Lampiran 1. Nilai baris ui dan kolom vj untuk setiap tabel iterasi dari metode MODI
Nilai Baris ui dan Kolom vj untuk Tabel 4.28 ui vj u1=c11−v1=5–14=−9 v1=c31−u3=14–0=14 u2 =c21−v1=0–14=−14 v2=c32−u3=0−0= 0 u3 =0 v3=c43−u4=0−(8−M)=M−8 u4 =c44−v4=8−M v4=c34−u3=M–0=M u5 =c54−u5=15−M v5=c55−u5=0−(15−M)=M−15 Nilai Baris ui dan Kolom vj untuk Tabel 4.29 ui vj u1=c11−v=5–0 =5 v1=0 u2=c21−v1=0–0 =0 v2=c32−u3=0–14=−14 u3=c31−v1=14–0 =14 v3=c43−u4=0–4=−4 u4=c44−v4=8– 4=4 v4=c24−u2=4–0=4 u5=c54−v5=15– 4=11 v5=c55−u5=0–11=−11
Nilai Baris ui dan Kolom vj untuk Tabel 4.30 ui vj u1=c11−v1=5−0=5 v1=0 u2=c21−v1=0−0=0 v2=c32−u3=0−14=−14 u3=c31−v1=14−0=14 v3=c43−u4=0−4=−4 u4=c44−v4=8−4=4 v4=c24−u2=4−0=4 u5=c54−v5=15−4=11 v5=c55−u5=0−14=−14
Nilai Baris ui dan Kolom vj untuk Tabel 4.31 ui vj u1 =c11−v1=5−0=5 v1=0 u2=c21−v1=0−0=0 v2=c32−u3=0−14=−14 u3=c31−v1=14−0=14 v3=c43−u4=0−3=−3 u4=c41−v1=3−0=3 v4=c24−u2=4−0=4 u5=c53−v3=6−(−3)=9 v5=c35−u3=0−14=−14
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Nilai Baris ui dan Kolom vj untuk Tabel 4.32 ui vj u1 =c11−v1=5−0=5 v1=0 u2=c21−v1=0−0=0 v2=c32−u3=0−14=−14 u3=c31−v1=14−0=14 v3=c43−u4=0−3=−3 u4=c41−v1=3−0=3 v4=c24−u2=4−0=4 u5=c53−v3=6−(−3)=9 v5=c35−u3=0−14=−14 Nilai Baris ui dan Kolom vj untuk Tabel 4.33 ui vj u1 =c11−v1=5−0=5 v1=0 u2=c21−v1=0−0=0 v2=c32−u3=0−13=−13 u3=c33−v3=10−(−3)=13 v3=c43−u4=0−3=−3 u4=c41−v1=3−0=3 v4=c24−u2=4−0=4 u5=c53−v3=6−(−3)=9 v5=c35−u3=0−13=−13
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Lampiran 2. Indeks perbaikan untuk setiap tabel iterasi dari metode MODI
Catatan: Indeks Perbaikan yang berwarna abu-abu pada masing-masing tabel adalah indeks perbaikan terpilih untuk masuk ke iterasi selanjutnya.
Indeks Perbaikan untuk Tabel 4.28 Sel X12 = k12 = c12−u1−v2 = 3+9 = 12 Sel X13 = k13 = c13−u1−v3 = 3+9−M+8 = 20−M Sel X14 = k14 = c14−u1−v4 = M+9−M = 9 Sel X15 = k15 = c15−u1−v5 = 0+9−M+15 =24−M Sel X22 = k22 = c22−u2−v2 = 14+14−0 = 28 Sel X23 = k23 = c23−u2−v3 = 3+14−M+8 = 25−M Sel X24 = k24 = c24−u2−v4 = 4+14−M = 18−M Sel X25 = k25 = c25−u2−v5 = 0+14−M+15 = 29−M Sel X33 = k33 = c33−u3−v3 = 10−0−M+8 = 18−M Sel X35 = k35 = c35−u3−v5 = 0−0−10 = −10 Sel X41 = k41 = c41−u4−v1 = 3−8+M−14 = M−19 Sel X42 = k42 = c42−u4−v2 = 10−8+M−0 = M+2 Sel X45 = k45 = c45−u4−v5 = 0−8+M−M+15 = 7 Sel X51 = k51 = c51−u5−v1 = M−15+M−14 = 2M−29 Sel X52 = k52 = c52−u5−v2 = M−15+M−0 = 2M−15 Sel X53 = k53 = c53−u5−v3 = 6−15+M−M+8 = −1 Indeks Perbaikan untuk Tabel 4.29 Sel X12 = k12 = c12−u1−v2 = 3−5+14 = 12 Sel X13 = k13 = c13−u1−v3 = 3−5+4 = 2 Sel X14 = k14 = c14−u1−v4 = M−5−4 = M−9 Sel X15 = k15 = c15−u1−v5 = 0−5+11 = 6 Sel X22 = k22 = c22−u2−v2 = 14−0+14 = 28 Sel X23 = k23 = c23−u2−v3 = 3−0+4 = 7 Sel X25 = k25 = c25−u2−v5 = 0−0+11 = 11 Sel X33 = k33 = c33−u3−v3 = 10−14+4 = 0 Sel X34 = k34 = c34−u3−v4 = M−14−4 = M−18 Sel X35 = k35 = c35−u3−v5 = 0−14+11 = −3 Sel X41 = k41 = c41−u4−v1 = 3−4−0 = −1 Sel X42 = k42 = c42−u4−v2 = 10−4+14 = 20 Sel X45 = k45 = c45−u4−v5 = 0−4+11 = 7 Sel X51 = k51 = c51−u5−v1 = M−11−0 = M−11 Sel X52 = k52 = c52−u5−v2 = M−11+14 = M+3 Sel X53 = k53 = c53−u5−v3 = 6−11+4 = −1
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Indeks Perbaikan untuk Tabel 4.30 Sel X12 = k12 = c12−u1−v2 = 3−5+14 = 12 Sel X13 = k13 = c13−u1−v3 = 3−5+4 = 2 Sel X14 = k14 = c14−u1−v4 = M−5−4 = M−9 Sel X15 = k15 = c15−u1−v5 = 0−5+14 = 9 Sel X22 = k22 = c22−u2−v2 = 14−0+14 = 28 Sel X23 = k23 = c23−u2−v3 = 3−0+4 = 7 Sel X25 = k25 = c25−u2−v5 = 0−0+14 = 14 Sel X33 = k33 = c33−u3−v3 = 10−14+4 = 0 Sel X34 = k34 = c34−u3−v4 = M−14−4 = M−18 Sel X41 = k41 = c41−u4−v1 = 3−4−0 = −1 Sel X42 = k42 = c42−u4−v2 = 10−4+14 = 20 Sel X45 = k45 = c45−u4−v5 = 0−4+14 = 10 Sel X51 = k51 = c51−u5−v1 = M−11−0 = M−11 Sel X52 = k52 = c52−u5−v2 = M−11+14 = M+3 Sel X53 = k53 = c53−u5−v3 = 6−11+4 = −1 Sel X55 = k55 = c55−u5−v5 = 0−11+14 = 3 Indeks Perbaikan untuk Tabel 4.31 Sel X12 = k12 = c12−u1−v2 = 3−5+14 = 12 Sel X13 = k13 = c13−u1−v3 = 3−5+3 = 1 Sel X14 = k14 = c14−u1−v4 = M−5−4 = M−9 Sel X15 = k15 = c15−u1−v5 = 0−5+14 = 9 Sel X22 = k22 = c22−u2−v2 = 14−0+14 = 28 Sel X23 = k23 = c23−u2−v3 = 3−0+3 = 6 Sel X25 = k25 = c25−u2−v5 = 0−0+14 = 14 Sel X33 = k33 = c33−u3−v3 = 10−14+3 = −1 Sel X34 = k34 = c34−u3−v4 = M−14−4 = M−18 Sel X42 = k42 = c42−u4−v2 = 10−3+14 = 21 Sel X44 = k44 = c44−u4−v4 = 8−3−4 = 1 Sel X45 = k45 = c45−u4−v5 = 0−11+14 = 3 Sel X51 = k51 = c51−u5−v1 = M−11−0 = M−11 Sel X52 = k52 = c52−u5−v2 = M−11+14 = M+3 Sel X53 = k53 = c53−u5−v3 = 6−11+3 = −2 Sel X54 = k54 = c54−u5−v4 = 0−11+14 = 3
