PENGAMBILAN KEPUTUSAN DENGANProses Hirarki Analitik (Analytical Hierarchy Process-AHP)Disampaikan Erdi Suroso

Decision MakingWe need to prioritize both tangible and intangible criteria:

In most decisions, intangibles such as political factors and social factorstake precedence over tangibles such as economic factors and technical factors 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.

How do we assign importance to all the factors and synthesize this diverse information to make the best decision?

AHP Main Features

The Analytic Hierarchy Process (AHP)is the Method of Prioritization AHP captures priorities from paired comparison judgments of the elements of the decision with respect to each of their parent criteria.

Paired comparison judgments can be arranged in a matrix.

Priorities are derived from the matrix as its principal eigenvector, which defines a ratio scale. Thus, the eigenvector is an intrinsic concept of a correct prioritization process. It also allows for the measurement of inconsistency in judgment.

Knowing Less, Understanding MoreYou dont need to know every-thing to get to the answer.

Expert after expert missed therevolutionary significance of what Darwin had collected.Darwin, who knew less, somehow understood more.

Do Numbers Have an Objective Meaning?Butter: 1, 2,, 10 lbs.; 1,2,, 100 tons

Sheep: 2 sheep (1 big, 1 little)

Temperature: 30 degrees Fahrenheit to New Yorker, Indonesian, Eskimo

Since we deal with Non-Unique Scales such as [lbs., kgs], [yds, meters], [Fahr., Celsius] and such scales cannot be combined, we needthe idea of PRIORITY.

PRIORITY becomes an abstract unit valid across all scales.

A priority scale based on preference is the AHP way to standardize non-unique scales in order to combine multiple criteria.

Nonmonotonic Relative Nature of Absolute ScalesGood forpreserving food

Bad for preserving food

Good for preserving foodBad forcomfort

Good forcomfort

Bad forcomfort1000Temperature

Relative MeasurementIn relative measurement a preferencejudgment is expressed on each pair of elements with respect to a common propertythey share.

In practice this means that a pair of elementsin a level of the hierarchy are compared with respect to parent elements to which they relate in the level above.

If, for example, we are comparing two applesaccording to weight we ask:

Which apple is bigger?

How much bigger is the larger than the smaller apple? Use the smaller as the unit and estimate how many more times bigger is the larger one.

The apples must be relatively close (homogeneous) if we hope to make an accurate estimate.Relative Measurement cont.

Comparison MatrixGiven:Three apples of different sizes.

SizeComparisonApple AApple B Apple CApple 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

Skala Perbandingan AHP (Saaty)

NilaiKeterangan1A Sama penting (Equal) Dengan B3A Sedikit lebih penting (Moderate) dari B5A Jelas lebih penting (Strong) dari B7A Sangat jelas penting (Very Strong) dari B9A Mutlak lebih penting (Extreme) dari B2,4,6,8Apabila ragu-ragu antara 2 nilai yang berdekatan1/(1-9)Kebalikan nilai tingkat kepentingan dari skala 1-9

Pairwise ComparisonsSizeApple AApple BApple CSizeComparisonApple A Apple B Apple C Apple A 1 2 66/10 A

Apple B 1/2 1 33/10 B

Apple C 1/6 1/3 11/10 CWhen the judgments are consistent, as they are here, any normalized column gives the priorities.ResultingPriority EigenvectorRelative Sizeof Apple

Power of Hierarchic ThinkingA hierarchy is an efficient way to organize complexsystems. It is efficient both structurally, for represent-ing a system, and functionally, for controlling and passing information down the system.

Unstructured problems are best grappled with in the systematic framework of a hierarchy or a feedbacknetwork.

Linear Hierarchycomponent,cluster(Level)elementA loop indicates that eachelement depends only on itself.GoalSubcriteriaCriteriaAlternatives

Best Beverage ContainerCustomers serviceEnvironmental wasteCostEnergy to ProduceGlassBimetallicAluminiumSteelFOCUS :Criteria:Alternatives:Choosing a Beverage Container

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

Gambar : Hubungan sasaran, kriteria dan alternatif dalam AHP

Latihan Klasifikasi Sistem:Susun Hirarki pada kasus: Pengembangan Kawasan Industri Pengembangan UMKM Dsb.

