Lampiran 1
Syntax Program LINGO 11.0 untuk Menyelesaikan Masalah Pemrograman Linear dengan
Metode Branch and Bound beserta Hasil yang Diperoleh
1) PL-relaksasi dari ILP (8)
Maksimumkan z = 16x
1+ 10x
2terhadap, 2x
1+ 2x
2≤ 12
18x
1+ 10x
2≤ 90
x
1, x
2≥ 0
Syntax program pada LINGO 11.0:
!Fungsi Objektif;
max=16*x1+10*x2;
!Kendala;
2*x1+2*x2<=12;
18*x1+10*x2<=90;
x1>=0;x2>=0;
end
Hasil yang diperoleh:
Global optimal solution found.
Objective value:82.50000
Infeasibilities:0.000000
Total solver iterations:2
Variable Value
Reduced Cost
X1 3.750000 0.000000
X2 2.250000 0.000000
2) Subproblem 2
Maksimumkan z = 16x
1+ 10x
2terhadap, 2x
1+ 2x
2≤ 12
18x
1+ 10x
2≤ 90
x
1≥ 4
x
1, x
2≥ 0
Syntax program pada LINGO 11.0:
!Fungsi Objektif;
max=16*x1+10*x2;
!Kendala;
2*x1+2*x2<=12;
18*x1+10*x2<=90;
x1>=4;
x1>=0;x2>=0;
end
Hasil yang diperoleh:
Global optimal solution found.
Objective value: 82.00000
Infeasibilities: 0.000000
Total solver iterations: 3
Variable Value
Reduced Cost
X1
4.000000 0.000000
X2 1.800000 0.000000
3) Subproblem 3
Maksimumkan z = 16x
1+ 10x
2terhadap, 2x
1+ 2x
2≤ 12
18x
1+ 10x
2≤ 90
x
1≤ 3
x
1, x
2≥ 0
Syntax program pada LINGO 11.0:
!Fungsi Objektif;
max=16*x1+10*x2;
!Kendala;
2*x1+2*x2<=12;
18*x1+10*x2<=90;
x1<=3; x1>=0; x2>=0;
end
Hasil yang diperoleh:
Global optimal solution found.
Objective value: 78.00000
Infeasibilities: 0.000000
Total solver iterations: 1
Variable Value Reduced Cost
X1 3.000000 0.000000
X2 3.000000 0.000000
4) Subproblem 4
Maksimumkan z = 16x
1+ 10x
2terhadap, 2x
1+ 2x
2≤ 12
18x
1+ 10x
2≤ 90
x
1≥ 4
x
2≥ 2
x
1, x
2≥ 0
Syntax program pada LINGO 11.0:
!Fungsi Objektif;
max=16*x1+10*x2;
!Kendala;
2*x1+2*x2<=12;
18*x1+10*x2<=90;
x1>=4; x2>=2;
x1>=0; x2>=0;
end
Hasil yang diperoleh:
5) Subproblem 5
Maksimumkan z = 16x
1+ 10x
2terhadap, 2x
1+ 2x
2≤ 12
18x
1+ 10x
2≤ 90
x
1≥ 4
x
2≤ 1
x
1, x
2≥ 0
Syntax program pada LINGO 11.0:
!Fungsi Objektif;
max=16*x1+10*x2;
!Kendala;
2*x1+2*x2<=12;
18*x1+10*x2<=90;
x1>=4; x2<=1;x1>=0; x2>=0;
end
Hasil yang diperoleh:
Global optimal solution found.
Objective value: 81.11111
Infeasibilities: 0.000000
Total solver iterations: 1
Variable Value Reduced Cost
X1 4.444444 0.000000
X2 1.000000 0.000000
6) Subproblem 6
Maksimumkan z = 16x
1+ 10x
2terhadap, 2x
1+ 2x
2≤ 12
18x
1+ 10x
2≤ 90
x
1≥ 4
x
2≤ 1
x
1≥ 5
x
1, x
2≥ 0
Syntax program pada LINGO 11.0:
!Fungsi Objektif;
max=16*x1+10*x2;
!Kendala;
2*x1+2*x2<=12;
18*x1+10*x2<=90;
x1>=4; x2<=1; x1>=5;
x1>=0; x2>=0;
end
Hasil yang diperoleh:
Global optimal solution found.
Objective value: 80.00000
Infeasibilities: 0.000000
Total solver iterations:0
Variable Value
Reduced Cost
X1 5.000000 0.000000
X2 0.000000 0.000000
7) Subproblem 7
Maksimumkan z = 16x
1+ 10x
2terhadap, 2x
1+ 2x
2≤ 12
18x
1+ 10x
2≤ 90
x
1≥ 4
x
2≤ 1
x
1≤ 4
x
1, x
2≥ 0
Syntax program pada LINGO 11.0:
!Fungsi Objektif;
max=16*x1+10*x2;
!Kendala;
2*x1+2*x2<=12;
18*x1+10*x2<=90;
x1>=4; x2<=1; x1<=4;
x1>=0; x2>=0;
end
Hasil yang diperoleh:
Global optimal solution found.
Objective value: 74.00000
Infeasibilities: 0.000000
Total solver iterations: 0
Variable Value Reduced Cost
X1 4.000000 0.000000
X2 1.000000 0.000000
Lampiran 2
Data Simulasi Penjadwalan MRT Lebak Bulus-Sisingamangaraja
Tabel 4 Data simulasi dari perjalanan MRT Lebak Bulus-Sisingamangaraja
Indeks
stasiun
Stasiun
Indeks
Petak
Blok (d
k)
Jarak
antarstasiun
(km)
Kecepatan
minimum
(km/jam)
Kecepatan
maksimum
(km/jam)
Waktu tempuh
minimum
(menit)
Waktu tempuh
maksimum
(menit)
Waktu tunggu
di stasiun
(menit)
MRT
Eko.
MRT
Eks.
MRT
Eko.
MRT
Eks.
MRT
Eko.
MRT
Eks.
MRT
Eko.
MRT
Eks.
MRT
Eko.
MRT
Eks.