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Indeks Perbaikan untuk Tabel 4.32 Sel X12 = k12 = c12−u1−v2 = 3−5+14 = 12 Sel X13 = k13 = c13−u1−v3 = 3−5+3 = 1 Sel X14 = k14 = c14−u1−v4 = M−5−4 = M−9 Sel X15 = k15 = c15−u1−v5 = 0−5+14 = 9 Sel X22 = k22 = c22−u2−v2 = 14−0+14 = 28 Sel X23 = k23 = c23−u2−v3 = 3−0+3 = 6 Sel X24 = k24 = c24−u2−v4 = 0−0+14 = 14 Sel X33 = k33 = c33−u3−v3 = 10−14+3 = −1 Sel X34 = k34 = c34−u3−v4 = M−14−4 = M−18 Sel X42 = k42 = c42−u4−v2 = 10−3+14 = 21 Sel X44 = k44 = c44−u4−v4 = 8−3−4 = 1 Sel X45 = k45 = c45−u4−v5 = 0−3+14 = 11 Sel X51 = k51 = c51−u5−v1 = M−9−0 = M−9 Sel X52 = k52 = c52−u5−v2 = M−9+14 = M+5 Sel X54 = k54 = c54−u5−v4 = 15−9−4 = 2 Sel X55 = k55 = c55−u5−v5 = 0−9+14 = 5 Indeks Perbaikan untuk Tabel 4.33 Sel X12 = k12 = c12−u1−v2 = 3−5+13 = 11 Sel X13 = k13 = c13−u1−v3 = 3−5+3 = 1 Sel X14 = k14 = c14−u1−v4 = M−5−4 = M−9 Sel X15 = k15 = c15−u1−v5 = 0−5+13 = 8 Sel X22 = k22 = c22−u2−v2 = 14−0+13 = 27 Sel X23 = k23 = c23−u2−v3 = 3−0+3 = 6 Sel X25 = k25 = c25−u2−v5 = 0−0+13 = 13 Sel X31 = k31 = c31−u3−v1 = 14−13−0 = 1 Sel X34 = k34 = c34−u3−v4 = M−13−4 = M−17 Sel X42 = k42 = c42−u4−v2 = 10−3+13 = 20 Sel X43 = k43 = c43−u4−v3 = 8−3−4 = 1 Sel X44 = k44 = c44−u4−v4 = 0−3+13 = 10 Sel X51 = k51 = c51−u5−v1 = M−9−0 = M−9 Sel X52 = k52 = c52−u5−v2 = M−9+13 = M+4 Sel X54 = k54 = c54−u5−v4 = 15−9−4 = 2 Sel X55 = k55 = c55−u5−v5 = 0−9+13 = 4
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Lampiran 3. Tahapan Penyelesaian Fisibel Awal dengan Metode Least Cost Untuk Posisi 2 Iterasi Ke 1
TB 0
TC 14
Tujuan TD TF 3
Persediaan
TG
4
0
SB Sumber
SA
70 5
3
3
M
0
10
M
0
20
0 14
15
SC 3
10
0
SD
8
M
6
90 0
70 M
0
70
0 15
0
SE Permintaan
Iterasi Ke 2
95
70
TB
TC
0
14
70
35
Tujuan TD TF 3
30
0 10
Persediaan
TG
4
0
SB Sumber
SA
70 5
3
3
M
0
10
M
0
14
SC
15
3
10
0
8
70 M
M
95
Permintaan
Iterasi Ke 3
TB 0
SB Sumber
90 0
6
70
15
70
0
3
30
0 10
35
Tujuan TC TD TF 14
70
0
SE
Persediaan
TG
4
0
70
70 5
3
3
M
0
10
M
0
20
0 14
SC
15
0
90
70 3
10
0
SD
8
0
70 M
M
6
95
70
70
70
0 15
0
SE Permintaan
0
70
SD
SA
20
0
35
0 10
30
Universitas Sumatera Utara
75
Iterasi Ke 4
TB 0
SB Sumber
SA
TC 14
Tujuan TD TF 3
4
0
70
70 5
3
3
M
0
0
10
14
0
SC
10
M
15
3
10
0
8
90 0
70 M
M
6
70
0 15
0
SE Permintaan
Iterasi Ke 5
95
70
TB
TC
0
SB Sumber
14
35
0 10
Tujuan TD TF
TG
70
3
4
0
70 3
3
M
0
10 14
10 0
SC
10
M
15
10
0
SD
8
90 0
70 M
M
6
70
0 15
0
SE 95
Permintaan
Iterasi Ke 6
TB 0
SB Sumber