Misalnya hasil perbandingan berpasangan untuk contoh diatas adalah:

NilaiKeterangan1Sama penting (Equal)3Sedikit lebih penting (Moderate)5Jelas lebih penting (Strong)7Sangat jelas penting (Very Strong)9Mutlak lebih penting (Extreme)2,4,6,8Apabila ragu-ragu antara 2 nilai yang berdekatan1/(1-9)Kebalikan nilai tingkat kepentingan dari skala 1-9

E1Bahan Baku PemasaranTeknologi ProsesBahan Baku1/13/1Pemasaran2/11/14/1Teknologi Proses1/31/1

Penyelesaian untuk contoh diatas (misalnya dengan syarat nilai eigen sudah tidak berubah sampai 4 angka dibelakang koma): Ubah matrik menjadi bilangan desimal: Iterasi ke I :Kuadratkan matrik diatas

Jumlahkan nilai setiap baris matrik dan hitung nilai hasil normalisasinya:Jml BarisHasil Normalisasi3.00005.33331.16661.75003.00000.66678.000014.00003.000012.750022.33334.833312.7500/39.9166 = 0.319422.3333/39.9166 = 0.5595 4.8333/39.9166 = 0.1211Jumlah39.91661.0000

Iterasi ke II :Kuadratkan kembali matrik diatas

Jumlahkan nilai setiap baris matrik dan hitung nilai hasil normalisasinya:Hitung Perbedaan nilai eigen sebelum dan sesudah nilai eigen sekarang:Terlihat bahwa perbedaan tersebut tidak terlalu besar sampai dengan 4 desimal

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, 0.1220Apakah makna dari nilai eigen di atas?Berikut ini adalah matrik berpasangan berserta dengan nilai eigennya:Berdasarkan nilai eigen maka kita tahu bahwa kriteria yang paling penting adalah Pemasaran, kemudian Bahan Baku dan terakhir Teknologi Proses

Bahan Baku PemasaranTeknologi ProsesNilai EigenBahan Baku1.0000.5003.0000.3196Pemasaran2.0001.0004.0000.5584Teknologi Proses0.3330.2501.0000.1220

PEMBOBOTAN ALTERNATIF Susunlah matrik berpasangan untuk alternatif-alternatif bagi setiap kriteria, misalnya untuk kriteria bahan baku adalah :

Bahan BakuMinyak Sawit CokelatKaret TehMinyak Sawit1/11/44/11/6Cokelat4/11/14/11/4Karet1/41/41/11/5Teh6/14/15/11/1

Misalnya untuk kriteria Pemasaran adalah :

PasarMinyak Sawit CokelatKaret TehMinyak Sawit1/12/15/11/1Cokelat1/21/13/12/1Karet1/51/31/11/4Teh1/11/24/11/1

Memilih Komoditi Agroindustri 1.00Bahan Baku 0.3196 Pemasaran 0.5584Teknologi Proses 0.1220 Minyak Sawit (0.1160)Cokelat (0.2470)Karet (0.0600)Teh (0.5700)Minyak Sawit (0.3790)Cokelat (0.2900)Karet (0.0740)Teh (0.2570)Minyak Sawit (0.3010)Cokelat (0.2390)Karet (0.2120)Teh (0.2480)Gambar : Hasil Akhir Seluruh Bobot

Dari hasil analisa di atas, maka jawaban dapat kita peroleh dengan jalan mengalikan matrik nilai eigen dari alternatif dengan matrik bobot matrik:

Bahan Baku PemasaranTeknologi Proses Bobot KriteriaMinyak Sawit0.11600.37900.30100.3196Cokelat0.24700.29000.23900.5584Karet0.06000.07400.21200.1220Teh0.57700.25700.2480

Hasilnya : Jadi rangking yang diperoleh :

ConsistencyIn this example Apple B is 3 times larger than Apple C. We can obtain this value directly from the comparisons of Apple A with Apples B & C as 6/2 = 3. But if we were to use judgmentwe may have guessed it as 4. In that case we would have been inconsistent.

Now guessing it as 4 is not as bad as guessing it as 5 or more. The farther we are from the true value the more inconsistent we are. The AHP provides a theory for checking the inconsistency throughout the matrix and allowing a certain level of overall inconsistency but not more.

Consistency itself is a necessary condition for a better understanding of relations in the world but it is not sufficient. For example we could judge all three of the apples to be the same size and we would be perfectly consistent, but very wrong.

We also need to improve our validity by using redundant information.

It is fortunate that the mind is not programmed to be always consistent. Otherwise, it could not integrate new information by changing old relations. Consistency cont.

Consistency Ratio (CR)Consistency Ratio merupakan parameter yang digunakan untuk memeriksa apakah perbaikan berpasangan telah dilakukan dengan kosekwen atau tidak.Penentuan parameter ini dapat dilakukan dengan proses sebagai berikut, misalnya kita akan menghitung CR untuk kriteria bahan baku pada contoh diatas:

Bahan BakuMinyak Sawit CokelatKaret TehMinyak Sawit1/11/44/11/6Cokelat4/11/14/11/4Karet1/41/41/11/5Teh6/14/15/11/1

Dari nilai faktor (nilai eigen) dari kriteria bahan baku adalah:Kita dapat Weighted Sum Vector dengan jalan mengalikan ke dua matrik tsb.