1
Lebak Bulus (LB)
-
-
-
-
-
-
-
-
-
-
5
3
2
Fatmawati (FA
d
17.95
43.36
79.50
53.00
119.25
11
6
9
4
1
0
3
Cipete Raya (CR)
d
28.25
38.08
61.88
45.00
82.50
13
8
11
6
1
0
4
Haji Nawi (HN)
d
37.30
43.80
87.60
54.75
146.00
10
5
8
3
1
1
5
Blok A (BA)
d
45.25
35.00
78.75
45.00
157.50
9
4
7
2
1
0
6
Blok M (BM)
d
56.70
36.55
67.00
44.67
100.50
11
6
9
4
1
0
7
Sisingamangaraja (SI)
d
67.25
33.46
54.38
39.55
72.50
13
8
11
6
5
3
Keterangan: Eko. = MRT Ekonomi, Eks. = MRT Ekspres.
Tabel 5 Waktu kedatangan setiap MRT di stasiun pertama
Indeks MRT
Jenis MRT
Waktu Kedatangan (menit ke-)
1
MRT Ekonomi
5
2
MRT Ekonomi
10
3
MRT Ekonomi
20
4
MRT Ekonomi
35
5
MRT Ekonomi
40
6
MRT Ekonomi
50
7
MRT Ekspres
15
8
MRT Ekspres
25
9
MRT Ekspres
30
10
MRT Ekspres
45
11
MRT Ekonomi
5
12
MRT Ekonomi
15
13
MRT Ekonomi
20
14
MRT Ekonomi
30
15
MRT Ekonomi
40
16
MRT Ekspres
10
17
MRT Ekspres
25
18
MRT Ekspres
35
Lampiran 3
Syntax Program LINGO 11.0 untuk Simulasi Penjadwalan MRT Lebak
Bulus-Sisingamangaraja beserta Hasil yang Diperoleh
model: sets: kereta/1..18/;stasiun/1..7/;petakb lok/1..6/; link1(kereta,stasiun):Xd,Xa,S,D; link2(kereta,kereta,petakblok):A,B ; endsets data: h=5; M=100; S= 5 1 1 1 1 1 5 5 1 1 1 1 1 5 5 1 1 1 1 1 5 5 1 1 1 1 1 5 5 1 1 1 1 1 5 5 1 1 1 1 1 5 3 0 0 1 0 0 3 3 0 0 1 0 0 3 3 0 0 1 0 0 3 3 0 0 1 0 0 3 5 1 1 1 1 1 5 5 1 1 1 1 1 5 5 1 1 1 1 1 5 5 1 1 1 1 1 5 5 1 1 1 1 1 5 3 0 0 1 0 0 3 3 0 0 1 0 0 3 3 0 0 1 0 0 3 ; enddata !Fungsi Objektif; min=@sum(kereta(i)|i#LE#10:Xd(i,7) -Xa(i,1))+@sum(kereta(i)|i#GT#10:Xd (i,7)-Xa(i,1));
!kendala 1: Urutan operasi pada setiap kereta api;
!outbound; @for(kereta(i)|i#LE#10:@for(stasiu n(l):Xa(i,l)+S(i,l)+D(i,l)=Xd(i,l) )); !inbound; @for(kereta(i)|i#GT#10:@for(stasiu n(l):Xa(i,l)+S(i,l) +D(i,l)=Xd(i,l)));
!Kendala 2: Aturan penyusulan; !kereta j mendahului kereta i;
!outbound; @for(kereta(i)|i#LE#10:@for(kereta (j)|j#NE#i#AND#j#LE#10:@for(petakb lok(k):@for(stasiun(l)|l#GE#2:M*A( i,j,k)+Xa(i,l)>Xa(j,l)+h)))); @for(kereta(i)|i#LE#10:@for(kereta (j)|j#NE#i#AND#j#LE#10:@for(petakb lok(k):@for(stasiun(l):M*A(i,j,k)+ Xd(i,l)>Xd(j,l)+h)))); !inbound; @for(kereta(i)|i#GT#10:@for(kereta (j)|j#NE#i#AND#j#GT#10:@for(petakb lok(k):@for(stasiun(l)|l#GE#2:M*B( i,j,k)+Xa(i,l)>Xa(j,l)+h)))); @for(kereta(i)|i#GT#10:@for(kereta (j)|j#NE#i#AND#j#GT#10:@for(petakb lok(k):@for(stasiun(l):M*B(i,j,k)+ Xd(i,l)>Xd(j,l)+h))));
!kereta i mendahului kereta j; !outbound; @for(kereta(i)|i#LE#10:@for(kereta (j)|j#NE#i#AND#j#LE#10:@for(petakb lok(k):@for(stasiun(l)|l#GE#2:M*(1 -A(i,j,k))+Xa(j,l)>Xa(i,l)+h)))); @for(kereta(i)|i#LE#10:@for(kereta (j)|j#NE#i#AND#j#LE#10:@for(petakb lok(k):@for(stasiun(l):M*(1-A(i,j,k))+Xd(j,l)>Xd(i,l)+h)))); !inbound; @for(kereta(i)|i#GT#10:@for(kereta (j)|j#NE#i#AND#j#GT#10:@for(petakb lok(k):@for(stasiun(l)|l#GE#2:M*(1 -B(i,j,k))+Xa(j,l)>Xa(i,l)+h)))); @for(kereta(i)|i#GT#10:@for(kereta (j)|j#NE#i#AND#j#GT#10:@for(petakb lok(k):@for(stasiun(l):M*(1-B(i,j,k))+Xd(j,l)>Xd(i,l)+h)))); !kendala 3: Rata-rata kecepatan setiap kereta api untuk menempuh masing-masing petak blok;
!outbound; @for(kereta(i)|i#LE#6:9<(Xa(i,2)-Xd(i,1))); @for(kereta(i)|i#LE#6:(Xa(i,2)-Xd(i,1))<11); @for(kereta(i)|i#LE#6:11<(Xa(i,3)-Xd(i,2))); @for(kereta(i)|i#LE#6:(Xa(i,3)-Xd(i,2))<13); @for(kereta(i)|i#LE#6:8<(Xa(i,4)-Xd(i,3)));
