Kajian Masalah Transshipment Tidak Seimbang Menggunakan Metode Least Cost - Stepping Stone dan Metode Least Cost - MODI
Lampiran 1. Nilai baris u i dan kolom vj untuk setiap tabel iterasi dari metode
MODI
Nilai Baris u i 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 u i 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 u i 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 u i 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
v5=c35−u3=0−14=−14
u5=c53−v3=6−(−3)=9
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Nilai Baris u i 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 u i 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−u 2−v4 = 4+14−M = 18−M
Sel X25 = k25 = c25−u2−v5 = 0+14−M+15 = 29−M
Sel X33 = k33 = c33−u 3−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−u 3−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−u 4−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−u 5−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−u 5−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−u 3−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
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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
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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
10
0
8
0
70
M
6
SE
95
70
90
5
70
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
(+)
0
(−)
�33
M
�43
8
70
(1)
�34
(−)
5
�44
(+)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 �33 (1) dan Hasil Perbaikan Sel �33 (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
�21
(+) 10
14
�31
(−) 15
5
�22
3
0
70
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
�23
3
�32
�33
5
10
M
M
�24
�34
0
(−)
0
(+)
�25
10
�35
(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
(+)
�43
8
65
�53
15
(1)
�44
(+)
5
�54
(−)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
(2)
Loop Terpilih Pada Sel �53 (1) dan Hasil Perbaikan Sel �53 (2)
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80
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
�31
5
(−)
3
�41
(+)
14
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
70
10
�32
�42
(1)
�33
(+) 5
0
�43
(−) 35
10
10
0
70
3
10
0
10
5
30
(2)
Loop Terpilih Pada Sel X41 (1) dan Hasil Perbaikan Sel X41 (2)
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81
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
�11
(−) 70
5
�21
20
14
�31
0
3
5 �31
(+)
14
3
0
10
�12
�22
M
M
�32
70
�31
10
0
30
(1)
�13
�23
�33
10
�31
0
(+)
0
M
8
�14
�24
�34
35 �31
(−)
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
3
3
M
0
10
M
14
0
10
M
3
10
0
35
5
35
20
70
10
0
8
40
(2)
Loop Terpilih Pada Sel X14 (1) dan Hasil Perbaikan Sel X14 (2)
Universitas Sumatera Utara
82
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
(+)
�22
70
�32
5
3
10
�23
�33
(1)
4
(+)
M
(−)
5
�24
�34
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
0
3
4
10
M
65
14
10
5
5
(2)
Loop Terpilih Pada Sel �24 (1) dan Hasil Perbaikan Sel �24 (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
(+)
�43
8
70
�53
15
(1)
�44
(+)
0
�54
(−)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
(2)
Loop Terpilih Pada Sel �53 (1) dan Hasil Perbaikan Sel �53 (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
�22
(−) 65
14
�32
10
3
�42
(+)
0
3
10
0
�23
�33
4
(+)
M
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
�24
5
�34
�43
�44
40 (−) 30
(1)
8
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
(+)
�32
10
10
�42
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
�33
(+)
�43
(−)40
14
10
10
3
0
40
30
(2)
Loop Terpilih Pada Sel �33 (1) dan Hasil Perbaikan Sel �33 (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
MODI
Nilai Baris u i 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 u i 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 u i 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 u i 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
v5=c35−u3=0−14=−14
u5=c53−v3=6−(−3)=9
Universitas Sumatera Utara
70
Nilai Baris u i 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 u i 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
Universitas Sumatera Utara
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−u 2−v4 = 4+14−M = 18−M
Sel X25 = k25 = c25−u2−v5 = 0+14−M+15 = 29−M
Sel X33 = k33 = c33−u 3−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−u 3−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
Universitas Sumatera Utara
72
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−u 4−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−u 5−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−u 5−v3 = 6−11+3 = −2
Sel X54 = k54 = c54−u5−v4 = 0−11+14 = 3
Universitas Sumatera Utara
73
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−u 3−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
Universitas Sumatera Utara
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
76
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
Universitas Sumatera Utara
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
10
0
8
0
70
M
6
SE
95
70
90
5
70
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
(+)
0
(−)
�33
M
�43
8
70
(1)
�34
(−)
5
�44
(+)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 �33 (1) dan Hasil Perbaikan Sel �33 (2)
Universitas Sumatera Utara
78
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
�21
(+) 10
14
�31
(−) 15
5
�22
3
0
70
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
�23
3
�32
�33
5
10
M
M
�24
�34
0
(−)
0
(+)
�25
10
�35
(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)
Universitas Sumatera Utara
79
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
(+)
�43
8
65
�53
15
(1)
�44
(+)
5
�54
(−)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
(2)
Loop Terpilih Pada Sel �53 (1) dan Hasil Perbaikan Sel �53 (2)
Universitas Sumatera Utara
80
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
�31
5
(−)
3
�41
(+)
14
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
70
10
�32
�42
(1)
�33
(+) 5
0
�43
(−) 35
10
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
81
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
�11
(−) 70
5
�21
20
14
�31
0
3
5 �31
(+)
14
3
0
10
�12
�22
M
M
�32
70
�31
10
0
30
(1)
�13
�23
�33
10
�31
0
(+)
0
M
8
�14
�24
�34
35 �31
(−)
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
3
3
M
0
10
M
14
0
10
M
3
10
0
35
5
35
20
70
10
0
8
40
(2)
Loop Terpilih Pada Sel X14 (1) dan Hasil Perbaikan Sel X14 (2)
Universitas Sumatera Utara
82
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
(+)
�22
70
�32
5
3
10
�23
�33
(1)
4
(+)
M
(−)
5
�24
�34
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
0
3
4
10
M
65
14
10
5
5
(2)
Loop Terpilih Pada Sel �24 (1) dan Hasil Perbaikan Sel �24 (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
(+)
�43
8
70
�53
15
(1)
�44
(+)
0
�54
(−)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
(2)
Loop Terpilih Pada Sel �53 (1) dan Hasil Perbaikan Sel �53 (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
�22
(−) 65
14
�32
10
3
�42
(+)
0
3
10
0
�23
�33
4
(+)
M
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
�24
5
�34
�43
�44
40 (−) 30
(1)
8
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
(+)
�32
10
10
�42
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
�33
(+)
�43
(−)40
14
10
10
3
0
40
30
(2)
Loop Terpilih Pada Sel �33 (1) dan Hasil Perbaikan Sel �33 (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