Bobot : Simple Additive Weighting (SAW) + Smart-C

🎯 Studi Kasus: Evaluasi Pegawai dengan SMART-C

📌 Kriteria dan Bobot:

Kriteria	Jenis	Bobot
C1 – Kedisiplinan	Benefit	0.2
C2 – Kualitas Kerja	Benefit	0.3
C3 – Kerjasama Tim	Benefit	0.2
C4 – Kehadiran	Benefit	0.1
C5 – Waktu Penyelesaian	Cost	0.2
Total		1.0

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👤 Data Pegawai:

Pegawai	Kedisiplinan (1–10)	Kualitas Kerja (1–100)	Kerjasama Tim (1–10)	Kehadiran (%)	Penyelesaian (hari)
A	9	85	8	95	4
B	7	90	9	98	5
C	8	80	7	92	3

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✳️ Langkah 1: Skor Utility (0–100)

Kita konversi nilai aktual ke skala utility 0–100, berdasarkan min dan max tiap kriteria.

Rumus:

• Benefit:

  $$U_{ij} = \frac{x_{ij} - x_{\text{min}}}{x_{\text{max}} - x_{\text{min}}} \times 100$$

• Cost:

  $$U_{ij} = \frac{x_{\text{max}} - x_{ij}}{x_{\text{max}} - x_{\text{min}}} \times 100$$

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🔢 Hasil Skor Utility:

Pegawai	C1 (9–7)	C2 (90–80)	C3 (9–7)	C4 (98–92)	C5 (3–5) Cost
A	(9–7)/(9–7) = 100	(85–80)/(10) = 50	(8–7)/2 = 50	(95–92)/6 = 50	(5–4)/2 = 50
B	(7–7)/2 = 0	(90–80)/10 = 100	(9–7)/2 = 100	(98–92)/6 = 100	(5–5)/2 = 0
C	(8–7)/2 = 50	(80–80)/10 = 0	(7–7)/2 = 0	(92–92)/6 = 0	(5–3)/2 = 100

(semua hasil dikalikan 100)

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Pegawai	C1	C2	C3	C4	C5
A	100	50	50	50	50
B	0	100	100	100	0
C	50	0	0	0	100

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✳️ Langkah 2: Normalisasi Utility (0–1)

Bagi semua nilai dengan 100.

Pegawai	C1	C2	C3	C4	C5
A	1.0	0.5	0.5	0.5	0.5
B	0.0	1.0	1.0	1.0	0.0
C	0.5	0.0	0.0	0.0	1.0

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✳️ Langkah 3: Hitung Skor Akhir SMART-C

Gunakan:

$$V_i = \sum (w_j \cdot U_{ij})$$

Pegawai A:

$$V_A = (0.2 \cdot 1.0) + (0.3 \cdot 0.5) + (0.2 \cdot 0.5) + (0.1 \cdot 0.5) + (0.2 \cdot 0.5) = 0.2 + 0.15 + 0.1 + 0.05 + 0.1 = **0.6**$$

Pegawai B:

$$V_B = (0.2 \cdot 0.0) + (0.3 \cdot 1.0) + (0.2 \cdot 1.0) + (0.1 \cdot 1.0) + (0.2 \cdot 0.0) = 0.0 + 0.3 + 0.2 + 0.1 + 0.0 = **0.6**$$

Pegawai C:

$$V_C = (0.2 \cdot 0.5) + (0.3 \cdot 0.0) + (0.2 \cdot 0.0) + (0.1 \cdot 0.0) + (0.2 \cdot 1.0) = 0.1 + 0.0 + 0.0 + 0.0 + 0.2 = **0.3**$$

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✅ Hasil Akhir (SMART-C Score):

Pegawai	Skor Akhir
A	0.6
B	0.6
C	0.3

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🏆 Kesimpulan:

• Pegawai A dan B memiliki skor SMART-C yang sama tinggi.

• Jika perusahaan ingin memilih satu, bisa lanjut dengan:

  • Kriteria tambahan,

  • Penilaian langsung manajer (tiebreak),

  • Preferensi strategi SDM (misal lebih mengutamakan kualitas kerja atau kedisiplinan).

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🎯 Studi Kasus: Evaluasi Kinerja Pegawai

Misalnya kamu ingin memilih pegawai terbaik bulan ini berdasarkan kriteria:

📌 Kriteria:

1. Kedisiplinan (C1) – Benefit

2. Kualitas Kerja (C2) – Benefit

3. Kerjasama Tim (C3) – Benefit

4. Kehadiran (C4) – Benefit

5. Waktu Penyelesaian Tugas (C5) – Cost (semakin cepat semakin baik)

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🧮 Bobot Kriteria:

Kriteria	Bobot
Kedisiplinan (C1)	0.2
Kualitas Kerja (C2)	0.3
Kerjasama Tim (C3)	0.2
Kehadiran (C4)	0.1
Waktu Penyelesaian (C5)	0.2
Total	1.0

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👤 Alternatif Pegawai:

Pegawai	Kedisiplinan (1-10)	Kualitas Kerja (1-100)	Kerjasama Tim (1-10)	Kehadiran (%)	Waktu Penyelesaian (hari)
A	9	85	8	95	4
B	7	90	9	98	5
C	8	80	7	92	3

