Promethee Ranking .1. Arah Dalam Grafik Nilai Outranking
}
a P
+
b jika Φ
+
a Φ
+
b a I
+
b jika Φ
+
a = Φ
+
b
Melalui complete preorder, informasi bagi pembuat keputusan lebih realistik.
1 2
3 4
5 6
Gambar 2.13 Contoh Complete Ranking Promethee II Sebagai contoh perhitungan manual dapat digunakan 7 kriteria dan
menggunakan alternatif rumah makan yang ditampilkan dalam tabel 2.1
Tabel 2.1
Nilai Kriteria untuk Masing-masing Rumah Makan
Kriteria Preferensi parameter Data Rumah Makan
p q
RM 1 RM 2
RM3
jenis makanan f1.
1 biasa – max
1 1
1 harga rp
f2. 2 quasi
– min 1000
5000 6000
6500 jarak m
f3. 2 quasi
– min 100
1000 700
750 rasa
f4. 3 linear
–max 10
70 90
80 kenyamanan
tempat f5.
2 quasi – max
75 80
90 70
pelayanan f6.
3 linear – max 50
75 60
60 kebersihan
f7. 3 linear
– max 50 80
85 75
Langkah-langkah penyelesaiannya adalah : 1. Menghitung nilai preferensi
Pada tahap ini dilakukan perbandingan antara satu alternatif dengan alternatif lainnya untuk setiap kriteria, dengan cara mengurangkan
nilai alternatif pertama dengan alternatif kedua, kemudian di hitung nilai preferensinya sesuai dengan tipe preferensi yang digunakan.
Untuk lebih lengkapnya dapat di lihat pada perhitungan di bawah ini : a. Untuk kriteria jenis makanan
1. f1rm1,rm2 = d = frm1
– frm2 = 1
– 1 = 0
berdasarkan kriteria usual d
0 Hd = 0
2. f1rm2,rm1 = d
= frm2 – frm1
= 1 – 1
= 0
berdasarkan kriteria usual d
0 Hd = 0
3. f1rm1,rm3 = d
= frm1 – frm3
= 1 – 1
= 0
berdasarkan kriteria usual d
0 Hd = 0
4. f1rm3,rm1 = d
= frm3 – frm1
= 1 – 1
= 0 berdasarkan kriteria usual
d 0
Hd = 0
5. f1rm2,rm3 = d
= frm2 – frm3
= 1 – 1
= 0 berdasarkan kriteria usual
d 0
Hd = 0
6. f1rm3,rm2 = d = frm3
– frm2
= 1 – 1
= 0 berdasarkan kriteria usual
d 0
Hd = 0
b. Untuk kriteria harga makanan 1. f2rm1,rm2
= d = frm1 – frm2
= 5000 – 6000
= - 1000 berdasarkan kriteria quasi
- q ≤ d ≤ q
Hd = 0
2. f2rm2,rm1 = d
= frm2 – frm1
= 6000 – 5000
= 1000 berdasarkan kriteria quasi
- q ≤ d ≤ q
Hd = 0
3. f2rm1,rm3 = d = frm1
– frm3 = 5000
– 6500
= - 1500 berdasarkan kriteria quasi
d - q Hd = 0
4. f2rm3,rm1 = d = frm2
– frm1 = 6500
– 5000 = 1500
berdasarkan kriteria quasi d q
Hd = 1
5. f2rm2,rm3 = d = frm2
– frm3 = 6000
– 6500 = - 500
berdasarkan kriteria quasi - q
≤ d ≤ q Hd = 0
6. f2rm3,rm2 = d = frm3
– frm2 = 6500
– 6000 = 500
berdasarkan kriteria quasi
- q ≤ d ≤ q
Hd = 0
c. Untuk kriteria jarak 1. f3rm1,rm2
= d = frm1 – frm2
= 1000 – 700
= 300 berdasarkan kriteria quasi
d q Hd = 1
2. f3rm2,rm1 = d = frm2
– frm1 = 700
– 1000 = - 300
berdasarkan kriteria quasi -
q ≤ d ≤ q Hd = 0
3. f3rm1,rm3 = d = frm1
– frm3 = 1000
– 750 = 250
berdasarkan kriteria quasi d q
Hd = 1
4. f3rm3,rm1 = d = frm3
– frm1 = 750
– 1000 = - 250
berdasarkan kriteria quasi -
q ≤ d ≤ q Hd = 0
5. f3rm2,rm3 = d = frm2
– frm3 = 700
– 750 = - 50
berdasarkan kriteria quasi -
q ≤ d ≤ q Hd = 0
6. f3rm3,rm2 = d = frm3
– frm2 = 750
– 700 = 50
berdasarkan kriteria quasi -
q ≤ d ≤ q Hd = 0
d. Untuk kriteria rasa 1. f4rm1,rm2
= d = frm1
– frm2 = 70
– 90 = - 20
berdasarkan kriteria linear - p
≤ d ≤ p
Hd = -2
2. f4rm2,rm1 = d = frm2
– frm1 = 90
– 70 = 20
berdasarkan kriteria linear d p
Hd = 1
3. f4rm1,rm3 = d = frm1
– frm3 = 70
– 80 = - 10
berdasarkan kriteria linear - p
≤ d ≤ p
Hd = -1
4. f4rm3,rm1 = d = frm3
– frm1 = 80
– 70 = 10
berdasarkan kriteria linear - p
≤ d ≤ p
