perhitungan metode ahp

Perhitungan manual metode AHP

Perhitungan manual metode AHP

Pembobotan kriteria untuk tingkat 2

Langkah-langkah:

1. Membuat matriks perbandingan berpasangan antar criteria ( weight=bobot2. Memberikan penilaian terhadap elemen yang dibandingkan dalam matriks

GoalKoHoAgJkUsTu

Ko1.0001.0005.0003.0003.0001.000

Ho1.0001.0005.0003.0003.0001.000

Ag0.2000.2001.0000.3330.2000.333

Jk0.3330.3333.0001.0000.3330.333

Us0.3330.3335.0003.0001.0000.200

Tu1.0001.0003.0003.0005.0001.000

Keterangan:

P dan P : Pemerataan dan Perluasan

3. Menghitung normalisasi matriks

a. Menjumlahkan tiap kolom

Ko= (1.000 + 1.000 + 0.200 + 0.333 + 0.333 + 1.000) = 3.867Ho= (1.000 + 1.000 + 0.200 + 0.333 + 0.333 + 1.000) = 3.867Ag = (5.000 + 5.000 + 1.000 + 3.000 + 5.000 + 3.000) = 22.000

Jk= (3.000 + 3.000 + 0.333 + 1.000 + 3.000 + 3.000) = 13.330

Us= (3.000 + 3.000 + 0.200 + 0.333 + 1.000 + 5.000) = 12.500

Tu= (1.000 + 1.000 + 0.333 + 0.333 + 0.200 + 1.000) = 3.867

b. Tiap cell dari kolom dibagi berdasarkan hasil (a)

GoalKoHoAgJkUsTu

Ko1.000/3.867=0.2591.000/3.867=0.2595.000/22.000=0.2273.000/13.330=0.2253.000/12.500=0.0241.000/3.867=0.259

Ho1.000/3.867=0.2591.000/3.867=0.2595.000/22.000=0.2273.000/13.330=0.2253.000/12.500=0.0241.000/3.867=0.259

Ag0.200/3.867=0.0520.200/3.867=0.0521.000/22.000=0.0450.333/13.330=0.0250.200/12.500=0.0160.333/3.867=0.086

Jk0.333/3.867=0.0860.333/3.867=0.0863.000/22.000=0.1361.000/13.330=0.0750.333/12.500=0.0270.333/3.867=0.086

Us0.333/3.867=0.0860.333/3.867=0.0865.000/22.000=0.2273.000/13.330=0.2251.000/12.500=0.0680.200/3.867=0.052

Tu1.000/3.867=0.2591.000/3.867=0.2593.000/22.000=0.1363.000/13.330=0.2255.000/12.500=0.4001.000/3.867=0.259

4. Menghitung Eigen Vektor / Bobot

Menghitung Eigen value:

Ko= (1.000 * 1.000 * 5.000 * 3.000 * 3.000 * 1.000) ^ (1/6) = 1.866Ho= (1.000 * 1.000 * 5.000 * 3.000 * 3.000 * 1.000) ^ (1/6) = 1.866Ag= (0.200 * 0.200 * 1.000 * 0.333 * 0.222 * 0.333) ^ (1/6) = 0.310Jk= (0.333 * 0.333 * 3.000 * 1.000 * 0.333 * 0.333) ^ (1/6) = 0.577Us= (0.333 * 0.333 * 5.000 * 3.000 * 1.000 * 0.200) ^ (1/6) = 0.833Tu = (1.000 * 1.000 * 3.000 * 3.000 * 5.000 * 1.000) ^ (1/6) = 1.866 +

7.373

Menghitung bobot prioritas:

Ko= 1.866 / 70373= 0.256Ho= 1.866 / 70373= 0.256Ag = 0.310/ 70373= 0.042Jk= 0.577/ 70373= 0.078

Us= 0.833/ 70373= 0.113

Tu= 1.866 / 70373= 0.256

Menghitung bobot sintesa:

Bobot sintesa:

Ko= (0.259 + 0.259 + 0.227 + 0.225 + 0.240 + 0.259) = 1.469Ho= (0.259 + 0.259 + 0.227 + 0.225 + 0.240 + 0.259) = 1.469Ag= (0.052 + 0.052 + 0.045 + 0.025 + 0.016 + 0.259) = 0.276Jk= (0.086 + 0.086 + 0.136 + 0.075 + 0.027 + 0.086) = 0.496Us= (0.086 + 0.086 + 0.227 + 0.225 + 0.680 + 0.052) = 0.756Tu= (0.259 + 0.259 + 0.136 + 0.225 + 0.400 + 0.259) = 1.538Bobot prioritasBobot sintesis