SA
70
TC 14
35
0 10
Tujuan TD TF
TG
70
3
4
0
70 3
3
M
0
10 14
SC
10 0
15 3
10
M
15
10
0
8
6
95
70
70
70
0 15
0
SE Permintaan
90 0
70 M
20
0
70
SD M
30
Persediaan
70 5
20
0
70 3
30
Persediaan
70 5
20
0
70
SD
SA
Persediaan
TG
35
0 10
30
Universitas Sumatera Utara
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Iterasi Ke 7
TB 0
SB Sumber
SA
TC 14
Tujuan TD TF 3
4
5
70 3
3
M
10 0
15 3
10
M
10
8
0
70 M
M
6
Iterasi Ke 8
95
70
TB
TC
0
SB
14
70
0 15
SE Permintaan
90
5 0
0
30
30 35
70
10
Tujuan TD TF 3
Persediaan
TG
4
0
70
70 5
3
3
M
0
10 14
SC
10 0
15 3
10
M
70 10
0
8
70 M
6
SE 95
70
70
20
0
90
5
SD M
20
0
70
SD
Sumber
0
10 14
Permintaan
0
70
SC
SA
Persediaan
TG
0
70
0 15
0
30 35
30 10
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Lampiran 4. Tahapan Uji Optimalitas dengan Metode Stepping Stone Untuk Posisi 2 Iterasi Ke 0
TB
TC
0
14
SB Sumber
SA
Tujuan TD TF 3
4
0
70
70 5
3
3
M
0
10 14
15 3
10
M
0
70 10
0
8
0
70 M
6
SE 95
70
90
5
SD M
20
10 0
SC
Permintaan
Persediaan
TG
70
70
0 15
0
30
30 35
10
Indeks Perbaikan Iterasi Ke 0 Sel X12 = 14−0+14−0 = 28 Sel X13 = 3−0+8−M+14−0 = 25−M Sel X14 = 4−M+14−0 = 18−M Sel X15 = 0−0+5−0 = 5 Sel X22 = 3−0+14−5 = 12 Sel X23 = 3−0+8−M+14−5 = 20−M Sel X24 = M−M+14−5 = 9 Sel X33 = 10−M+8−0 = 18−M
10
𝑋33
M
(+) 0
(−)
𝑋43
8
70 (1)
𝑋34 (−) 5 𝑋44 (+)0
Sel X35 = 0−14+5−0 = −9 Sel X41 = 3−14+M−8 = M−19 Sel X42 = 10−0+M−8 = M+2 Sel X45 = 0−8+M−14+5−0 = M−17 Sel X51 = M−14+M−15 = 2M−29 Sel X52 = M−0+M−15 = 2M−15 Sel X53 = 6−0+8−15 = −1 Sel X55 = 0−15+M−14+5−0 = M−24
10
M
5 0
8
65
5
(2)
Loop Terpilih Pada Sel 𝑋33 (1) dan Hasil Perbaikan Sel 𝑋33 (2)
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Iterasi Ke 1
TB 0
14
SB Sumber
SA
Tujuan TD TF
TC
3
4
0
70
70 5
3
3
M
0
10
20
10
14
0
SC
15
10
M
70
3
0
90
5
10
0
SD
8
0
65 M
M
95
6
70
70
5 15
SE Permintaan
Persediaan
TG
0
30 35
70
30 10
Indeks Perbaikan Iterasi Ke 1 Sel X12 = 14−0+14−0 = 28 Sel X13 = 3−10+14−0 = 7 Sel X14 = 4−8+0−10+14−0 = 0 Sel X15 = 0−0+5−0 = 5 Sel X22 = 3−0+14−5 = 12 Sel X23 = 3−10+14−5 = 2 Sel X24 = M−8+0−10+14−5 = M−9 Sel X34 = M−8+0−10 = M−8
𝑋21 (+) 10 14 𝑋31 (−) 15 5
3
0
Sel X35 = 0−14+5−0 = −9 Sel X41 = 3−14+10−0 = −1 Sel X42 = 10−0+10−0 = 20 Sel X45 = 0−0+10−14+5−0=1 Sel X51 = M−14+10−0+8−15 = M−11 Sel X52 = M−0+10−0+8−15 = M+3 Sel X53 = 6−0+8−15 = −1 Sel X55 = 0−15+8−0+10−14+5−0 = −6