@for(kereta(i)|i#LE#6:(Xa(i,4)-Xd(i,3))<10); @for(kereta(i)|i#LE#6:7<(Xa(i,5)-Xd(i,4))); @for(kereta(i)|i#LE#6:(Xa(i,5)-Xd(i,4))<9); @for(kereta(i)|i#LE#6:9<(Xa(i,6)-Xd(i,5))); @for(kereta(i)|i#LE#6:(Xa(i,6)-Xd(i,5))<11); @for(kereta(i)|i#LE#6:11<(Xa(i,7)-Xd(i,6))); @for(kereta(i)|i#LE#6:(Xa(i,7)-Xd(i,6))<13); @for(kereta(i)|i#LE#10#AND#i#GT#6: 4<(Xa(i,2)-Xd(i,1))); @for(kereta(i)|i#LE#10#AND#i#GT#6: (Xa(i,2)-Xd(i,1))<6); @for(kereta(i)|i#LE#10#AND#i#GT#6: 6<(Xa(i,3)-Xd(i,2))); @for(kereta(i)|i#LE#10#AND#i#GT#6: (Xa(i,3)-Xd(i,2))<8); @for(kereta(i)|i#LE#10#AND#i#GT#6: 3<(Xa(i,4)-Xd(i,3))); @for(kereta(i)|i#LE#10#AND#i#GT#6: (Xa(i,4)-Xd(i,3))<5); @for(kereta(i)|i#LE#10#AND#i#GT#6: 2<(Xa(i,5)-Xd(i,4))); @for(kereta(i)|i#LE#10#AND#i#GT#6: (Xa(i,5)-Xd(i,4))<4); @for(kereta(i)|i#LE#10#AND#i#GT#6: 4<(Xa(i,6)-Xd(i,5))); @for(kereta(i)|i#LE#10#AND#i#GT#6: (Xa(i,6)-Xd(i,5))<6); @for(kereta(i)|i#LE#10#AND#i#GT#6: 6<(Xa(i,7)-Xd(i,6))); @for(kereta(i)|i#LE#10#AND#i#GT#6: (Xa(i,7)-Xd(i,6))<8); !inbound; @for(kereta(i)|i#GT#10#AND#i#LE#15 :11<(Xa(i,2)-Xd(i,1))); @for(kereta(i)|i#GT#10#AND#i#LE#15 :9<(Xa(i,3)-Xd(i,2))); @for(kereta(i)|i#GT#10#AND#i#LE#15 :7<(Xa(i,4)-Xd(i,3))); @for(kereta(i)|i#GT#10#AND#i#LE#15 :8<(Xa(i,5)-Xd(i,4))); @for(kereta(i)|i#GT#10#AND#i#LE#15 :11<(Xa(i,6)-Xd(i,5))); @for(kereta(i)|i#GT#10#AND#i#LE#15 :9<(Xa(i,7)-Xd(i,6))); @for(kereta(i)|i#GT#10#AND#i#LE#15 :(Xa(i,2)-Xd(i,1))<13); @for(kereta(i)|i#GT#10#AND#i#LE#15 :(Xa(i,3)-Xd(i,2))<11); @for(kereta(i)|i#GT#10#AND#i#LE#15 :(Xa(i,4)-Xd(i,3))<9); @for(kereta(i)|i#GT#10#AND#i#LE#15 :(Xa(i,5)-Xd(i,4))<10); @for(kereta(i)|i#GT#10#AND#i#LE#15 :(Xa(i,6)-Xd(i,5))<13); @for(kereta(i)|i#GT#10#AND#i#LE#15 :(Xa(i,7)-Xd(i,6))<11); @for(kereta(i)|i#LE#18#AND#i#GT#15 :6<(Xa(i,2)-Xd(i,1))); @for(kereta(i)|i#LE#18#AND#i#GT#15 :4<(Xa(i,3)-Xd(i,2))); @for(kereta(i)|i#LE#18#AND#i#GT#15 :2<(Xa(i,4)-Xd(i,3))); @for(kereta(i)|i#LE#18#AND#i#GT#15 :3<(Xa(i,5)-Xd(i,4))); @for(kereta(i)|i#LE#18#AND#i#GT#15 :6<(Xa(i,6)-Xd(i,5))); @for(kereta(i)|i#LE#18#AND#i#GT#15 :4<(Xa(i,7)-Xd(i,6))); @for(kereta(i)|i#LE#18#AND#i#GT#15 :(Xa(i,2)-Xd(i,1))<8); @for(kereta(i)|i#LE#18#AND#i#GT#15 :(Xa(i,3)-Xd(i,2))<6); @for(kereta(i)|i#LE#18#AND#i#GT#15 :(Xa(i,4)-Xd(i,3))<4); @for(kereta(i)|i#LE#18#AND#i#GT#15 :(Xa(i,5)-Xd(i,4))<5); @for(kereta(i)|i#LE#18#AND#i#GT#15 :(Xa(i,6)-Xd(i,5))<8); @for(kereta(i)|i#LE#18#AND#i#GT#15 :(Xa(i,7)-Xd(i,6))<6);
!Waktu kedatangan masing-masing kereta di stasiun pertama; !outbound; Xa(1,1)=5;Xa(2,1)=10;Xa(3,1)=20;Xa (4,1)=35;Xa(5,1)=40;Xa(6,1)=50; Xa(7,1)=15;Xa(8,1)=25;Xa(9,1)=30;X a(10,1)=45; !inbound; Xa(11,1)=5;Xa(12,1)=15;Xa(13,1)=20 ;Xa(14,1)=30;Xa(15,1)=40; Xa(16,1)=10;Xa(17,1)=25;Xa(18,1)=3 5; ! Kendala 4: Pemberhentian Ekspress; ! Outbound; Xa(7,2)=Xd(7,2); Xa(7,3)=Xd(7,3); Xa(7,5)=Xd(7,5); Xa(7,6)=Xd(7,6);
Xa(8,2)=Xd(8,2); Xa(8,3)=Xd(8,3); Xa(8,5)=Xd(8,5); Xa(8,6)=Xd(8,6); Xa(9,2)=Xd(9,2); Xa(9,3)=Xd(9,3); Xa(9,5)=Xd(9,5); Xa(9,6)=Xd(9,6); Xa(10,2)=Xd(10,2); Xa(10,3)=Xd(10,3); Xa(10,5)=Xd(10,5); Xa(10,6)=Xd(10,6); !inbound; Xa(16,2)=Xd(16,2); Xa(16,3)=Xd(16,3); Xa(16,5)=Xd(16,5); Xa(16,6)=Xd(16,6); Xa(17,2)=Xd(17,2); Xa(17,3)=Xd(17,3); Xa(17,5)=Xd(17,5); Xa(17,6)=Xd(17,6); Xa(18,2)=Xd(18,2); Xa(18,3)=Xd(18,3); Xa(18,5)=Xd(18,5); Xa(18,6)=Xd(18,6);