0.2561.469

0.2561.469

0.0420.276

0.0780.496

0.1130.756

0.2561.538

5. Menghitung nilai eigen maksimum ((maks)

Pengecekan apakah matrik konsisten atau tidak konsisten -> Penjumlahan dari (bobot sintesa / bobot prioritas)

Ko= (1.469/ 0.256) = 5.378Ho= (1.469/ 0.256) = 5.378Ag= (0.276/ 0.042) = 6.571Jk= (0.496/ 0.078) = 6.359Us= (0.756/ 0.113) = 6.690Tu= (1.538/ 0.256) = 5.938 +

37.034 ( = x)

(maks = (x) / jumlah kriteria = 37.034 / 6 = 6.172

6. Menguji konsistensi

CI = ((maks jumlah kriteria) / (jumlah kriteria 1) = (6.172 6) / (6-1)

= 0.034CR = CI / IR = 0.034 / 1.24 = 0.0274Karena Nilai Ratio Konsistensi < 0.1 maka matrik diatas konsistenPembobotan kriteria untuk tingkat 3

Kriteria Kota:Langkah-langkah:

1. Membuat matriks perbandingan berpasangan

2. Memberikan penilaian terhadap elemen yang dibandingkan dalam matriks

GoalJaBaCiSmJoSoSbMl

Ja1.0003.0003.0005.0007.0007.0009.0009.000

Ba0.3331.0003.0005.0005.0007.0009.0009.000

Ci0.3330.3331.0003.0005.0007.0009.0009.000

Sm0.2000.2000.3331.0003.0005.0007.0007.000

Jo0.1430.2000.2000.3331.0003.0007.0007.000

So0.1430.1430.1430.2000.3331.0005.0005.000

Sb0.1110.1110.1110.1430.1430.2001.0001.000

Ml0.1110.1110.1110.1430.1430.2001.0001.000

Keterangan:

3. Menghitung normalisasi matriksa. Menjumlahkan tiap kolom

Ko= (1.000 + 0.333 + 0.333 + 0.200 + 0.143 + 0.143 + 0.111 + 0.111) = 2.375Ho= (3.000 + 1.000 + 0.333 + 0.200 + 0.200 + 0.143 + 0.111 + 0.111) = 5.098Ag = (3.000 + 3.000 + 1.000 + 0.333 + 0.200 + 0.143 + 0.111 + 0.111) = 70898Jk= (5.000 + 5.000 + 3.000 + 1.000 + 0.333 + 0.200 + 0.143 + 0.143) = 14.819Us= (7.000 + 5.000 + 5.000 + 3.000 + 1.000 + 0.333 +0.143 + 0.143) = 21.619TU= (7.000 + 7.000 + 7.000 + 5.000 + 3.000 + 1.000 + 0.200 + 0.200) = 30.4TU= (9.000 + 9.000 + 9.000 + 7.000 + 7.000 + 5.000 + 1.000 + 1.000) = 48TU= (9.000 + 9.000 + 9.000 + 7.000 + 7.000 + 5.000 + 1.000 + 1.000) = 48b. Tiap cell dari kolom dibagi berdasarkan hasil (a)

GoalJaBaCISmJoSoSbMl

Ja0.4210.5880.3790.3370.3230.2300.1870.187

Ba0.1400.1960.3790.3370.2310.2300.1870.187

Ci0.1400.0650.1270.2020.2310.2300.1870.187

Sm0.0840.0390.0420.0670.1390.1640.1460.146

Jo0.0600.0390.0250.0220.0460.0990.1460.146

So0.0600.0280.0180.0130.0150.0330.1040.104

Sb0.0470.0220.0140.0090.0060.0070.0210.021

Ml0.0470.0220.0140.0090.0060.0070.0210.021

4. Menghitung Eigen Vektor / BobotMenghitung Eigen value:

Ko = (1.000 * 3.000 * 3.000 * 5.000 * 7.000 * 7.000 * 9.000 * 9.000) ^ (1/8) = 4.534Ba = 3.303Ci = 2.355Sm = 1.330Jo = 0.853So = 0.514Sb = 0.221