1/11/44/11/60.11600.51394/11/14/11/40.24701.09531/41/41/11/5*0.0600=0.26626/14/15/11/10.57702.5610

Kemudian kita menghitung Consistency Vector dengan menentukan nilai rata-rata dari weighted sum vector:Nilai rata-rata dari Consistency Vector adalah : = (4.4303 + 4.4342 + 4.4358 + 4.4385) / 4 = 4.4347Nilai Consistency Index dapat dihitung dengan menggunakan rumus :CI= ( - n) / (n 1) ; n : banyak alternatif= (4.4347 4) / (4 1)= 0.1449

Untuk menghitung Consistency Ratio, dibutuhkan nilai RI, yaitu indeks random yang didapat dari tabel berikut:

nRI20.0030.5840.9051.1261.2471.3281.41

PENYELESAIAN AHP DENGAN CRITERIUM DECISION PLUSJalankan program Criterium Decision Plus : Start / Programs / Criterium Decision PlusBuat file brainstorming, dengan perintah File/NewBuat struktur hirarki dengan perintah View / Generate HierarchyTentukan model AHP dengan perintah Model / Technique / AHPLakukan penilaian terhadap kriteria dengan perintah :a. Klik kotak Goalb. Lakukan perintah : Block/Rate subcriteriac. Penilaian kroteria dilakukan dengan jalan melakukan perintah: Methods/Full Pairwise

d. Lakukan penilaian perbandingan antara dua alternatif untuk setiap kriteria yang tersediae. Setelah selesai kliklah tombol OKUntuk melihat hasil akhir, gunakan perintah Result/ Decision ScoresUntuk melihat hasil akhir dalam bentuk tabel data, gunakan perintah View / Result Data

METODE PENILAIAN DENGAN AHP Perbandingan Alternatif A, B, C, DMisalnya pada kasusAlternatif A :Alternatif B :Alternatif C :Alternatif D :

Penggabungan Matrik IndividuNG (ij) =N1 (ij) =N2 (ij) =NG (ij) =N1 (ij) x N2 (ij) x x Ne(ij)e

FaktorBobotPrioritasKinerja kebun0.4371Kualitas teh pelanggan0.3122Proses produksi0.2513

AktorBobotPrioritasPelanggan 0.0335Pemerintah 0.0326KPB0.0444Direksi0.4681Administratur 0.3072Sinder kebun0.1153

TujuanBobotPrioritasPeningkatan harga teh0.4331Peningkatan pangsa pasar teh0.3472Penurunan jumlah teh yang tidak terjual0.2203

StrategiBobotPrioritasISO 9001;20000.4111TQM0.2533HACCP0.3362

Protect rights and maintain high Incentive to make and sell products in China (0.696)Rule of Law Bring China to responsible free-trading 0.206)Help trade deficit with China (0.098)BENEFITSYes 0.729No 0.271$ Billion Tariffs make Chinese productsmore expensive (0.094)Retaliation(0.280)Being locked out of big infrastructurebuying: power stations, airports (0.626)COSTSYes 0.787No 0.213Long Term negative competition(0.683)Effect on human rights and other issues (0.200)Harder to justify China joining WTO(0.117)RISKSYes 0.597No 0.403Result: Benefits

Costs x Risks;YES .729

.787 x .597= 1.55NO .271

.213 x .403=3.16Should U.S. Sanction China? (Feb. 26, 1995)YesNo.80.20YesNo.60.40YesNo.50.50YesNo.70.30YesNo.90.10YesNo.75.25YesNo.70.30YesNo.30.70YesNo.50.50

AHP dengan Penilaian Multi PerspektifPerspektif yang dipertimbangkan:

Menyeluruh. Opportunity (O) Benefit (B). Risk (R) Cost (C) Terdapat tiga skenario penilaian

Normal (most likely) = (B)(O) / (C)(R)Optimis = (B)(O) / (C)Pesimis = (B) / (C)(R)

*Baca buku/bahan pendukungnyaPilih persoalan kasus Manajemen dan Bisnis Kemudian selesaikan kasus pengambilan keputusan strategisnya dengan AHPSusun hiraki dan kuisionernya. Isi kuisioner oleh pakar. Olah datanya dengan software AHP bahas serta simpulkan. Tugas dikerjakan individu

Marimin, 2004, Teknik dan Aplikasi Pengambilan Keputusan Kriteria Majemuk, Grassindo, Jakarta. Marimin, 2009, Teknik dan Aplikasi Sistem Pakar dalam Teknologi Manajerial, IPB Press, Bogor Turban, E., 2001, Decision Support System and Intelligent System, Prentice Hall, New Jersey.