Contoh Perhitungan SPK Metode TOPSIS

Data Kriteria Pendukung Data Matrix

Kode Kriteria Bobot Alternatif C01

C01 Kriteria A 1 A1

3

C02 Kriteria B 2 A2

2

C03 Kriteria C 3 A3

3

C04 Kriteria D 5 A4

4

A5

4

1. Menghitung Ranking Setiap Alternatif 2. Menghitung Keputusan ternormalisasi Terbobot |X1| |X1| 7.3484692283 Nilai X r11 --> 0.4082482905 0.40825 r21 --> 0.272165527 0.27217 r31 --> 0.4082482905 0.40825 r41 --> 0.544331054 0.54433 r51 --> 0.544331054 0.54433 1 |X2| 0.40825 |X2| 7.6157731059 0.27217 r12 --> 0.5252257314 0.40825 r22 --> 0.3939192986 0.54433 r32--> 0.6565321643 0.54433 r42--> 0.2626128657 r52 --> 0.2626128657

|X3| 3. Menghitung Solusi Ideal Positiif dan Negatif

|X3| 8.3666002653 a) Solusi Ideal Positif

r13 --> 0.4780914437 y1 r23 --> 0.5976143047 y2 r33 --> 0.4780914437 y3 r43 --> 0.2390457219 y4 r53 --> 0.3585685828 |X4| |X4| 8.1853527719

r14 --> 0.2443388887 4. Menghitung Jarak dengan Solusi Ideal r24 --> 0.2443388887 a) Menghitung Jarak Solusi Ideal Positif

r34 --> 0.3665083331 d1

r44 --> 0.6108472218 d2

r54 --> 0.6108472218 d3

d4 d5

b) Menghitung Jarak Solusi Ideal Negatif d1 d2 d3 d4 √(7,892_+8,862_+8,002_+7,932_+8,892 ) √(7,872_+8,502_+7,902_+9,892_+8,912 ) √(32₊₂2₊₂2_+8,782_+8,562 ) √(8,562_+7,982_+8,942_+6,942_+8,922 )

d5

5. Menghitung Nilai Preferensi Setiap Alternatif V1

V2 V3 V4 V5

Data Matrix C02 C03 C04

4

4

2

3

5

2

5

4

3

2

2

5

2

3

5

2. Menghitung Keputusan ternormalisasi Terbobot

0.52523 0.47809 0.24434 0.39392 0.59761 0.24434 0.65653 0.47809 0.36651 0.26261 0.23905 0.61085 0.26261 0.35857 0.61085 2 3 5 1.05046 1.43427 1.2217 0.78784 1.79283 1.2217 1.31306 1.43427 1.83255 0.52522 0.71715 3.05425 0.52522 1.07571 3.05425

3. Menghitung Solusi Ideal Positiif dan Negatif

a) 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

4. Menghitung Jarak dengan Solusi Ideal a) Menghitung Jarak Solusi Ideal Positif

1.89058 1.92566 1.28048 1.33333 1.06534

b) Menghitung Jarak Solusi Ideal Negatif 0.89925

1.10727 1.23556 1.85265

1.88703

5. Menghitung Nilai Preferensi Setiap Alternatif 0.32233

0.36508 0.49107 0.5815 0.63916

Data Kriteria Pendukung Data Matrix

Kode Kriteria Bobot Alternatif C1

C1 Kriteria A 2 A1 3

C2 Kriteria B 2 A2 2

C3 Kriteria C 4 A3 4

C4 Kriteria D 2

C5 Kriteria E 1

1. Menghitung Ranking Setiap Alternatif 2. Menghitung Keputusan ternormalisasi Terbobot |X1| |X1| 5.3851648071 Nilai X r11 --> 0.5570860145 0.55709 r21 --> 0.3713906764 0.37139 r31 --> 0.7427813527 0.74278 2 |X2| 1.11418 |X2| 6.7082039325 0.74278 r12 --> 0.298142397 1.48556 r22 --> 0.596284794 r32--> 0.7453559925

|X3| 3. Menghitung Solusi Ideal Positiif dan Negatif

|X3| 4.6904157598 a) Solusi Ideal Positif

r13 --> 0.6396021491 y1 r23 --> 0.6396021491 y2 r33 --> 0.4264014327 y3 y4 y5 |X4| |X4| 3.7416573868

r14 --> 0.5345224838 4. Menghitung Jarak dengan Solusi Ideal r24 --> 0.2672612419 a) Menghitung Jarak Solusi Ideal Positif

r34 --> 0.8017837257 d1 d2 d3 d4 |X5| d5 |X5| 4.582575695

r15 --> 0.8728715609 b) Menghitung Jarak Solusi Ideal Negatif

r25 --> 0.4364357805 d1 √(7,892_+8,862_+8,002_+7,932_+8,892 ) √(7,872_+8,502_+7,902_+9,892_+8,912 ) √(8,562_+9,072_+8,902_+8,782_+8,562 ) √(8,562_+7,982_+8,942_+6,942_+8,922 ) √(7,892_+8,862_+8,002_+7,932_+8,892 ) √(7,872_+8,502_+7,902_+9,892_+8,912 ) √(8,562_+9,072_+8,902_+8,782_+8,562 ) √(8,562_+7,982_+8,942_+6,942_+8,922 ) √(7,752_+8,672_+8,052_+7,332_+8,922 )