𝑋22
3
𝑋32
10
70
𝑋23
M
𝑋33 5
M
𝑋24 𝑋34
0
(−) 0
𝑋25 10 𝑋35
(+)
(1) 5
3
3
M
0
0
10
M
0
20 14
5
70
5
10
(2) Loop Terpilih Pada Sel X35 (1) dan Hasil Perbaikan Sel X35 (2)
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Iterasi Ke 2
TB
TC
0
14
SB Sumber
SA
Tujuan TD TF 3
4
0
70
70 5
3
3
M
0
20 14
5 3
10
70 10
M
0
90
5 0
SD
8
0
65 M
M
6
70
70
70
5 15
SE 95
20
10 0
SC
Permintaan
Persediaan
TG
0
30
30 35
10
Indeks Perbaikan Iterasi Ke 2 Sel X12 = 14−0+14−0 = 28 Sel X13 = 3−10+14−0 = 7 Sel X14 = 4−8+0−10+14−0 = 0 Sel X15 = 0−0+14−0 = 14 Sel X22 = 3−0+14−5 = 12 Sel X23 = 3−10+14−5 = 2 Sel X24 = M−8+0−10+14−5 = M−9 Sel X25 = 0−0+14−5 = 9
0
(−) 6
8
𝑋43 65 𝑋53
15
(+)
𝑋44 (+) 5 𝑋54 (−)30
Sel X34 = M−8+0−10 = M−8 Sel X41 = 3−14+10−0 = −1 Sel X42 = 10−0+10−0 = 20 Sel X45 = 0−0+10−0=10 Sel X51 = M−14+10−0+8−15 = M−11 Sel X52 = M−0+10−0+8−15 = M+3 Sel X53 = 6−0+8−15 = −1 Sel X55 = 0−15+8−0+10−0 = 3
0
8
35 6
35 15
30 (1)
(2)
Loop Terpilih Pada Sel 𝑋53 (1) dan Hasil Perbaikan Sel 𝑋53 (2)
Universitas Sumatera Utara
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Iterasi Ke 3
TB
TC
0
SB Sumber
SA
Tujuan TD TF
14
3
4
0
70
70 5
3
3
M
0
0
10
M
0
20
20 14
SC
5
70
3
5
10
10
0
SD
8
35 M
M
95
15
70 0
30
30 70
70
90
0
35
6
SE Permintaan
Persediaan
TG
35
10
Indeks Perbaikan Iterasi Ke 3 Sel X12 = 14−0+14−0 = 28 Sel X13 = 3−10+14−0 = 7 Sel X14 = 4−8+0−10+14−0 = 0 Sel X15 = 0−0+14−0 = 14 Sel X22 = 3−0+14−5 = 12 Sel X23 = 3−10+14−5 = 2 Sel X24 = M−8+0−10+14−5 = M−9 Sel X25 = 0−0+14−5 = 9
𝑋31 5 (−) 3 𝑋41 (+) 14
Sel X34 = M−8+0−10 = M−8 Sel X41 = 3−14+10−0 = −1 Sel X42 = 10−0+10−0 = 20 Sel X45 = 0−0+10−0=10 Sel X51 = M−14+10−6 = M−10 Sel X52 = M−0+10−6 = M+4 Sel X54 = 15−6+0−8 = 1 Sel X55 = 0−6+10−0 = 4
0
𝑋32
70 10
𝑋42
𝑋33 (+) 5 0 𝑋43 (−) 35 10
(1) 14
10
0
70 3
10 0
10
5
30 (2)
Loop Terpilih Pada Sel X41 (1) dan Hasil Perbaikan Sel X41 (2)
Universitas Sumatera Utara
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Iterasi Ke 4
TB
TC
0
SB
3
Persediaan
TG
4
0
70
70 5
SA Sumber
14
Tujuan TD TF
3
3
M
0
0
10
M
0
20
20 14
SC
70 3
10
SD
10 0
M
M
SE 95
Permintaan
8
30
5
70
6
30 70
90
10 0
70
35 15
0
30 35
10
Indeks Perbaikan Iterasi Ke 4 Sel X12 = 14−0+10−0+3−0 = 27 Sel X13 = 3−0+3−0 = 6 Sel X14 = 4−8+3−0 = −1 Sel X15 = 0−0+10−0+3−3 = 13 Sel X22 = 3−0+10−0+3−5 = 11 Sel X23 = 3−0+3−5 = 1 Sel X24 = M−8+3−5 = M−10 Sel X25 = 0−0+10−0+3−5 = 8
