Contoh Perhitungan SPK Metode TOPSIS

Data Kriteria Pendukung Kode Kriteria C01 Kriteria A C02 Kriteria B C03 Kriteria C C04 Kriteria D

Bobot 1 2 3 5

1. Menghitung Ranking Setiap Alternatif √(32+22+22+8,782+8,562 ) |X1| |X1| 7.3484692283 r11 --> 0.4082482905 r21 --> 0.272165527 r31 --> 0.4082482905 r41 --> 0.544331054 r51 --> 0.544331054 |X2| |X2|

|X3| |X3|

√(7,892+8,862+8,002+7,932+8,892 ) 7.6157731059 r12 --> r22 --> r32--> r42--> r52 -->

√(7,872+8,502+7,902+9,892+8,912 ) r13 r23 r33 r43 r53

|X4| |X4|

0.5252257314 0.3939192986 0.6565321643 0.2626128657 0.2626128657

8.3666002653 --> --> --> --> -->

0.4780914437 0.5976143047 0.4780914437 0.2390457219 0.3585685828

Data Matrix Alternatif A1 A2 A3 A4 A5

C01

3 2 3 4 4

2. Menghitung Keputusan te Nilai X 0.40825 0.27217 0.40825 0.54433 0.54433 1 0.40825 0.27217 0.40825 0.54433 0.54433

3. Menghitung Solusi Ideal P a) Solusi Ideal Positif y1 y2 y3 y4

√(8,562+7,982+8,942+6,942+8,922 ) r14 r24 r34 r44 r54

8.1853527719 --> --> --> --> -->

0.2443388887 0.2443388887 0.3665083331 0.6108472218 0.6108472218

4. Menghitung Jarak dengan a) Menghitung Jarak Solusi Ideal d1 d2 d3 d4 d5

b) Menghitung Jarak Solusi Ideal d1 d2 d3 d4

d5

5. Menghitung Nilai Preferensi S V1 V2 V3 V4 V5

C02

C03

C04

4 3 5 2 2

4 5 4 2 3

2 2 3 5 5

Menghitung Keputusan ternormalisasi Terbobot

0.52523 0.39392 0.65653 0.26261 0.26261 2 1.05046 0.78784 1.31306 0.52522 0.52522

0.47809 0.59761 0.47809 0.23905 0.35857 3 1.43427 1.79283 1.43427 0.71715 1.07571

0.24434 0.24434 0.36651 0.61085 0.61085 5 1.2217 1.2217 1.83255 3.05425 3.05425

Menghitung Solusi Ideal Positiif dan Negatif Solusi Ideal Positif b) Solusi Ideal Negatif 0.54433 y1 0.27217 1.31306 y2 0.52522 1.79283 y3 0.71715 3.05425 y4 1.2217

Menghitung Jarak dengan Solusi Ideal Menghitung Jarak Solusi Ideal Positif 1.89058 1.92566 1.28048 1.33333 1.06534

Menghitung Jarak Solusi Ideal Negatif 0.89925 1.10727 1.23556 1.85265

1.88703

Menghitung Nilai Preferensi Setiap Alternatif 0.32233 0.36508 0.49107 0.5815 0.63916

Data Kode C1 C2 C3 C4 C5

Kriteria Pendukung Kriteria Bobot Kriteria A Kriteria B Kriteria C Kriteria D Kriteria E

2 2 4 2 1

1. Menghitung Ranking Setiap Alternatif 2 2 2 2 2) |X1| √(8,56 +9,07 +8,90 +8,78 +8,56 |X1| 5.3851648071 r11 --> 0.5570860145 r21 --> 0.3713906764 r31 --> 0.7427813527

|X2| |X2|

√(7,892+8,862+8,002+7,932+8,892 ) 6.7082039325 r12 --> 0.298142397 r22 --> 0.596284794 r32--> 0.7453559925

|X3| |X3|

√(7,872+8,502+7,902+9,892+8,912 )

|X4| |X4|

√(8,562+7,982+8,942+6,942+8,922 )

|X5| |X5|

4.6904157598 r13 --> 0.6396021491 r23 --> 0.6396021491 r33 --> 0.4264014327

3.7416573868 r14 --> 0.5345224838 r24 --> 0.2672612419 r34 --> 0.8017837257

Data Matrix Alternatif C1 A1 A2 A3

3 2 4

2. Menghitung Keputusan terno Nilai X 0.55709 0.37139 0.74278

2 1.11418 0.74278 1.48556

3. Menghitung Solusi Ideal Posi a) Solusi Ideal Positif y1 y2 y3 y4 y5

√(7,752+8,672+8,052+7,332+8,922 )

