BAB III Transportasi - BAB II. Pengenalan Program Linear

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83

5
B

B

B
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1
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X ijcij

X ij = per min taan D j
$

X ij = kapasitas O i

! &'8&& ; (8&' ;) 8&/ ; *8&( ; )8&* ; ,8'& ; &8'' ; -8'/ ; -8'(
; .8'* ; &8/& ; &'8/' ; (8// ; .8/( ; .8/* ; &+8(& ; &* 8(' ; -8(/ ; )8(( ; &8(*
8&& ; 8'& ; 8/& ; 8(& 9 ,+
8&' ; 8'' ; 8/' ; 8(' 9 *+
8&/ ; 8'/ ; 8// ; 8(/ 9 )+

84

8&( ; 8'( ; 8/( ; 8(( 9 -+
8&* ; 8'* ; 8/* ; 8(* 9 .+
8&& ; 8&' ; 8&/ ; 8&( ; 8&* 9&++
8'& ; 8'' ; 8'/ ; 8'( ; 8'* 9 )+
8/& ; 8/' ; 8// ; 8/( ; 8/* 9.+
8(& ; 8(' ; 8(/ ; 8(( ; 8(* 9 )+
8 ≥+
B
MIN

12X11+4X12+9X13+5X14+9X15+8X21+1X22+6X23+6X24+7X25
+1X31+12X32+4X33+7X34+7X35+10X41+15X42+6X43+9X44+1X45

SUBJECT TO
X11+X12+X13+X14+X15=100
X21+X22+X23+X24+X25=90
X31+X32+X33+X34+X35=70
X41+X42+X43+X44+X45=90
X11+X21+X31+X41=80
X12+X22+X32+X42=50
X13+X23+X33+X43=90
X14+X24+X34+X44=60
X15+X25+X35+X45=7
END

B
LP OPTIMUM FOUND AT STEP

8

OBJECTIVE FUNCTION VALUE
1)
VARIABLE
X11
X12
X13
X14
X15
X21
X22
X23
X24
X25

1230.000
VALUE
0.000000
40.000000
0.000000
60.000000
0.000000
10.000000
10.000000
70.000000
0.000000
0.000000

REDUCED COST
1.000000
0.000000
0.000000
0.000000
5.000000
0.000000
0.000000
0.000000
4.000000
6.000000

85

X31
X32
X33
X34
X35
X41
X42
X43
X44
X45

ROW
2)
3)
4)
5)
6)
7)
8)
9)
10)

70.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
20.000000
0.000000
70.000000

0.000000
18.000000
5.000000
12.000000
13.000000
2.000000
14.000000
0.000000
7.000000
0.000000

SLACK OR SURPLUS
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000

NO. ITERATIONS=

DUAL PRICES
0.000000
3.000000
10.000000
3.000000
-11.000000
-4.000000
-9.000000
-5.000000
-4.000000

8

RANGES IN WHICH THE BASIS IS UNCHANGED:

VARIABLE
X11
X12
X13
X14
X15
X21
X22
X23
X24
X25
X31
X32
X33
X34
X35
X41
X42
X43
X44
X45

ROW
2

CURRENT
COEF
12.000000
4.000000
9.000000
5.000000
9.000000
8.000000
1.000000
6.000000
6.000000
7.000000
1.000000
12.000000
4.000000
7.000000
7.000000
10.000000
15.000000
6.000000
9.000000
1.000000

CURRENT
RHS
100.000000

OBJ COEFFICIENT RANGES
ALLOWABLE
ALLOWABLE
INCREASE
DECREASE
INFINITY
1.000000
0.000000
4.000000
INFINITY
0.000000
4.000000
INFINITY
INFINITY
5.000000
1.000000
5.000000
4.000000
0.000000
0.000000
2.000000
INFINITY
4.000000
INFINITY
6.000000
5.000000
INFINITY
INFINITY
18.000000
INFINITY
5.000000
INFINITY
12.000000
INFINITY
13.000000
INFINITY
2.000000
INFINITY
14.000000
2.000000
5.000000
INFINITY
7.000000
5.000000
INFINITY
RIGHTHAND SIDE RANGES
ALLOWABLE
INCREASE
0.000000

ALLOWABLE
DECREASE
0.000000

86

3
4
5
6
7
8
9
10

90.000000
70.000000
90.000000
80.000000
50.000000
90.000000
60.000000
70.000000

0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000

0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000

%
& 1

& '/+

OBJECTIVE FUNCTION VALUE
1)

1230.000

2. Alokasi pengiriman barang dapat diketahui dari nilai
value pada hasil berikut.
VARIABLE
X11
X12
X13
X14
X15
X21
X22
X23
X24
X25
X31
X32
X33
X34
X35
X41
X42
X43
X44
X45