!Kendala 5: nilai biner untuk A dan B; @for(kereta(i)|i#LE#10:@for(kereta (j)|j#LE#10:@for(petakblok(k):@bin (A(i,j,k))))); @for(kereta(i)|i#GT#10:@for(kereta (j)|j#GT#10:@for(petakblok(k):@bin (B(i,j,k))))); !Outbound; A(1,2,1)=1; A(1,3,1)=1; A(1,4,1)=1; A(1,5,1)=1; A(1,6,1)=1; A(1,7,1)=1; A(1,8,1)=1; A(1,9,1)=1; A(1,10,1)=1; A(2,3,1)=1; A(2,4,1)=1; A(2,5,1)=1; A(2,6,1)=1; A(2,7,1)=1; A(2,8,1)=1; A(2,9,1)=1; A(2,10,1)=1; A(7,3,1)=1; A(7,4,1)=1; A(7,5,1)=1; A(7,6,1)=1; A(7,8,1)=1; A(7,9,1)=1; A(7,10,1)=1; A(3,4,1)=1; A(3,5,1)=1; A(3,6,1)=1; A(3,8,1)=1; A(3,9,1)=1; A(3,10,1)=1; A(8,4,1)=1; A(8,5,1)=1; A(8,6,1)=1; A(8,9,1)=1; A(8,10,1)=1; A(9,4,1)=1; A(9,5,1)=1; A(9,6,1)=1; A(9,10,1)=1; A(4,5,1)=1; A(4,6,1)=1; A(4,10,1)=1; A(5,6,1)=1; A(5,10,1)=1; A(10,6,1)=1; !inbound; B(11,12,1)=1; B(11,13,1)=1; B(11,14,1)=1; B(11,15,1)=1; B(11,16,1)=1; B(11,17,1)=1; B(11,18,1)=1; B(16,12,1)=1; B(16,13,1)=1; B(16,14,1)=1; B(16,15,1)=1; B(16,17,1)=1; B(16,18,1)=1; B(12,13,1)=1; B(12,14,1)=1; B(12,15,1)=1; B(12,17,1)=1; B(12,18,1)=1; B(13,14,1)=1; B(13,15,1)=1; B(13,17,1)=1; B(13,18,1)=1; B(17,14,1)=1; B(17,15,1)=1; B(17,18,1)=1; B(14,15,1)=1; B(14,18,1)=1; B(18,15,1)=1; end
Global optimal solution found.
Objective value: 1502.000
Objective bound: 1502.000
Infeasibilities: 0.000000
Extended solver steps: 0
Total solver iterations: 1303
Variable Value Reduced Cost H 5.000000 0.000000 M 100.0000 0.000000 XD( 1, 1) 10.00000 0.000000 XD( 1, 2) 20.00000 0.000000 XD( 1, 3) 32.00000 0.000000 XD( 1, 4) 41.00000 0.000000 XD( 1, 5) 49.00000 0.000000 XD( 1, 6) 59.00000 0.000000 XD( 1, 7) 75.00000 0.000000 XD( 2, 1) 15.00000 0.000000 XD( 2, 2) 25.00000 0.000000 XD( 2, 3) 37.00000 0.000000 XD( 2, 4) 46.00000 0.000000 XD( 2, 5) 54.00000 0.000000 XD( 2, 6) 64.00000 0.000000 XD( 2, 7) 80.00000 0.000000 XD( 3, 1) 36.00000 0.000000 XD( 3, 2) 46.00000 0.000000 XD( 3, 3) 58.00000 0.000000 XD( 3, 4) 67.00000 0.000000 XD( 3, 5) 75.00000 0.000000 XD( 3, 6) 85.00000 0.000000 XD( 3, 7) 101.0000 0.000000 XD( 4, 1) 62.00000 0.000000 XD( 4, 2) 72.00000 0.000000 XD( 4, 3) 84.00000 0.000000 XD( 4, 4) 93.00000 0.000000 XD( 4, 5) 101.0000 0.000000 XD( 4, 6) 111.0000 0.000000 XD( 4, 7) 127.0000 0.000000 XD( 5, 1) 67.00000 0.000000 XD( 5, 2) 77.00000 0.000000 XD( 5, 3) 89.00000 0.000000 XD( 5, 4) 98.00000 0.000000 XD( 5, 5) 106.0000 0.000000 XD( 5, 6) 116.0000 0.000000 XD( 5, 7) 132.0000 0.000000 XD( 6, 1) 88.00000 0.000000 XD( 6, 2) 98.00000 0.000000 XD( 6, 3) 110.0000 0.000000 XD( 6, 4) 119.0000 0.000000 XD( 6, 5) 127.0000 0.000000 XD( 6, 6) 137.0000 0.000000 XD( 6, 7) 153.0000 0.000000 XD( 7, 1) 31.00000 0.000000 XD( 7, 2) 37.00000 0.000000 XD( 7, 3) 45.00000 0.000000 XD( 7, 4) 62.00000 0.000000 XD( 7, 5) 66.00000 0.000000 XD( 7, 6) 72.00000 0.000000 XD( 7, 7) 85.00000 0.000000 XD( 8, 1) 52.00000 0.000000 XD( 8, 2) 58.00000 0.000000 XD( 8, 3) 66.00000 0.000000 XD( 8, 4) 83.00000 0.000000 XD( 8, 5) 87.00000 0.000000 XD( 8, 6) 93.00000 0.000000 XD( 8, 7) 106.0000 0.000000 XD( 9, 1) 57.00000 0.000000 XD( 9, 2) 63.00000 0.000000 XD( 9, 3) 71.00000 0.000000 XD( 9, 4) 88.00000 0.000000 XD( 9, 5) 92.00000 0.000000 XD( 9, 6) 98.00000 0.000000 XD( 9, 7) 111.0000 0.000000 XD( 10, 1) 83.00000 0.000000 XD( 10, 2) 89.00000 0.000000 XD( 10, 3) 97.00000 0.000000 XD( 10, 4) 114.0000 0.000000 XD( 10, 5) 118.0000 0.000000 XD( 10, 6) 124.0000 0.000000 XD( 10, 7) 137.0000 0.000000 XD( 11, 1) 10.00000 0.000000 XD( 11, 2) 22.00000 0.000000 XD( 11, 3) 32.00000 