4. Menghitung Jarak dengan So a) Menghitung Jarak Solusi Ideal Po d1 d2 d3 d4 d5

4.582575695 r15 --> 0.8728715609 r25 --> 0.4364357805

b) Menghitung Jarak Solusi Ideal Ne d1

r35 -->

0.2182178902

d2 d3 d4 d5

5. Menghitung Nilai Preferensi Setia V1 V2 V3

C2

C3 2 4 5

C4 3 3 2

C5 2 1 3

4 2 1

Menghitung Keputusan ternormalisasi Terbobot

0.29814 0.59628 0.74536

0.6396 0.6396 0.4264

0.53452 0.26726 0.80178

0.87287 0.43644 0.21822

2 0.59628 1.19256 1.49072

4 2.5584 2.5584 1.7056

2 1.06904 0.53452 1.60356

1 0.87287 0.43644 0.21822

Menghitung Solusi Ideal Positiif dan Negatif Solusi Ideal Positif b) Solusi Ideal Negatif 1.48556 y1 0.74278 1.49072 y2 0.59628 2.5584 y3 1.7056 1.60356 y4 0.53452 0.87287 y5 0.21822

Menghitung Jarak dengan Solusi Ideal Menghitung Jarak Solusi Ideal Positif 1.10619 1.40497 1.0751 3.78257 3.78257

Menghitung Jarak Solusi Ideal Negatif 1.39105

1.06322 1.57943 2.03708 2.03708

Menghitung Nilai Preferensi Setiap Alternatif 0.55703 0.43077 0.59499

Data Kode C1 C2 C3 C4 C5

Kriteria Pendukung Kriteria Bobot Kriteria A Kriteria B Kriteria C Kriteria D Kriteria E

2 2 2 1 1

1. Menghitung Ranking Setiap Alternatif 2 2 2 2 2) |X1| √(8,56 +9,07 +8,90 +8,78 +8,56 |X1| 3.7416573868 r11 --> 0.2672612419 r21 --> 0.5345224838 r31 --> 0.2672612419 r41 --> 0.5345224838 r51 --> 0.5345224838 |X2| |X2|

√(7,892+8,862+8,002+7,932+8,892 ) 3.7416573868 r12 --> 0.5345224838 r22 --> 0.2672612419 r32--> 0.2672612419 r42--> 0.5345224838 r52 --> 0.5345224838

|X3| |X3|

√(7,872+8,502+7,902+9,892+8,912 ) r13 r23 r33 r43 r53

|X4| |X4|

0.4850712501 0.242535625 0.4850712501 0.4850712501 0.4850712501

1 2 1 2 2

2. Menghitung Keputusan tern Nilai X 0.26726 0.53452 0.26726 0.53452 0.53452 2 0.53452 1.06904 0.53452 1.06904 1.06904

3. Menghitung Solusi Ideal Pos a) Solusi Ideal Positif y1 y2 y3 y4 y5

√(8,562+7,982+8,942+6,942+8,922 ) r14 r24 r34 r44 r54

|X5| |X5|

4.1231056256 --> --> --> --> -->

Data Matrix Alternatif C1 A1 A2 A3 A4 A5

3.3166247904 --> --> --> --> -->

0.6030226892 0.6030226892 0.3015113446 0.3015113446 0.3015113446

√(7,752+8,672+8,052+7,332+8,922 )

4. Menghitung Jarak dengan So a) Menghitung Jarak Solusi Ideal Po d1 d2 d3 d4 d5

2.8284271247 r15 --> 0.3535533906 r25 --> 0.3535533906

b) Menghitung Jarak Solusi Ideal N d1

r35 --> r45 --> r55 -->

0.3535533906 0.7071067812 0.3535533906

d2 d3 d4 d5

5. Menghitung Nilai Preferensi Seti V1 V2 V3 V4 V5

C2

C3 2 1 1 2 2

C4 2 1 2 2 2

C5 2 2 1 1 1

1 1 1 2 1

Menghitung Keputusan ternormalisasi Terbobot

0.53452 0.26726 0.26726 0.53452 0.53452 2 1.06904 0.53452 0.53452 1.06904 1.06904

0.48507 0.24254 0.48507 0.48507 0.48507 2 0.97014 0.48508 0.97014 0.97014 0.97014

0.60302 0.60302 0.30151 0.30151 0.30151 1 0.60302 0.60302 0.30151 0.30151 0.30151

0.35355 0.35355 0.35355 0.70711 0.35355 1 0.35355 0.35355 0.35355 0.70711 0.35355

Menghitung Solusi Ideal Positiif dan Negatif Solusi Ideal Positif b) Solusi Ideal Negatif 1.06904 y1 0.53452 1.06904 y2 0.53452 0.97014 y3 0.48508 0.60302 y4 0.30151 0.70711 y5 0.35355

Menghitung Jarak dengan Solusi Ideal Menghitung Jarak Solusi Ideal Positif 0.64087 0.80374 0.88732 0.30151 0.46466

Menghitung Jarak Solusi Ideal Negatif 0.78224

0.61369 0.48506 0.96525 0.89817

Menghitung Nilai Preferensi Setiap Alternatif 0.54967 0.43296 0.35344 0.76198 0.65905