Ml = 0.221 +

13.331Menghitung bobot prioritas:

Ja= 4.534/ 13.331= 0.340Ba= 3.303/ 13.331= 0.248Ci = 2.355/ 13.331= 0.177Sm= 1.330/ 13.331= 0.099Jo= 0.853/ 13.331= 0.064So= 0.514/ 13.331= 0.039Sb= 0.221/ 13.331= 0.016

Ml= 0.221/ 13.331= 0.016


Bobot sintesa:

Ja= (0.421 + 0.588 + 0.379 + 0.337 + 0.323 + 0.230 + 0.187 + 0.187) = 2.652Ba= 1.887Ci= 1.369Sm= 0.827Jo= 0.583So= 0.375Sb= 0.147

Ml= 0.147

Bobot prioritasBobot sintesis

0.3402.652

0.2481.887

0.1771.369

0.0990.827

0.0640.583

0.0390.375

0.0160.147

0.0160.147



Ja= (2.652/ 0.340) = 7.800Ba= (1.887/ 0.248) = 7.608Ci= (1.369/ 0.177) = 7.734Sm= (0.827/ 0.099) = 8.353Jo= (0.583/ 0.064) = 9.109So= (0.375/ 0.039) = 9.165 Sb= (0.147/ 0.016) = 9.188

Ml= (0.147/ 0.016) = 9.188 +

68.145 ( = x)




= 0.074CR = CI / IR = 0.074/ 1.41 = 0.0525Karena Nilai Ratio Konsistensi < 0.1 maka matrik diatas konsistenKriteria Agama:

Langkah-langkah:



GoalIsKpKBH

Is1.0001.0001.0001.0001.000

Kp1.0001.0001.0001.0001.000

Kp1.0001.0001.0001.0001.000

B1.0001.0001.0001.0001.000

H1.0001.0001.0001.0001.000

Keterangan:


Is= 5

Kp= 5K = 5B= 5H= 5b. Tiap cell dari kolom dibagi berdasarkan hasil (a)

GoalIsKpKBH

Is0.2000.2000.2000.2000.200

Kp0.2000.2000.2000.2000.200

Kp0.2000.2000.2000.2000.200

B0.2000.2000.2000.2000.200

H0.2000.2000.2000.2000.200


Is= (1 * 1 * 1 * 1 * 1) ^ (1/5) = 1Kp= 1K = 1B = 1H= 1 + 5Menghitung bobot prioritas:

Is= (1/5) = 0.200Kp= (1/5) = 0.200K = (1/5) = 0.200

B = (1/5) = 0.200

H= (1/5) = 0.200


Bobot sintesa:

Is= (0.200 + 0.200 + 0.200 + 0.200 + 0.200) = 1Kp= (0.200 + 0.200 + 0.200 + 0.200 + 0.200) = 1K = (0.200 + 0.200 + 0.200 + 0.200 + 0.200) = 1

B = (0.200 + 0.200 + 0.200 + 0.200 + 0.200) = 1

H= (0.200 + 0.200 + 0.200 + 0.200 + 0.200) = 1

.Bobot prioritasBobot sintesis

0.2001

0.2001

0.2001

0.2001

0.2001

0.2001



Is= (1/.200) = 5.00Kp= (1/.200) = 5.00K = (1/.200) = 5.00

B = (1/.200) = 5.00

H= (1/.200) = 5.00 +

25.00 ( = x)

(maks = (x) / jumlah kriteria = 25.00 / 5 = 5


CI = ((maks jumlah kriteria) / (jumlah kriteria 1) = (5 5) / (5-1)

= 05CR = CI / IR = 0/ 1.12 = 0Kriteria Hobi:

Langkah-langkah:



GoalMskSprBcTrvShpMknNtnln

Msk1.0005.0005.0005.0003.0003.0003.0003.000

Spr0.2001.0003.0003.0000.3333.0001.0005.000

Bc0.2000.3330.3333.0003.0003.0000.3333.000

Trv0.2000.3330.3331.0001.0003.0001.0005.000

Shp0.3333.0000.3331.0001.0005.0001.0005.000

Mkn0.3330.3330.3330.3330.2001.0000.2000.333

Ntn0.3331.0003.0001.0001.0005.0001.0005.000

ln0.3330.2000.2000.20000.2003.0000.2001.000

Keterangan:


Msk= 2.933Spr= 11.200Bc = 13.333Trv= 14.533Shp= 9.733Mkn= 2.600

Ntn= 7.333

Ln= 27.333

b. Tiap cell dari kolom dibagi berdasarkan hasil (a)

GoalMskSprBcTrvShpMknNtnln

Msk0.3410.4460.3750.3440.3080.1150.3880.109

Spr0.0680.0890.2250.2060.0340.1150.1290.183

Bc0.0680.0290.0750.2060.3080.1150.0430.109

Trv0.0680.0290.0250.0690.1030.1150.1290.183

Shp0.1140.2680.0250.0690.1030.1920.1290.183

Mkn0.1140.0290.0250.0230.0210.0380.0260.012

Ntn0.1140.0890.2250.0690.1030.1920.1290.183

ln0.1140.0180.0250.0140.0210.1150.0260.037


Msk= 3.167Spr= 1.316Bc = 1.076Trv= 0.872Shp= 1.303Mkn= 0.337

Ntn= 1.495

Ln= 0.390 +

9.956

Menghitung bobot prioritas:Msk= (3.167/5) = 0.318Spr= (1.316/5) = 0.132Bc = (1.076/5) = 0.108

Trv= (0.872/5) = 0.088

Shp= (1.303/5) = 0.131

Mkn= (0.337/5) = 0.034

Ntn= (1.495/5) = 0.150

Ln= (0.390/5) = 0.039Menghitung bobot sintesa:

Bobot sintesa:

Msk= 2.426Spr= 1.049Bc = 0.953Trv= 0.721Shp= 1.083Mkn= 0.288Ntn= 1.104Ln= 0.370

.


0.3182.426

0.1321.049

0.1080.953

0.0880.721

0.1311.083

0.0340.288

0.1501.104

0.0390.230


Pengecekan apakah matrik konsisten atau tidak konsisten -> Penjumlahan dari (bobot sintesa / bobot prioritas)Ja= (0.318/ 2.426) = 7.629Ba= (0.132/ 1.049) = 7.947Ci= (0.108/ 0.953) = 8.824Sm= (0.088/ 0.721) = 8.193

Jo= (0.131/ 1.083) = 8.267So= (0.034/ 0.288) = 8.471

Sb= (0.150/ 1.104) = 7.360

Ml= (0.039/ 0.230) = 9.487 +

88.168 ( = x)




= 0.039CR = CI / IR = 0.039/ 1.41 = 0.02Karena Nilai Ratio Konsistensi < 0.1 maka matrik diatas konsistenKriteria Usia:

Langkah-langkah:


2. Memberikan penilaian terhadap elemen yang dibandingkan dalam matriksGoal12-1415-2020-2526-3031-4041-50> 50

12-141.0000.3331.0001.0005.0007.0009.000

15-203.0001.0003.0005.0007.0009.0009.000

20-251.0000.3331.0003.0003.0005.0007.000

26-301.0000.2000.3331.0003.0003.0005.000

31-400.2000.1430.3330.3331.0001.0005.000

41-500.1430.1110.2000.3331.0001.0003.000

> 500.1110.1110.1430.2000.2000.3330.1000

Keterangan:


12-14= 6.45415-20= 2.23220-25 = 6.00926-30= 10.86731-40= 20.20041-50= 26.333> 50= 39.000b. Tiap cell dari kolom dibagi berdasarkan hasil (a)Goal12-1415-2020-2526-3031-4041-50> 50

12-140.1550.1490.1660.0920.2480.2660.231

15-200.4650.4480.4990.4680.3470.3420.231

20-250.1550.1490.1660.2710.1490.1890.179

26-300.1550.0890.0550.0920.1490.1140.128

31-400.0310.0640.0550.0310.0490.0380.128

41-500.0220.0490.0330.0310.0490.0380.077

> 500.0170.0490.0240.0180.0090.0130.026


12-14= 1.94415-20= 4.26120-25 = 1.94426-30= 1.17031-40= 0.55341-50= 0.439> 50= 0.218 +

10.529Menghitung bobot prioritas:12-14= 0.189

15-20= 0.41520-25 = 0.185

26-30= 0.111

31-40= 0.053

41-50= 0.042

> 50= 0.021Menghitung bobot sintesa:

Bobot sintesa:

12-14= 1.307

15-20= 2.75020-25 = 1.258

26-30= 0.782

31-40= 0.396

41-50= 0.299

> 50= 0.156

.