0.000000 XD( 11, 4) 40.00000 0.000000 XD( 11, 5) 49.00000 0.000000 XD( 11, 6) 61.00000 0.000000 XD( 11, 7) 75.00000 0.000000 XD( 12, 1) 31.00000 0.000000 XD( 12, 2) 43.00000 0.000000 XD( 12, 3) 53.00000 0.000000 XD( 12, 4) 61.00000 0.000000 XD( 12, 5) 70.00000 0.000000 XD( 12, 6) 82.00000 0.000000 XD( 12, 7) 96.00000 0.000000 XD( 13, 1) 36.00000 0.000000 XD( 13, 2) 48.00000 0.000000 XD( 13, 3) 58.00000 0.000000 XD( 13, 4) 66.00000 0.000000 XD( 13, 5) 75.00000 0.000000 XD( 13, 6) 87.00000 0.000000 XD( 13, 7) 101.0000 0.000000 XD( 14, 1) 57.00000 0.000000 XD( 14, 2) 69.00000 0.000000 XD( 14, 3) 79.00000 0.000000 XD( 14, 4) 87.00000 0.000000 XD( 14, 5) 96.00000 0.000000 XD( 14, 6) 108.0000 0.000000 XD( 14, 7) 122.0000 0.000000 XD( 15, 1) 78.00000 0.000000 XD( 15, 2) 90.00000 0.000000 XD( 15, 3) 100.0000 0.000000 XD( 15, 4) 108.0000 0.000000 XD( 15, 5) 117.0000 0.000000 XD( 15, 6) 129.0000 0.000000 XD( 15, 7) 143.0000 0.000000 XD( 16, 1) 26.00000 0.000000 XD( 16, 2) 34.00000 0.000000 XD( 16, 3) 40.00000 0.000000 XD( 16, 4) 56.00000 0.000000 XD( 16, 5) 61.00000 0.000000 XD( 16, 6) 69.00000 0.000000 XD( 16, 7) 80.00000 0.000000 XD( 17, 1) 52.00000 0.000000 XD( 17, 2) 60.00000 0.000000 XD( 17, 3) 66.00000 0.000000 XD( 17, 4) 82.00000 0.000000 XD( 17, 5) 87.00000 0.000000 XD( 17, 6) 95.00000 0.000000 XD( 17, 7) 106.0000 0.000000 XD( 18, 1) 73.00000 0.000000 XD( 18, 2) 81.00000 0.000000 XD( 18, 3) 87.00000 0.000000 XD( 18, 4) 103.0000 0.000000 XD( 18, 5) 108.0000 0.000000 XD( 18, 6) 116.0000 0.000000 XD( 18, 7) 127.0000 0.000000 XA( 1, 1) 5.000000 0.000000 XA( 1, 2) 19.00000 0.000000 XA( 1, 3) 31.00000 0.000000 XA( 1, 4) 40.00000 0.000000 XA( 1, 5) 48.00000 0.000000 XA( 1, 6) 58.00000 0.000000 XA( 1, 7) 70.00000 0.000000 XA( 2, 1) 10.00000 0.000000 XA( 2, 2) 24.00000 0.000000
XA( 2, 3) 36.00000 0.000000 XA( 2, 4) 45.00000 0.000000 XA( 2, 5) 53.00000 0.000000 XA( 2, 6) 63.00000 0.000000 XA( 2, 7) 75.00000 0.000000 XA( 3, 1) 20.00000 0.000000 XA( 3, 2) 45.00000 0.000000 XA( 3, 3) 57.00000 0.000000 XA( 3, 4) 66.00000 0.000000 XA( 3, 5) 74.00000 0.000000 XA( 3, 6) 84.00000 0.000000 XA( 3, 7) 96.00000 0.000000 XA( 4, 1) 35.00000 0.000000 XA( 4, 2) 71.00000 0.000000 XA( 4, 3) 83.00000 0.000000 XA( 4, 4) 92.00000 0.000000 XA( 4, 5) 100.0000 0.000000 XA( 4, 6) 110.0000 0.000000 XA( 4, 7) 122.0000 0.000000 XA( 5, 1) 40.00000 0.000000 XA( 5, 2) 76.00000 0.000000 XA( 5, 3) 88.00000 0.000000 XA( 5, 4) 97.00000 0.000000 XA( 5, 5) 105.0000 0.000000 XA( 5, 6) 115.0000 0.000000 XA( 5, 7) 127.0000 0.000000 XA( 6, 1) 50.00000 0.000000 XA( 6, 2) 97.00000 0.000000 XA( 6, 3) 109.0000 0.000000 XA( 6, 4) 118.0000 0.000000 XA( 6, 5) 126.0000 0.000000 XA( 6, 6) 136.0000 0.000000 XA( 6, 7) 148.0000 0.000000 XA( 7, 1) 15.00000 0.000000 XA( 7, 2) 37.00000 0.000000 XA( 7, 3) 45.00000 0.000000 XA( 7, 4) 50.00000 0.000000 XA( 7, 5) 66.00000 0.000000 XA( 7, 6) 72.00000 0.000000 XA( 7, 7) 80.00000 0.000000 XA( 8, 1) 25.00000 0.000000 XA( 8, 2) 58.00000 0.000000 XA( 8, 3) 66.00000 0.000000 XA( 8, 4) 71.00000 0.000000 XA( 8, 5) 87.00000 0.000000 XA( 8, 6) 93.00000 0.000000 XA( 8, 7) 101.0000 0.000000 XA( 9, 1) 30.00000 0.000000 XA( 9, 2) 63.00000 0.000000 XA( 9, 3) 71.00000 0.000000 XA( 9, 4) 76.00000 0.000000 XA( 9, 5) 92.00000 0.000000 XA( 9, 6) 98.00000 0.000000 XA( 9, 7) 106.0000 0.000000 XA( 10, 1) 45.00000 