𝑋11 (−) 70 5 𝑋21 20 14 𝑋31 0
3
5 𝑋31 (+)
14
𝑋12
M
𝑋13
0
𝑋14
(+) 3 0
𝑋22
M
𝑋32 70
10
10
𝑋23
0
𝑋33 10
M
0
𝑋31 30 (1)
0
3
3
M
0
10
M
10
M
35
35
𝑋24
5
𝑋34
14
0
3
10
8
𝑋31
Sel X31 = 14−10+0−3 = 1 Sel X34 = M−8+0−10 = M−8 Sel X42 = 10−0+10−0 = 20 Sel X45 = 0−0+10−0=10 Sel X51 = M−3+0−6 = M−9 Sel X52 = M−0+10−6 = M+4 Sel X54 = 15−6+0−8 = 1 Sel X55 = 0−6+10−0 = 4
35 𝑋31 (−)
20 70
10 0
8
40 (2)
Loop Terpilih Pada Sel X14 (1) dan Hasil Perbaikan Sel X14 (2)
Universitas Sumatera Utara
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Iterasi Ke 5
TB
TC
0
SB Sumber
SA
14
3
4
Persediaan
TG 0
70
70 5
3
3
M
0
0
10
M
0
20
20 14
SC
70 3
10
SD
10 0
M
M
95
10 8
30
5
SE Permintaan
Tujuan TD TF
70
6
0
70
35 15
30 70
90
0
30 35
10
Indeks Perbaikan Iterasi Ke 5 Sel X12 = 14−0+10−0+3−0 = 27 Sel X13 = 3−0+3−0 = 6 Sel X15 = 0−0+10−0+3−3 = 13 Sel X22 = 3−0+10−0+3−5 = 11 Sel X23 = 3−0+3−5 = 1 Sel X24 = M−5+0−4 = M−9 Sel X25 = 0−0+10−0+3−5 = 8 Sel X31 = 14−10+0−3 = 1
Sel X34 = M−10+0−3+0−4 = M−17 Sel X42 = 10−0+10−0 = 20 Sel X44 = 8−3+0−4 = 1 Sel X45 = 0−0+10−0=10 Sel X51 = M−3+0−6 = M−9 Sel X52 = M−0+10−6 = M+4 Sel X54 = 15−6+0−3+0−4 = 2 Sel X55 = 0−6+10−0 = 4
Universitas Sumatera Utara
Lampiran 5. Tahapan Penyelesaian Fisibel Awal dengan Metode Least Cost Untuk Posisi 3 Iterasi Ke 1
TC
TB
Tujuan TD TF
3
5
3
Persediaan
TG
M
0
SA Sumber
SB
20 14
0
3
4
14
10
M
0
15
0
10 10
3
0
8
70
0 M
M
6
15
0
Iterasi Ke 2
95
70
35
0 10
TC
TB
Tujuan TD TF
TG
3
5
3
70
M
30
Persediaan
0
SA Sumber
SB
20 14
0
3
4
14
10
M
0
0
15
0
10 10
3
0
SD
8
70 M
M
6
70
0 15
0
70
95
70
35
0 10
TC
TB
Tujuan TD TF
TG
3
5
3
M
30
Persediaan
0
SA Sumber
SB
20 14
0
3
4
10
M
0
70
70 0
14
SC
15
0
10 10
3
0
SD
8
70 M
M
6
70
95
70
90
0
70
0 15
0
SE Permintaan
90
0
SE
Iterasi Ke 3
70
0
SC
Permintaan
90
0
SE Permintaan
70
0
SC SD
0
35
0 10
30
Universitas Sumatera Utara
84
TC
TB
Tujuan TD TF
3
5
3
Iterasi Ke 4
Persediaan
TG
M
0
SA Sumber
SB
20 14
0
3
4
0
10
M
0
SC
14
15
10
10
3
0
8
70 M
M
6
70
Permintaan
TC 3
15
0
Sumber
35
TB
Tujuan TD TF
14
M
0
20
0
3
4
10
M
0
14
15
0
70 10
10 3
0
SD
8
70 M
M
6
70
95
70
0 15
0
TC
TB
3
5
SA Sumber
Tujuan TD TF
TG
3
M
14
0
0
20 3
4
10
M
0
70 10
15
3
10 0
8
M
6
95
70
70
0 15
0
SE 70
90
0
70 M
0
5
SD
Permintaan
70
70 14
30
Persediaan
20
0
SC
35