r35 --> 0.2182178902 d2 d3 d4 d5

5. Menghitung Nilai Preferensi Setiap Alternatif V1

V2 V3

Data Matrix

C2 C3 C4 C5

2 3 2 4

4 3 1 2

5 2 3 1

2. Menghitung Keputusan ternormalisasi Terbobot

0.29814 0.6396 0.53452 0.87287 0.59628 0.6396 0.26726 0.43644 0.74536 0.4264 0.80178 0.21822 2 4 2 1 0.59628 2.5584 1.06904 0.87287 1.19256 2.5584 0.53452 0.43644 1.49072 1.7056 1.60356 0.21822

3. Menghitung Solusi Ideal Positiif dan Negatif

a) 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

4. Menghitung Jarak dengan Solusi Ideal a) Menghitung Jarak Solusi Ideal Positif

1.10619 1.40497 1.0751 3.78257 3.78257

b) Menghitung Jarak Solusi Ideal Negatif 1.39105

1.06322 1.57943 2.03708 2.03708

5. Menghitung Nilai Preferensi Setiap Alternatif 0.55703

0.43077 0.59499

Data Kriteria Pendukung Data Matrix

Kode Kriteria Bobot Alternatif C1

C1 Kriteria A 2 A1 1

C2 Kriteria B 2 A2 2

C3 Kriteria C 2 A3 1

C4 Kriteria D 1 A4 2

C5 Kriteria E 1 A5 2

1. Menghitung Ranking Setiap Alternatif 2. Menghitung Keputusan ternormalisasi Terbobot |X1| |X1| 3.7416573868 Nilai X r11 --> 0.2672612419 0.26726 r21 --> 0.5345224838 0.53452 r31 --> 0.2672612419 0.26726 r41 --> 0.5345224838 0.53452 r51 --> 0.5345224838 0.53452 2 |X2| 0.53452 |X2| 3.7416573868 1.06904 r12 --> 0.5345224838 0.53452 r22 --> 0.2672612419 1.06904 r32--> 0.2672612419 1.06904 r42--> 0.5345224838 r52 --> 0.5345224838

|X3| 3. Menghitung Solusi Ideal Positiif dan Negatif

|X3| 4.1231056256 a) Solusi Ideal Positif

r13 --> 0.4850712501 y1 r23 --> 0.242535625 y2 r33 --> 0.4850712501 y3 r43 --> 0.4850712501 y4 r53 --> 0.4850712501 y5 |X4| |X4| 3.3166247904

r14 --> 0.6030226892 4. Menghitung Jarak dengan Solusi Ideal r24 --> 0.6030226892 a) Menghitung Jarak Solusi Ideal Positif

r34 --> 0.3015113446 d1 r44 --> 0.3015113446 d2 r54 --> 0.3015113446 d3 d4 |X5| d5 |X5| 2.8284271247

r15 --> 0.3535533906 b) Menghitung Jarak Solusi Ideal Negatif

r25 --> 0.3535533906 d1 √(7,892_+8,862_+8,002_+7,932_+8,892 ) √(7,872_+8,502_+7,902_+9,892_+8,912 ) √(8,562_+9,072_+8,902_+8,782_+8,562 ) √(8,562_+7,982_+8,942_+6,942_+8,922 ) √(7,752_+8,672_+8,052_+7,332_+8,922 )

r35 --> 0.3535533906 d2

r45 --> 0.7071067812 d3

r55 --> 0.3535533906 d4

d5

5. Menghitung Nilai Preferensi Setiap Alternatif V1

V2 V3 V4 V5

Data Matrix C2 C3 C4 C5 2 2 2 1 1 1 2 1 1 2 1 1 2 2 1 2 2 2 1 1

2. Menghitung Keputusan ternormalisasi Terbobot

0.53452 0.48507 0.60302 0.35355 0.26726 0.24254 0.60302 0.35355 0.26726 0.48507 0.30151 0.35355 0.53452 0.48507 0.30151 0.70711 0.53452 0.48507 0.30151 0.35355 2 2 1 1 1.06904 0.97014 0.60302 0.35355 0.53452 0.48508 0.60302 0.35355 0.53452 0.97014 0.30151 0.35355 1.06904 0.97014 0.30151 0.70711 1.06904 0.97014 0.30151 0.35355