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✳️ Langkah 1: Normalisasi

Kriteria Benefit:

$$r_{ij} = \frac{x_{ij}}{\max(x_{ij})}$$

Kriteria Cost:

$$r_{ij} = \frac{\min(x_{ij})}{x_{ij}}$$

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Pegawai	C1	C2	C3	C4	C5
A	9/9 = 1.00	85/90 = 0.944	8/9 = 0.889	95/98 = 0.969	3/4 = 0.75
B	7/9 = 0.778	90/90 = 1.00	9/9 = 1.00	98/98 = 1.00	3/5 = 0.6
C	8/9 = 0.889	80/90 = 0.889	7/9 = 0.778	92/98 = 0.939	3/3 = 1.00

Catatan: Untuk C5 (Waktu Penyelesaian, cost), nilai minimum = 3 hari.

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✳️ Langkah 2: Hitung Skor Akhir (SAW)

$$V_i = \sum (w_j \cdot r_{ij})$$

Pegawai A:

$$V_A = (0.2 \cdot 1.00) + (0.3 \cdot 0.944) + (0.2 \cdot 0.889) + (0.1 \cdot 0.969) + (0.2 \cdot 0.75) = 0.2 + 0.2832 + 0.1778 + 0.0969 + 0.15 = **0.9079**$$

Pegawai B:

$$V_B = (0.2 \cdot 0.778) + (0.3 \cdot 1.00) + (0.2 \cdot 1.00) + (0.1 \cdot 1.00) + (0.2 \cdot 0.6) = 0.1556 + 0.3 + 0.2 + 0.1 + 0.12 = **0.8756**$$

Pegawai C:

$$V_C = (0.2 \cdot 0.889) + (0.3 \cdot 0.889) + (0.2 \cdot 0.778) + (0.1 \cdot 0.939) + (0.2 \cdot 1.00) = 0.1778 + 0.2667 + 0.1556 + 0.0939 + 0.2 = **0.8939**$$

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✅ Hasil Akhir:

Pegawai	Skor SAW	Ranking
A	0.9079	🥇 1
C	0.8939	🥈 2
B	0.8756	🥉 3

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🏆 Kesimpulan:

Pegawai A memiliki skor tertinggi berdasarkan metode SAW dan layak dinobatkan sebagai pegawai terbaik bulan ini.

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Studi Kasus: Memilih Laptop Terbaik

Kriteria:

1. Harga (C1) – Cost

2. RAM (C2) – Benefit

3. Kapasitas SSD (C3) – Benefit

4. Daya Tahan Baterai (jam) (C4) – Benefit

🧮 Bobot Kriteria:

Kriteria	Bobot
Harga (C1)	0.3
RAM (C2)	0.25
SSD (C3)	0.25
Baterai (C4)	0.2
Total	1.0

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💻 Alternatif Laptop:

Laptop	Harga (juta)	RAM (GB)	SSD (GB)	Baterai (jam)
A	10	16	512	8
B	8	8	256	6
C	12	32	1024	10

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Langkah 1: Normalisasi

Kriteria Cost (Harga):

$$r_{ij} = \frac{\min(x)}{x_{ij}} \Rightarrow \min(8, 10, 12) = 8$$

Kriteria Benefit (RAM, SSD, Baterai):

$$r_{ij} = \frac{x_{ij}}{\max(x)}$$

Matriks Normalisasi:

Laptop	C1 (Harga)	C2 (RAM)	C3 (SSD)	C4 (Baterai)
A	8/10 = 0.80	16/32 = 0.50	512/1024 = 0.50	8/10 = 0.80
B	8/8 = 1.00	8/32 = 0.25	256/1024 = 0.25	6/10 = 0.60
C	8/12 = 0.667	32/32 = 1.00	1024/1024 = 1.00	10/10 = 1.00

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Langkah 2: Hitung Skor Akhir

$$V_i = \sum (w_j \cdot r_{ij})$$

Laptop A:

$$V_A = (0.3 \cdot 0.80) + (0.25 \cdot 0.50) + (0.25 \cdot 0.50) + (0.2 \cdot 0.80) = 0.24 + 0.125 + 0.125 + 0.16 = **0.65**$$

Laptop B:

$$V_B = (0.3 \cdot 1.00) + (0.25 \cdot 0.25) + (0.25 \cdot 0.25) + (0.2 \cdot 0.60) = 0.30 + 0.0625 + 0.0625 + 0.12 = **0.545**$$

Laptop C:

$$V_C = (0.3 \cdot 0.667) + (0.25 \cdot 1.00) + (0.25 \cdot 1.00) + (0.2 \cdot 1.00) = 0.2001 + 0.25 + 0.25 + 0.2 = **0.9001**$$

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Hasil Akhir (Ranking):

Laptop	Skor Akhir
C	0.9001
A	0.65
B	0.545

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🏆 Kesimpulan:

Laptop C adalah pilihan terbaik berdasarkan metode Simple Additive Weighting (SAW) karena memiliki skor tertinggi.