0 10
70
90
0
SE
SB
70
70 0
Iterasi Ke 6
Persediaan
TG
20
SC
Permintaan
30
0 10
70
3
70
0
95
5
SA
90
0
SE
SB
0
70
SD
Iterasi Ke 5
70
70
35
0 10
30
Universitas Sumatera Utara
85
Iterasi Ke 7
TC 3
5
SA Sumber
SB
Tujuan TD TF
TB
3
M
14
20
0
3
4
10
M
14
70 10
3
0
8
M
70
6
95
TC 3
15
0
30 35
0 10
Tujuan TD TF
5
3
M
0
0
20 3
4
0
10
M
0
70
70 0
14
70 10
5 3
5 0
SD
8
70 M
M
6
SE 70
95
30
Persediaan
TG
20 14
90 70
0
70
TB
SA Sumber
0
0
70 M
Permintaan
70 10
SE
SC
15
5
SD
SB
0
70 0
Iterasi Ke 8
0
20
SC
Permintaan
Persediaan
TG
70
10
90
0
70
0 15
0
30 35
0 10
30
Universitas Sumatera Utara
Lampiran 6. Tahapan Uji Optimalitas dengan Metode Stepping Stone Untuk Posisi 3 Iterasi Ke 0
TC 3
5
3
SA
Persediaan
TG
M
0
20
20 14
SB Sumber
Tujuan TD TF
TB
0
0 14
70 10
SD
4
0
10
M
0
5 3
5 0
0 M
70 M
6
70
95
70
90
10
8
SE Permintaan
70
70
0
SC
3
0
0
70
0
15
0
30 35
30
0 10
Indeks Perbaikan Iterasi Ke 0 Sel X11 = 3−5+14−0 = 12 Sel X13 = 3−0+8−M+14−5 = 20−M Sel X14 = M−M+14−5 = 9 Sel X15 = 0−0+14−5 = 9 Sel X21 = 14−0+14−0 = 28 Sel X23 = 3−0+8−M+14−0 = 25−M Sel X24 = 4−M+14−0 = 18−M Sel X25 = 0−0+14−0 = 14
0
(−) 14
(+)
𝑋22
3
70 𝑋32
10
𝑋23
4
(+)
Sel X33 = 10−M+8−0 = 18−M Sel X41 = 10−0+M−8 = M+2 Sel X42 = 3−14+M−8 = M−9 Sel X45 = 0−8+M−0 = M−8 Sel X51 = M−0+M−15 = 2M−15 Sel X52 = M−14+M−15 = 2M−29 Sel X53 = 6−0+8−15 = −1 Sel X55 = 0−15+M−0 = M−15
𝑋24 0
𝑋33
5 (1)
M
(−) 5
3
4
10
M
65
𝑋34 14
10
5 5 (2)
Loop Terpilih Pada Sel 𝑋24 (1) dan Hasil Perbaikan Sel 𝑋24 (2)
Universitas Sumatera Utara
87
Iterasi Ke 1
TC
TB
3
5
SA Sumber
SB
3
14
M
0
20
0
0
3
4
0
65
0
14
70
10
3
M
0
0
8
0
70 M
6
SE 70
95
90
10
0 M
70
5
10
10
Permintaan
Persediaan
TG
20
SC SD
Tujuan TD TF
70
0 15
70
0 0
30 35
30
0 10
Indeks Perbaikan Iterasi Ke 1 Sel X11 = 3−5+14−0 = 12 Sel X13 = 3−0+8−4+0−5 = 2 Sel X14 = M−4+0−5 = M−9 Sel X15 = 0−0+14−5 = 9 Sel X21 = 14−0+14−0 = 28 Sel X23 = 3−4+8−0 = 7 Sel X25 = 0−0+14−0 = 14 Sel X33 = 10−14+0−4+8−0 = 0
0
(−) 6
8
𝑋43 70 𝑋53
15
(+)
𝑋44 (+) 0 𝑋54 (−)30
Sel X34 = M−14+0−4 = M−18 Sel X41 = 10−0+14−0+4−8 = 20 Sel X42 = 3−0+4−8 = −1 Sel X45 = 0−0+14−0+4−8 = 10 Sel X51 = M−0+14−0+4−15 = M+3 Sel X52 = M−0+14−15 =2M−11 Sel X53 = 6−0+8−15 = −1 Sel X55 = 0−0+14−0+4−15 = 3
0
8
40 6
30 15
30 (1)
(2)
Loop Terpilih Pada Sel 𝑋53 (1) dan Hasil Perbaikan Sel 𝑋53 (2)
Universitas Sumatera Utara
88
Iterasi Ke 2
TC 3