0.1891.307

0.4152.750

0.1851.258

0.1110.782

0.0530.396

0.0420.299

0.0210.156


Pengecekan apakah matrik konsisten atau tidak konsisten -> Penjumlahan dari (bobot sintesa / bobot prioritas)12-14= 6.91515-20= 6.62220-25 = 6.80026-30= 7.04531-40= 7.74241-50= 7.119> 50= 7.429 +

49.402 (= x)




= 0.0096CR = CI / IR = 0.0096/ 1.32 = 0.0072Karena Nilai Ratio Konsistensi < 0.1 maka matrik diatas konsistenKriteria Top Usage:

Langkah-langkah:


2. Memberikan penilaian terhadap elemen yang dibandingkan dalam matriksGoal10-2525-5050-100100-150150-200200-250> 250

10-251.0000.3330.2000.2000.1430.1430.111

25-503.0001.0000.3330.3330.2000.2000.143

50-1005.0003.0001.0000.3330.33302000.200

100-1505.0003.0003.0001.0000.3330.3330.200

150-2007.0005.0003.0003.0001.0001.0000.333

200-2507.0005.0005.0003.0001.0001.0000.200

> 2509.0007.0005.0005.0003.0005.0001.000

Keterangan:


10-25

= 6.454

25-50

= 2.23250-100

= 6.009

100-150= 10.867

150-200= 20.200

200-250= 26.333

> 250

= 39.000

b. Tiap cell dari kolom dibagi berdasarkan hasil (a)Goal10-2525-5050-100100-150150-200200-250> 250

10-250.0270.0140.0110.0390.0240.0180.051

25-500.0810.0410.0190.0260.0330.0250.065

50-1000.1350.1230.0570.0260.0550.0250.091

100-1500.1350.1230.1710.0780.0550.0420.091

150-2000.1890.2050.1710.2330.1660.1260.152

200-2500.1890.2050.2850.2330.1660.1260.091

> 2500.2430.2880.2850.3890.4990.6350.457


10-25

= 0.22625-50

= 0.04950-100

= 0.679100-150= 1.000150-200= 1.944200-250= 1.944> 250

= 4.215 10.417Menghitung bobot prioritas:10-25

= 0.022

25-50

= 0.03950-100

= 0.065

100-150= 0.096

150-200= 0.187

200-250= 0.187

> 250

= 0.405


Bobot sintesa:

10-25

= 0.184

25-50

= 0.29050-100

= 0.512

100-150= 0.560

150-200= 1.242

200-250= 1.295

> 250

= 2.796

.


0.1890.184

0.0390.290

0.0650.512

0.0960.560

0.1871.242

0.1871.295

0.4052.796


Pengecekan apakah matrik konsisten atau tidak konsisten -> Penjumlahan dari (bobot sintesa / bobot prioritas)10-25

= 8.364

25-50

= 7.43650-100

= 7.877

100-150= 5.833

150-200= 6.642

200-250= 6.952

> 250

= 6.904 +

49.981 (= x)




= 0.0233CR = CI / IR = 0.0233/ 1.32 = 0.0176Karena Nilai Ratio Konsistensi < 0.1 maka matrik diatas konsistenKriteria Jenis Kelamin:

Langkah-langkah:


2. Memberikan penilaian terhadap elemen yang dibandingkan dalam matriksGoalLP

L1.0005.000

P0.2001.000

Keterangan:


L

= 1.200

P

= 6.000b. Tiap cell dari kolom dibagi berdasarkan hasil (a)GoalLP

L0.8330.833

P0.1670.167


L

= 2.236

P

= 0.447 + 2.683

Menghitung bobot prioritas:L

= 0.833

P

= 0.167Menghitung bobot sintesa:

Bobot sintesa:

L

= 1.666

P

= 0.334.

PrioritasSintesa

0.8331.666

0.1670.334


Pengecekan apakah matrik konsisten atau tidak konsisten -> Penjumlahan dari (bobot sintesa / bobot prioritas)L

= 2

P

= 2 + 4(maks = (x) / jumlah kriteria = 4 / 2 = 1


CI = ((maks jumlah kriteria) / (jumlah kriteria 1) = (1 2) / 2-1)

= -1CR = CI / IR = -1/ 0 = 0

perhitungan metode ahp

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