang koma): Ubah matrik menjadi bilangan desimal: 1.000 2.000 0.333 Iterasi ke I : Kuadratkan matrik diatas 1.000 2.000 0.333 0.500 1.000 0.250 3.000 4.000 1.000 X 1.000 2.000 0.333 0.500 1.000 0.250 3.000 4.000 1.000 0.500 1.000 0.250 3.000 4.000 1.000
17
=
3.0000 1.7500 8.0000 5.3333 3.0000 14.0000 1.1666 0.6667 3.0000
Jumlahkan nilai setiap baris matrik dan hitung nilai hasil normalisasinya: Jml Baris 3.0000 1.7500 8.0000 5.3333 3.0000 14.0000 1.1666 0.6667 3.0000 Jumlah 12.7500 22.3333 4.8333 39.9166 Hasil Normalisasi 12.7500/39.9166 = 0.3194 22.3333/39.9166 = 0.5595 4.8333/39.9166 = 0.1211 1.0000
18
Iterasi ke II : Kuadratkan kembali matrik diatas 3.0000 1.7500 8.0000 5.3333 3.0000 14.0000 X 1.1666 0.6667 3.0000 = 27.6658 48.3311 10.5547 15.8330 3.0000 1.7500 8.0000 5.3333 3.0000 14.0000 1.1666 0.6667 3.0000
72.4984
27.6662 126.6642 6.0414 24.6653
19
Jumlahkan nilai setiap baris matrik dan hitung nilai hasil normalisasinya: Jml Baris 27.6658 15.8330 72.4984 48.3311 27.6662 126.6642 10.5547 6.0414 24.6653 Jumlah 115.9967 202.6615 44.2614 362.9196 Hasil Normalisasi 0.3196 0.5584 0.1210 1.0000
Hitung Perbedaan nilai eigen sebelum dan sesudah nilai eigen sekarang: 0.3194 0.5595 0.1211 0.3196 = - 0.0002 0.5584 = 0.0011 0.1210 = - 0.0009
Terlihat bahwa perbedaan tersebut tidak terlalu besar sampai dengan 4 desimal20
Iterasi ke III : Bila kita melakukan iterasi satu kali lagi, maka syarat akan terpenuhi (nilai eigen sudah tidak berbeda sampai 4 desimal) Jadi nilai eigen yang diperoleh adalah : 0.3196, 0.5584, 0.1220 Apakah makna dari nilai eigen di atas? Berikut ini adalah matrik berpasangan berserta dengan nilai eigennya:Komatibilitas Kompatibilitas Unjuk kerja Purna jual 1.000 2.000 0.333 Unjuk kerja 0.500 1.000 0.250 Purna jual 3.000 4.000 1.000 Nilai Eigen 0.3196 0.5584 0.1220
Berdasarkan nilai eigen maka kita tahu bahwa kriteria yang paling penting adalah Unjuk kerja, kemudian Kompatibilitas dan terakhir Purna jual21
Memilih Komputer 1.00 Sasaran Kriteria
Kompatibil. 0.3196
Unjuk kerja 0.5584
Purna jual 0.1220
IBM ACER Hp Compaq
IBM ACER Hp Compaq
IBM ACER Hp Compaq
Gambar : Hasil Perhitungan Bobot Kriteria22
PEMBOBOTAN ALTERNATIFSusunlah matrik berpasangan untuk alternatif-alternatif bagi setiap kriteria, misalnya untuk kriteria Kompatibilitas adalah :Kompatibilitas IBM ACER Hp Compaq IBM 1/1 4/1 1/4 6/1 ACER 1/4 1/1 1/4 4/1 Hp 4/1 4/1 1/1 5/1 Compacq 1/6 1/4 1/5 1/1
23
Misalnya untuk kriteria Unjuk kerja adalah :Unjuk Kerja IBM ACER Hp Compaq IBM 1/1 1/2 1/5 1/1 ACER 2/1 1/1 1/3 1/2 Hp 5/1 3/1 1/1 4/1 Compaq 1/1 2/1 1/4 1/1
24
Memilih Komputer 1.00
Kompatibil 0.3196
Unjuk kerja 0.5584
Purna jual 0.1220
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 : Hasil Akhir Seluruh Bobot25
Dari hasil analisa di atas, maka jawaban dapat kita peroleh dengan jalan mengalikan matrik nilai eigen dari alternatif dengan matrik bobot matrik:Kompatibilitas IBM ACER Hp Compac 0.1160 0.2470 0.0600 0.5770 Unjuk kerja 0.3790 0.2900 0.0740 0.2570 Purnajual 0.3010 0.2390 0.2120 0.2480 Bobot Kriteria 0.3196 0.5584 0.1220
26
Hasilnya : IBM Acer Hp Compaq : 0.3060 : 0.2720 : 0.0940 : 0.3280
Jadi rangking yang diperoleh : Compaq IBM Acer Hp : 0.3280 : 0.3060 : 0.2720 : 0.094027
Consistency Ratio (CR)Consistency Ratio merupakan parameter yang digunakan untuk memeriksa apakah perbandingan berpasangan telah dilakukan dengan kosekwen atau tidak. CR