5
3
SA Sumber
SB
14
M
0
20
0
3
0
4
0
65
0
14
M
0
10 3
0
8
40 M
6
SE 70
90
10
0 M
70
5 10
70 10
Permintaan
Persediaan
TG
20
SC SD
Tujuan TD TF
TB
30 70
95
0
30 15
70
0 0
35
30
0 10
Indeks Perbaikan Iterasi Ke 2 Sel X11 = 3−5+14−0 = 12 Sel X13 = 3−0+8−4+0−5 = 2 Sel X14 = M−4+0−5 = M−9 Sel X15 = 0−0+14−5 = 9 Sel X21 = 14−0+14−0 = 28 Sel X23 = 3−4+8−0 = 7 Sel X25 = 0−0+14−0 = 14 Sel X33 = 10−14+0−4+8−0 = 0
𝑋22 (−) 65 14 𝑋32 10 3 𝑋42 (+) 0
3
𝑋23
4
(+) 10 0
𝑋33
M 8
Sel X34 = M−14+0−4 = M−18 Sel X41 = 10−0+14−0+4−8 = 20 Sel X42 = 3−0+4−8 = −1 Sel X45 = 0−0+4−0+14−8 = 10 Sel X51 = M−0+14−0+4−15−8+0−6 = M+4 Sel X52 = M−0+4−8+0−6 = M−10 Sel X53 = 15−6+0−8 = 1 Sel X55 = 0−0+14−0+4−8+0−6 = 4
𝑋24 5 𝑋34
𝑋43 𝑋44 40 (−) 30 (1)
0
3
4
10
M
0
8
35 14
35
10 3
30
40 (2)
Loop Terpilih Pada Sel X42 (1) dan Hasil Perbaikan Sel X42 (2)
Universitas Sumatera Utara
89
Iterasi Ke 3
TC
TB
3
5
SA Sumber
SB
3
14
0
20
0
0
3
4
35
0
14
70 0
10
M
0
90
10 0
30
8
0
40
M
6
SE 70
70
35
3
M
0
10
10
Permintaan
M
Persediaan
TG
20
SC SD
Tujuan TD TF
30 70
95
70
0 15
0
30
0 10
35
Indeks Perbaikan Iterasi Ke 3 Sel X11 = 3−5+14−0 = 12 Sel X13 = 3−0+3−5 = 1 Sel X14 = M−4+0−5 = M−9 Sel X15 = 0−0+14−5 = 9 Sel X21 = 14−0+14−0 = 28 Sel X23 = 3−0+3−0 = 6 Sel X25 = 0−0+14−0 = 14 Sel X33 = 10−0+3−14 = −1
14
(−) 3
(+)
10
𝑋32 10 𝑋42
0
30 (1)
Sel X34 = M−14+0−4 = M−18 Sel X41 = 10−0+14−3 = 21 Sel X44 = 8−3+0−4 = 1 Sel X45 = 0−3+14−0 = 11 Sel X51 = M−0+14−3+0−6 = M+5 Sel X52 = M−3+0−6 = M−9 Sel X54 = 15−6+0−3+0−4 = 2 Sel X55 = 0−6+0−3+14−0 = 5
𝑋33 (+) 𝑋43 (−)40
14
10
10 3
0
40
30
(2)
Loop Terpilih Pada Sel 𝑋33 (1) dan Hasil Perbaikan Sel 𝑋33 (2)
Universitas Sumatera Utara
90
Iterasi Ke 4
TC 3
TB 5
SA Sumber
SB
3
14
0
0
0
20 3
4
35
0
14
10
3
0
40 M
95
70
0
10 8
0 15
30 70
90
0
30 6
SE 70
M
10
0 M
0
35
70 10
Permintaan
M
Persediaan
TG
20
SC SD
Tujuan TD TF
70
0
35
0 10
30
Indeks Perbaikan Iterasi Ke 4 Sel X11 = 3−5+3−0+10−0 = 11 Sel X13 = 3−0+3−5 = 1 Sel X14 = M−4+0−5 = M−9 Sel X15 = 0−0+10−0+3−5 = 8 Sel X21 = 14−0+3−0+10−0 = 27 Sel X23 = 3−0+3−0 = 6 Sel X25 = 0−0+10−0+3−0 = 13 Sel X32 = 14−10+0−3 = 1
Sel X34 = M−10+0−3+0−4 = M−17 Sel X41 = 10−0+10−0 = 20 Sel X44 = 8−3+0−4 = 1 Sel X45 = 0−0+10−0 = 10 Sel X51 = M−0+10−6 = M+4 Sel X52 = M−3+0−6 = M−9 Sel X54 = 15−6+0−3+0−4 = 2 Sel X55 = 0−6+10−0 = 4
Universitas Sumatera Utara