0.000000 XA( 10, 2) 89.00000 0.000000 XA( 10, 3) 97.00000 0.000000 XA( 10, 4) 102.0000 0.000000 XA( 10, 5) 118.0000 0.000000 XA( 10, 6) 124.0000 0.000000 XA( 10, 7) 132.0000 0.000000 XA( 11, 1) 5.000000 0.000000 XA( 11, 2) 21.00000 0.000000 XA( 11, 3) 31.00000 0.000000 XA( 11, 4) 39.00000 0.000000 XA( 11, 5) 48.00000 0.000000 XA( 11, 6) 60.00000 0.000000 XA( 11, 7) 70.00000 0.000000 XA( 12, 1) 15.00000 0.000000 XA( 12, 2) 42.00000 0.000000 XA( 12, 3) 52.00000 0.000000 XA( 12, 4) 60.00000 0.000000 XA( 12, 5) 69.00000 0.000000 XA( 12, 6) 81.00000 0.000000 XA( 12, 7) 91.00000 0.000000 XA( 13, 1) 20.00000 0.000000 XA( 13, 2) 47.00000 0.000000 XA( 13, 3) 57.00000 0.000000 XA( 13, 4) 65.00000 0.000000 XA( 13, 5) 74.00000 0.000000 XA( 13, 6) 86.00000 0.000000 XA( 13, 7) 96.00000 0.000000 XA( 14, 1) 30.00000 0.000000 XA( 14, 2) 68.00000 0.000000 XA( 14, 3) 78.00000 0.000000 XA( 14, 4) 86.00000 0.000000 XA( 14, 5) 95.00000 0.000000 XA( 14, 6) 107.0000 0.000000 XA( 14, 7) 117.0000 0.000000 XA( 15, 1) 40.00000 0.000000 XA( 15, 2) 89.00000 0.000000 XA( 15, 3) 99.00000 0.000000 XA( 15, 4) 107.0000 0.000000 XA( 15, 5) 116.0000 0.000000 XA( 15, 6) 128.0000 0.000000 XA( 15, 7) 138.0000 0.000000 XA( 16, 1) 10.00000 0.000000 XA( 16, 2) 34.00000 0.000000 XA( 16, 3) 40.00000 0.000000 XA( 16, 4) 44.00000 0.000000 XA( 16, 5) 61.00000 0.000000 XA( 16, 6) 69.00000 0.000000 XA( 16, 7) 75.00000 0.000000 XA( 17, 1) 25.00000 0.000000 XA( 17, 2) 60.00000 0.000000 XA( 17, 3) 66.00000 0.000000 XA( 17, 4) 70.00000 0.000000 XA( 17, 5) 87.00000 0.000000 XA( 17, 6) 95.00000 0.000000 XA( 17, 7) 101.0000 0.000000 XA( 18, 1) 35.00000 0.000000 XA( 18, 2) 81.00000 0.000000 XA( 18, 3) 87.00000 0.000000 XA( 18, 4) 91.00000 0.000000 XA( 18, 5) 108.0000 0.000000 XA( 18, 6) 116.0000 0.000000 XA( 18, 7) 122.0000 0.000000 S( 1, 1) 5.000000 0.000000 S( 1, 2) 1.000000 0.000000 S( 1, 3) 1.000000 0.000000 S( 1, 4) 1.000000 0.000000 S( 1, 5) 1.000000 0.000000 S( 1, 6) 1.000000 0.000000 S( 1, 7) 5.000000 0.000000 S( 2, 1) 5.000000 0.000000 S( 2, 2) 1.000000 0.000000 S( 2, 3) 1.000000 0.000000 S( 2, 4) 1.000000 0.000000 S( 2, 5) 1.000000 0.000000 S( 2, 6) 1.000000 0.000000 S( 2, 7) 5.000000 0.000000 S( 3, 1) 5.000000 0.000000 S( 3, 2) 1.000000 0.000000 S( 3, 3) 1.000000 0.000000 S( 3, 4) 1.000000 0.000000 S( 3, 5) 1.000000 0.000000 S( 3, 6) 1.000000 0.000000 S( 3, 7) 5.000000 0.000000 S( 4, 1) 5.000000 0.000000 S( 4, 2) 1.000000 0.000000 S( 4, 3) 1.000000 0.000000 S( 4, 4) 1.000000 0.000000 S( 4, 5) 1.000000 0.000000 S( 4, 6) 1.000000 0.000000 S( 4, 7) 5.000000 0.000000 S( 5, 1) 5.000000 0.000000
S( 5, 2) 1.000000 0.000000 S( 5, 3) 1.000000 0.000000 S( 5, 4) 1.000000 0.000000 S( 5, 5) 1.000000 0.000000 S( 5, 6) 1.000000 0.000000 S( 5, 7) 5.000000 0.000000 S( 6, 1) 5.000000 0.000000 S( 6, 2) 1.000000 0.000000 S( 6, 3) 1.000000 0.000000 S( 6, 4) 1.000000 0.000000 S( 6, 5) 1.000000 0.000000 S( 6, 6) 1.000000 0.000000 S( 6, 7) 5.000000 0.000000 S( 7, 1) 3.000000 0.000000 S( 7, 2) 0.000000 0.000000 S( 7, 3) 0.000000 0.000000 S( 7, 4) 1.000000 0.000000 S( 7, 5) 0.000000 0.000000 S( 7, 6) 0.000000 0.000000 S( 7, 7) 3.000000 0.000000 S( 8, 1) 3.000000 0.000000 S( 8, 2) 0.000000 0.000000 S( 8, 3) 0.000000 0.000000 S( 8, 4) 1.000000 0.000000 S( 8, 5) 0.000000 0.000000 S( 8, 6) 0.000000 0.000000 S( 8, 7) 3.000000 0.000000 S( 9, 1) 3.000000 