VALUE
0.000000
40.000000
0.000000
60.000000
0.000000
10.000000
10.000000
70.000000
0.000000
0.000000
70.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
20.000000
0.000000
70.000000

0& "

#

'"

#

(+

-+

(

0'
/

REDUCED COST
1.000000
0.000000
0.000000
0.000000
5.000000
0.000000
0.000000
0.000000
4.000000
6.000000
0.000000
18.000000
5.000000
12.000000
13.000000
2.000000
14.000000
0.000000
7.000000
0.000000

&

.+

&+

'

&+

87

E

0/

.+

0(

'+

&
/

4

,+

*

E

4

9(

9 (

RANGES IN WHICH THE BASIS IS UNCHANGED:

VARIABLE
X11
X12
X13
X14
X15
X21
X22
X23
X24
X25
X31
X32
X33
X34
X35
X41
X42
X43
X44
X45

&&
+

CURRENT
COEF
12.000000
4.000000
9.000000
5.000000
9.000000
8.000000
1.000000
6.000000
6.000000
7.000000
1.000000
12.000000
4.000000
7.000000
7.000000
10.000000
15.000000
6.000000
9.000000
1.000000

&&

OBJ COEFFICIENT RANGES
ALLOWABLE
ALLOWABLE
INCREASE
DECREASE
INFINITY
1.000000
0.000000
4.000000
INFINITY
0.000000
4.000000
INFINITY
INFINITY
5.000000
1.000000
5.000000
4.000000
0.000000
0.000000
2.000000
INFINITY
4.000000
INFINITY
6.000000
5.000000
INFINITY
INFINITY
18.000000
INFINITY
5.000000
INFINITY
12.000000
INFINITY
13.000000
INFINITY
2.000000
INFINITY
14.000000
2.000000
5.000000
INFINITY
7.000000
5.000000
INFINITY

&'

88

<
ROW

CURRENT
RHS

2
3
4
5
6
7
8
9
10

100.000000
90.000000
70.000000
90.000000
80.000000
50.000000
90.000000
60.000000
70.000000

B

"
B

RIGHTHAND SIDE RANGES
ALLOWABLE
INCREASE

ALLOWABLE
DECREASE

0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000

0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000

#

3

B

"

B

1

B

B

:

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89

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B
Model:
Sets:

ariable
/O1, O2, O3, O4/:Asal;
Permintaan/D1, D2, D3, D4, D5/ :Demand ;
Links(Kapasitas,Permintaan) :Ship, Cost ;
Endsets
Min=@sum(Links:Ship*Cost);
@for(Permintaan(j) :@sum(Kapasitas(i) :Ship(i,j))>Demand(j)) ;
@for(Kapasitas(i) :@sum(Permintaan(j) :Ship(i,j)) :
5, Obj=MIN, GUBs H
G&)

1

7
G&.

93

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MAX

20 AX + 26 AY
+ 17 CX + 14
SUBJECT TO
2)
AX +
3)
BX +
4)
CX +
5)
AX +
6)
AY +
7)
AZ +
END

<

B

#

+ 30 AZ + 10 BX + 15 BY + 19 BZ
CY + 12 CZ
AY
BY
CY
BX
BY
BZ

+
+
+
+
+
+

AZ
BZ
CZ
CX
CY
CZ

=
=
=
=
=
=

1
1
1
1
1
1

B

LP OPTIMUM FOUND AT STEP

!
7

OBJECTIVE FUNCTION VALUE
1)
VARIABLE
AX
AY
AZ

62.00000
VALUE
0.000000
0.000000
1.000000

REDUCED COST
9.000000
0.000000
0.000000

112
BX
BY
BZ
CX
CY
CZ

ROW
2)
3)
4)
5)
6)
7)

0.000000
1.000000
0.000000
1.000000
0.000000
0.000000

8.000000
0.000000
0.000000
0.000000
0.000000
6.000000

SLACK OR SURPLUS
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000

LP OPTIMUM FOUND AT STEP

DUAL PRICES
0.000000
-11.000000
-12.000000
29.000000
26.000000
30.000000
3

OBJECTIVE FUNCTION VALUE
1)

62.00000

VARIABLE
BX
BY
BZ
CX
CY
CZ
AX
AY
AZ

ROW
2)
3)
4)
5)
6)
7)

VALUE
0.000000
0.000000
1.000000
1.000000
0.000000
0.000000
0.000000
1.000000
0.000000

SLACK OR SURPLUS
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000

NO. ITERATIONS=

9+

3

REDUCED COST
0.000000
0.000000
0.000000
0.000000
8.000000
14.000000
1.000000
0.000000
0.000000

DUAL PRICES
0.000000
5.000000
9.000000
21.000000
10.000000
17.000000

113

C

114

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