Hd = 1
5. f4rm2,rm3 = d = frm2
– frm3 = 90
– 80 = 10
berdasarkan kriteria linear - p
≤ d ≤ p
Hd = 1
6. f4rm3,rm2 = d = frm3
– frm2 = 80
– 90 = - 10
berdasarkan kriteria linear - p
≤ d ≤ p
Hd = -1
e. Untuk kriteria kenyamanan tempat 1. f5rm1,rm2
= d = frm1 – frm2
= 80 – 90
= - 10 berdasarkan kriteria quasi
- q ≤ d ≤ q
Hd = 0
2. f5rm2,rm1 = d = frm2
– frm1 = 90
– 80 = 10
berdasarkan kriteria quasi -
q ≤ d ≤ q Hd = 0
3. f5rm1,rm3 = d = frm1
– frm3 = 80
– 70 = 10
berdasarkan kriteria quasi -
q ≤ d ≤ q Hd = 0
4. f5rm3,rm1 = d = frm3
– frm1
= 70 – 80
= - 10 berdasarkan kriteria quasi
- q ≤ d ≤ q
Hd = 0
5. f5rm2,rm3 = d = frm2
– frm3 = 90
– 70 = 20
berdasarkan kriteria quasi -
q ≤ d ≤ q Hd = 0
6. f5rm3,rm2 = d = frm3
– frm2 = 70
– 90 = - 20
berdasarkan kriteria quasi -
q ≤ d ≤ q Hd = 0
f. Untuk kriteria pelayanan 1. f6rm1,rm2
= d = frm1 – frm2
= 75 – 60
= 15 berdasarkan kriteria linear
- p ≤ d ≤ p
Hd = 0,3
2. f6rm2,rm1 = d = frm2
– frm1 = 60
– 75 = - 15
berdasarkan kriteria linear - p
≤ d ≤ p Hd = - 0,3
3. f6rm1,rm3 = d = frm1
– frm3 = 75
– 60 = 15
berdasarkan kriteria linear - p
≤ d ≤ p Hd = 0,3
4. f6rm3,rm1 = d = frm3
– frm1 = 60
– 75 = -15
berdasarkan kriteria linear - p
≤ d ≤ p Hd = - 0,3
5. f6rm2,rm3 = d = frm2
– frm3 = 60
– 60 = 0
berdasarkan kriteria linear - p
≤ d ≤ p Hd = 0
6. f6rm3,rm2 = d = frm3
– frm2 = 60
– 60 = 0
berdasarkan kriteria linear - p
≤ d ≤ p Hd = 0
g. Untuk kriteria kebersihan 1. f7rm1,rm2
= d = frm1 – frm2
= 80 – 85
= - 5
berdasarkan kriteria linear - p
≤ d ≤ p Hd = - 0,1
2. f7rm2,rm1 = d = frm2
– frm1 = 85
– 80 = 5
berdasarkan kriteria linear - p
≤ d ≤ p Hd = 0,1
3. f7rm1,rm3 = d = frm1
– frm3 = 80
– 75 = 5
berdasarkan kriteria linear - p
≤ d ≤ p Hd = 0,1
4. f7rm3,rm1 = d = frm3
– frm1 = 75
– 80 = - 5
berdasarkan kriteria linear - p
≤ d ≤ p Hd = - 0,1
5. f7rm2,rm3 = d = frm2
– frm3 = 85
– 75 = 10
berdasarkan kriteria linear - p
≤ d ≤ p Hd = 0,2
6. f7rm3,rm2 = d = frm3
– frm2 = 75
– 85 = - 10
berdasarkan kriteria linear - p
≤ d ≤ p Hd = - 0,2
2. Menghitung Indeks Preferensi Multikriteria
rm1,rm2 = 17 0+0+1+-2+0+0,3+-0,1
= - 0,87 = 0,114285714
rm2,rm1 = 17 0+0+1+1+0+-0,3+0.1
= 1,87 = 0,257142857
rm1,rm3 =17 0+1+1+1+0+0.3+0.1
= 3.47 = 0,485714286
rm3,rm1 = 17 0+1+1+-1+0+-0,3+-0,1
= 0,67 = 0.085714286
rm2,rm3 = 17 0+0+0+1+0+0+0.2
= 1.27 = 0,171428571
rm3,rm2 = 17 0+0+0+-1+0+0+-0,2
= - 1,27 = - 0,171428571
Tabel 2.2 Nilai indeks preferensi
rm1 rm2
rm3 rm1
- 0,1142857 0,485714286 rm2
0,257142857 0 0,171428571
rm3 0.085714286 - 0,171428571
3. Menghitung Leaving Flow
rm1 = 1 3-1 - 0,1142857 + 0,485714286
= 0.185714286 rm2
= 1 3-1 0,257142857 + 0,171428571 = 0,214285714
rm3 = 1 3-1 0.085714286+ - 0,171428571
= - 0,042857143 4. Menghitung Entering Flow
rm1 = 1 3
– 1 0,257142857 + 0.085714286 = 0,171428571
rm2 = 1 3
– 1 - 0,1142857 + - 0,171428571
= - 0,142857143 rm3
= 1 3 – 1 0,485714286+ 0,171428571
= 0,328571429
Tabel 2.3 PROMETHEE Tahap I
Alternatif Leaving Flow
Entering Flow rm1
0.185714286 0,171428571
rm2 0,214285714 - 0,142857143
rm3 0.085714286
0,328571429
5. Menghitung Net Flow
rm1 = 0.185714286 - 0,171428571
= 0,014285714 rm2
= 0,214285714 - - 0,142857143 = 0,357142857
rm3 = 0.085714286 - 0,328571429
= - 0,371428571
Tabel 2.4 Promethee Tahap II
Alternatif Net Flow
Ranking rm1
0,014285714 2
rm2 0,357142857
1
rm3 -0,371428571
3