0.000000 S( 9, 2) 0.000000 0.000000 S( 9, 3) 0.000000 0.000000 S( 9, 4) 1.000000 0.000000 S( 9, 5) 0.000000 0.000000 S( 9, 6) 0.000000 0.000000 S( 9, 7) 3.000000 0.000000 S( 10, 1) 3.000000 0.000000 S( 10, 2) 0.000000 0.000000 S( 10, 3) 0.000000 0.000000 S( 10, 4) 1.000000 0.000000 S( 10, 5) 0.000000 0.000000 S( 10, 6) 0.000000 0.000000 S( 10, 7) 3.000000 0.000000 S( 11, 1) 5.000000 0.000000 S( 11, 2) 1.000000 0.000000 S( 11, 3) 1.000000 0.000000 S( 11, 4) 1.000000 0.000000 S( 11, 5) 1.000000 0.000000 S( 11, 6) 1.000000 0.000000 S( 11, 7) 5.000000 0.000000 S( 12, 1) 5.000000 0.000000 S( 12, 2) 1.000000 0.000000 S( 12, 3) 1.000000 0.000000 S( 12, 4) 1.000000 0.000000 S( 12, 5) 1.000000 0.000000 S( 12, 6) 1.000000 0.000000 S( 12, 7) 5.000000 0.000000 S( 13, 1) 5.000000 0.000000 S( 13, 2) 1.000000 0.000000 S( 13, 3) 1.000000 0.000000 S( 13, 4) 1.000000 0.000000 S( 13, 5) 1.000000 0.000000 S( 13, 6) 1.000000 0.000000 S( 13, 7) 5.000000 0.000000 S( 14, 1) 5.000000 0.000000 S( 14, 2) 1.000000 0.000000 S( 14, 3) 1.000000 0.000000 S( 14, 4) 1.000000 0.000000 S( 14, 5) 1.000000 0.000000 S( 14, 6) 1.000000 0.000000 S( 14, 7) 5.000000 0.000000 S( 15, 1) 5.000000 0.000000 S( 15, 2) 1.000000 0.000000 S( 15, 3) 1.000000 0.000000 S( 15, 4) 1.000000 0.000000 S( 15, 5) 1.000000 0.000000 S( 15, 6) 1.000000 0.000000 S( 15, 7) 5.000000 0.000000 S( 16, 1) 3.000000 0.000000 S( 16, 2) 0.000000 0.000000 S( 16, 3) 0.000000 0.000000 S( 16, 4) 1.000000 0.000000 S( 16, 5) 0.000000 0.000000 S( 16, 6) 0.000000 0.000000 S( 16, 7) 3.000000 0.000000 S( 17, 1) 3.000000 0.000000 S( 17, 2) 0.000000 0.000000 S( 17, 3) 0.000000 0.000000 S( 17, 4) 1.000000 0.000000 S( 17, 5) 0.000000 0.000000 S( 17, 6) 0.000000 0.000000 S( 17, 7) 3.000000 0.000000 S( 18, 1) 3.000000 0.000000 S( 18, 2) 0.000000 0.000000 S( 18, 3) 0.000000 0.000000 S( 18, 4) 1.000000 0.000000 S( 18, 5) 0.000000 0.000000 S( 18, 6) 0.000000 0.000000 S( 18, 7) 3.000000 0.000000 D( 1, 1) 0.000000 10.00000 D( 1, 2) 0.000000 1.000000 D( 1, 3) 0.000000 1.000000 D( 1, 4) 0.000000 1.000000 D( 1, 5) 0.000000 1.000000 D( 1, 6) 0.000000 1.000000 D( 1, 7) 0.000000 1.000000 D( 2, 1) 0.000000 0.000000 D( 2, 2) 0.000000 9.000000 D( 2, 3) 0.000000 9.000000 D( 2, 4) 0.000000 5.000000 D( 2, 5) 0.000000 5.000000 D( 2, 6) 0.000000 5.000000 D( 2, 7) 0.000000 2.000000 D( 3, 1) 11.00000 0.000000 D( 3, 2) 0.000000 4.000000 D( 3, 3) 0.000000 4.000000 D( 3, 4) 0.000000 0.000000 D( 3, 5) 0.000000 3.000000 D( 3, 6) 0.000000 3.000000 D( 3, 7) 0.000000 3.000000 D( 4, 1) 22.00000 0.000000 D( 4, 2) 0.000000 4.000000 D( 4, 3) 0.000000 4.000000 D( 4, 4) 0.000000 4.000000 D( 4, 5) 0.000000 4.000000 D( 4, 6) 0.000000 4.000000 D( 4, 7) 0.000000 1.000000 D( 5, 1) 22.00000 0.000000 D( 5, 2) 0.000000 0.000000 D( 5, 3) 0.000000 0.000000 D( 5, 4) 0.000000 0.000000 D( 5, 5) 0.000000 0.000000 D( 5, 6) 0.000000 0.000000 D( 5, 7) 0.000000 2.000000 D( 6, 1) 33.00000 0.000000 D( 6, 2) 0.000000 0.000000 D( 6, 3) 0.000000 0.000000 D( 6, 4) 0.000000 0.000000 D( 6, 5) 0.000000 1.000000 D( 6, 6) 0.000000 1.000000 D( 6, 7) 0.000000 1.000000 D( 7, 1) 13.00000 0.000000 D( 7, 2) 0.000000 0.000000 D( 7, 3) 0.000000 0.000000 D( 7, 4) 11.00000 0.000000 D( 7, 5) 0.000000 0.000000 D( 7, 6) 0.000000 0.000000 D( 7, 7) 2.000000 0.000000