3. Menghitung Solusi Ideal Positiif dan Negatif

a) 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

4. Menghitung Jarak dengan Solusi Ideal a) Menghitung Jarak Solusi Ideal Positif

0.64087 0.80374 0.88732 0.30151 0.46466

b) Menghitung Jarak Solusi Ideal Negatif 0.78224

0.61369 0.48506 0.96525 0.89817

5. Menghitung Nilai Preferensi Setiap Alternatif 0.54967

0.43296 0.35344 0.76198 0.65905

Data Kriteria Pendukung Data Matrix

Kode Kriteria Bobot Alternatif C1

C1 Kriteria A 1 A1 8.56 C2 Kriteria B 3 A2 9.07 C3 Kriteria C 3 A3 8.9 C4 Kriteria D 2 A4 8.78 C5 Kriteria E 1 A5 8.65 C6 Kriteria F 1 C7 Kriteria G 1

1. Menghitung Ranking Setiap Alternatif 2. Menghitung Keputusan ternormalisasi Terbobot |X1| |X1| 19.6636568318 Nilai X r11 --> 0.4353208599 0.43532 r21 --> 0.4612570326 0.46126 r31 --> 0.4526116417 0.45261 r41 --> 0.4465090128 0.44651 r51 --> 0.4398978315 0.4399 1 |X2| 0.43532 |X2| 18.6190413287 0.46126 r12 --> 0.423759734 0.45261 r22 --> 0.4758569383 0.44651 r32--> 0.4296676643 0.4399 r42--> 0.4259080723 r52 --> 0.477468192

|X3| 3. Menghitung Solusi Ideal Positiif dan Negatif

|X3| 19.3338330395 a) Solusi Ideal Positif

r13 --> 0.4070584443 y1 r23 --> 0.439643809 y2 r33 --> 0.4086101284 y3 r43 --> 0.5115385025 y4 r53 --> 0.4608501574 y5 y6 |X4| y7 |X4| 18.5636095628

r14 --> 0.4611172181 4. Menghitung Jarak dengan Solusi Ideal r24 --> 0.4298732945 a) Menghitung Jarak Solusi Ideal Positif

r34 --> 0.481587375 d1 r44 --> 0.3738497072 d2 r54 --> 0.4805099983 d3 d4 |X5| d5 |X5| 18.2573053872

r15 --> 0.4244876139 b) Menghitung Jarak Solusi Ideal Negatif

r25 --> 0.4748784016 d1 r35 --> 0.4409193925 d2 √(7,892_+8,862_+8,002_+7,932_+8,892 ) √(7,872_+8,502_+7,902_+9,892_+8,912 ) √(8,562_+9,072_+8,902_+8,782_+8,562 ) √(8,562_+7,982_+8,942_+6,942_+8,922 ) √(7,752_+8,672_+8,052_+7,332_+8,922 )

r45 --> 0.4014831239 d3

r55 --> 0.4885715504 d4

d5 |X6|

|X6| 206.8816086558 5. Menghitung Nilai Preferensi Setiap Alternatif

r16 --> 0.4833682445 V1 r26 --> 0.3866945956 V2 r36 --> 0.4833682445 V3 r46 --> 0.4833682445 V4 r56 --> 0.3866945956 V5 |X7| Alternatif |X7| 3.0822070015 V5 r17 --> 0.4866642634 V1 r27 --> 0 V3 r37 --> 0.3244428423 V4 r47 --> 0 V2 r57 --> 0.8111071057 √(1002₊₈₀2₊₁₀₀2₊₁₀₀2₊₈₀2 ) √(1,502₊₀2_+1,002₊₀2_+2,52 )

Data Matrix C2 C3 C4 C5 C6 C7 7.89 7.87 8.56 7.75 100 1.5 8.86 8.5 7.98 8.67 80 0 8 7.9 8.94 8.05 100 1 7.93 9.89 6.94 7.33 100 0 8.89 8.91 8.92 8.92 80 2.5

2. Menghitung Keputusan ternormalisasi Terbobot

0.42376 0.40706 0.46112 0.42449 0.48337 0.48666 0.47586 0.43964 0.42987 0.47488 0.38669 0 0.42967 0.40861 0.48159 0.44092 0.48337 0.32444 0.42591 0.51154 0.37385 0.40148 0.48337 0 0.47747 0.46085 0.48051 0.48857 0.38669 0.81111 3 3 2 1 1 1 1.27128 1.22118 0.92224 0.42449 0.48337 0.48666 1.42758 1.31892 0.85974 0.47488 0.38669 0 1.28901 1.22583 0.96318 0.44092 0.48337 0.32444 1.27773 1.53462 0.7477 0.40148 0.48337 0 1.43241 1.38255 0.96102 0.48857 0.38669 0.81111

3. Menghitung Solusi Ideal Positiif dan Negatif

a) 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

4. Menghitung Jarak dengan Solusi Ideal a) Menghitung Jarak Solusi Ideal Positif

0.48573 0.85128 0.59591 0.85794 0.18148

b) Menghitung Jarak Solusi Ideal Negatif 0.52648

0.40402 0.92355 0.87351

5. Menghitung Nilai Preferensi Setiap Alternatif 0.52013 0.21223 0.40405 0.51841 0.82798 Hasil Ranking 0.82798 1 0.52013 2 0.40405 3 0.51841 4 0.21223 5