Data Kode C1 C2 C3 C4 C5 C6 C7

Kriteria Pendukung Kriteria Bobot Kriteria A Kriteria B Kriteria C Kriteria D Kriteria E Kriteria F Kriteria G

1 3 3 2 1 1 1

1. Menghitung Ranking Setiap Alternatif 2 2 2 2 2) |X1| √(8,56 +9,07 +8,90 +8,78 +8,56 |X1| 19.6636568318 r11 --> 0.4353208599 r21 --> 0.4612570326 r31 --> 0.4526116417 r41 --> 0.4465090128 r51 --> 0.4398978315 |X2| |X2|

√(7,892+8,862+8,002+7,932+8,892 ) 18.6190413287 r12 --> 0.423759734 r22 --> 0.4758569383 r32--> 0.4296676643 r42--> 0.4259080723 r52 --> 0.477468192

|X3| |X3|

√(7,872+8,502+7,902+9,892+8,912 )

|X4| |X4|

|X5| |X5|

19.3338330395 r13 --> r23 --> r33 --> r43 --> r53 -->

0.4070584443 0.439643809 0.4086101284 0.5115385025 0.4608501574

√(8,562+7,982+8,942+6,942+8,922 ) 18.5636095628 r14 --> r24 --> r34 --> r44 --> r54 -->

0.4611172181 0.4298732945 0.481587375 0.3738497072 0.4805099983

Data Matrix Alternatif C1 A1 A2 A3 A4 A5

8.56 9.07 8.9 8.78 8.65

2. Menghitung Keputusan te Nilai X 0.43532 0.46126 0.45261 0.44651 0.4399 1 0.43532 0.46126 0.45261 0.44651 0.4399

3. Menghitung Solusi Ideal P a) Solusi Ideal Positif y1 y2 y3 y4 y5 y6 y7

√(7,752+8,672+8,052+7,332+8,922 )

4. Menghitung Jarak dengan a) Menghitung Jarak Solusi Ideal d1 d2 d3 d4 d5

18.2573053872 r15 --> 0.4244876139 r25 --> 0.4748784016 r35 --> 0.4409193925

b) Menghitung Jarak Solusi Ideal d1 d2

r45 --> r55 --> |X6| |X6|

|X7| |X7|

0.4014831239 0.4885715504

d3 d4 d5

√(1002+802+1002+1002+802 ) 206.8816086558 r16 --> r26 --> r36 --> r46 --> r56 -->

0.4833682445 0.3866945956 0.4833682445 0.4833682445 0.3866945956

√(1,502+02+1,002+02+2,52 ) r17 r27 r37 r47 r57

3.0822070015 --> 0.4866642634 --> 0 --> 0.3244428423 --> 0 --> 0.8111071057

5. Menghitung Nilai Preferensi S V1 V2 V3 V4 V5 Alternatif V5 V1 V3 V4 V2

C2

C3 7.89 8.86 8 7.93 8.89

C4 7.87 8.5 7.9 9.89 8.91

C5 8.56 7.98 8.94 6.94 8.92

C6 7.75 8.67 8.05 7.33 8.92

C7 100 80 100 100 80

1.5 0 1 0 2.5

0.48337 0.38669 0.48337 0.48337 0.38669 1 0.48337 0.38669 0.48337 0.48337 0.38669

0.48666 0 0.32444 0 0.81111 1 0.48666 0 0.32444 0 0.81111

Menghitung Keputusan ternormalisasi Terbobot

0.42376 0.47586 0.42967 0.42591 0.47747 3 1.27128 1.42758 1.28901 1.27773 1.43241

0.40706 0.43964 0.40861 0.51154 0.46085 3 1.22118 1.31892 1.22583 1.53462 1.38255

0.46112 0.42987 0.48159 0.37385 0.48051 2 0.92224 0.85974 0.96318 0.7477 0.96102

0.42449 0.47488 0.44092 0.40148 0.48857 1 0.42449 0.47488 0.44092 0.40148 0.48857

Menghitung Solusi Ideal Positiif dan Negatif Solusi Ideal Positif b) Solusi Ideal Negatif 0.46126 y1 0.43532 1.43241 y2 1.27128 1.53462 y3 1.22118 0.96318 y4 0.7477 0.48857 y5 0.40148 0.48337 y6 0.38669 0.81111 y7 0

Menghitung Jarak dengan Solusi Ideal Menghitung Jarak Solusi Ideal Positif 0.48573 0.85128 0.59591 0.85794 0.18148

Menghitung Jarak Solusi Ideal Negatif 0.52648 0.22934

0.40402 0.92355 0.87351

Menghitung Nilai Preferensi Setiap Alternatif 0.52013 0.21223 0.40405 0.51841 0.82798 Hasil 0.82798 0.52013 0.40405 0.51841 0.21223

Ranking 1 2 3 4 5