D( 8, 1) 24.00000 0.000000 D( 8, 2) 0.000000 0.000000 D( 8, 3) 0.000000 0.000000 D( 8, 4) 11.00000 0.000000 D( 8, 5) 0.000000 0.000000 D( 8, 6) 0.000000 0.000000 D( 8, 7) 2.000000 0.000000 D( 9, 1) 24.00000 0.000000 D( 9, 2) 0.000000 0.000000 D( 9, 3) 0.000000 0.000000 D( 9, 4) 11.00000 0.000000 D( 9, 5) 0.000000 0.000000 D( 9, 6) 0.000000 0.000000 D( 9, 7) 2.000000 0.000000 D( 10, 1) 35.00000 0.000000 D( 10, 2) 0.000000 0.000000 D( 10, 3) 0.000000 0.000000 D( 10, 4) 11.00000 0.000000 D( 10, 5) 0.000000 0.000000 D( 10, 6) 0.000000 0.000000 D( 10, 7) 2.000000 0.000000 D( 11, 1) 0.000000 8.000000 D( 11, 2) 0.000000 8.000000 D( 11, 3) 0.000000 8.000000 D( 11, 4) 0.000000 2.000000 D( 11, 5) 0.000000 2.000000 D( 11, 6) 0.000000 2.000000 D( 11, 7) 0.000000 2.000000 D( 12, 1) 11.00000 0.000000 D( 12, 2) 0.000000 6.000000 D( 12, 3) 0.000000 6.000000 D( 12, 4) 0.000000 1.000000 D( 12, 5) 0.000000 1.000000 D( 12, 6) 0.000000 1.000000 D( 12, 7) 0.000000 1.000000 D( 13, 1) 11.00000 0.000000 D( 13, 2) 0.000000 0.000000 D( 13, 3) 0.000000 0.000000 D( 13, 4) 0.000000 5.000000 D( 13, 5) 0.000000 5.000000 D( 13, 6) 0.000000 5.000000 D( 13, 7) 0.000000 2.000000 D( 14, 1) 22.00000 0.000000 D( 14, 2) 0.000000 0.000000 D( 14, 3) 0.000000 0.000000 D( 14, 4) 0.000000 0.000000 D( 14, 5) 0.000000 3.000000 D( 14, 6) 0.000000 3.000000 D( 14, 7) 0.000000 2.000000 D( 15, 1) 33.00000 0.000000 D( 15, 2) 0.000000 0.000000 D( 15, 3) 0.000000 0.000000 D( 15, 4) 0.000000 0.000000 D( 15, 5) 0.000000 1.000000 D( 15, 6) 0.000000 1.000000 D( 15, 7) 0.000000 1.000000 D( 16, 1) 13.00000 0.000000 D( 16, 2) 0.000000 0.000000 D( 16, 3) 0.000000 0.000000 D( 16, 4) 11.00000 0.000000 D( 16, 5) 0.000000 0.000000 D( 16, 6) 0.000000 0.000000 D( 16, 7) 2.000000 0.000000 D( 17, 1) 24.00000 0.000000 D( 17, 2) 0.000000 0.000000 D( 17, 3) 0.000000 0.000000 D( 17, 4) 11.00000 0.000000 D( 17, 5) 0.000000 0.000000 D( 17, 6) 0.000000 0.000000 D( 17, 7) 2.000000 0.000000 D( 18, 1) 35.00000 0.000000 D( 18, 2) 0.000000 0.000000 D( 18, 3) 0.000000 0.000000 D( 18, 4) 11.00000 0.000000 D( 18, 5) 0.000000 0.000000 D( 18, 6) 0.000000 0.000000 D( 18, 7) 2.000000 0.000000 A( 1, 1, 1) 0.000000 0.000000 . . . A( 18, 18, 6) 0.000000 0.000000 B( 1, 1, 1) 0.000000 0.000000 . . . B( 18, 18, 6) 0.000000 0.000000
Lampiran 4
Hasil Simulasi Penjadwalan MRT dengan Nilai Delay MRT Ekspres Dibatasi
Gambar 12 Diagram ruang waktu dari simulasi penjadwalan MRT dari Lebak Bulus ke
Sisingamangaraja dengan waktu delay MRT Ekspres menjadi 6 menit.
1. MRT Ekonomi* 2. MRT Ekonomi* 3. MRT Ekonomi* 4. MRT Ekonomi* 5. MRT Ekonomi* 6. MRT Ekonomi* 7. MRT Ekspres* 8. MRT Ekspres* 9. MRT Ekspres* 10. MRT Ekspres* 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
LB(a) LB(d) FA(a) FA(d) CR(a) CR(d) HN(a) HN(d) BA(a) BA(d) BM(a) BM(d) SI(a) SI(d)
Lebak Bulus Fatmawati Cipete Raya Haji Nawi Blok A Blok M Sisingamangaraja
W ak tu (m eni t)
Gambar 13 Diagram ruang waktu dari simulasi penjadwalan MRT dari Sisingamangaraja ke Lebak
Bulus dengan waktu delay MRT Ekspres menjadi 6 menit.
11. MRT Ekonomi* 12. MRT Ekonomi* 13. MRT Ekonomi* 14. MRT Ekonomi* 15. MRT Ekonomi* 16. MRT Ekspres* 17. MRT Ekspres* 18. MRT Ekspres* 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160
SI(a) SI(d) BM(a) BM(d) BA(a) BA(d) HN(a) HN(d) CR(a) CR(d) FA(a) FA(d) LB(a) LB(d)
Sisingamangaraja Blok M Blok A Haji Nawi Cipete Raya Fatmawati Lebak Bulus
W ak tu (m eni t)