PROBLEMA ORIGINAL Maximizar el número de cajones que caben

PROBLEMA ORIGINAL
Maximizar el número de cajones que caben dentro de un estante de 90cm de alto.
Las alturas de los cajones son 7.5cm, 10cm, 15cm, 20cm y 30cm.
Si tenemos disponibles solamente 4 estantes, cual es el máximo numero de cajones a ocupar si
tenemos solamente 8 cajones de 7.5cm, 13 cajones de 10cm, 24 cajones de 15cm, 13 cajones de
20cm y 3 cajones de 30cm.
La suma de las alturas de los cajones no debe sobrepasar los 90cm, pues no habría espacio
disponible para los cajones y tampoco puede ser menor a 90cm pues habría un desperdicio de
espacio.
max
x11+x12+x13+x14+x21+x22+x23+x24+x31+x32+x33+x34+x41+x42+x43+x44+x51+x52+x53+x
54
subject to
x11+x12+x13+x14<=8
x21+x22+x23+x24<=13
x31+x32+x33+x34<=24
x41+x42+x43+x44<=13
x51+x52+x53+x54<=3
7.5x11+10x21+15x31+20x41+30x51<=90
7.5x12+10x22+15x32+20x42+30x52<=90
7.5x13+10x23+15x33+20x43+30x53<=90
7.5x14+10x24+15x34+20x44+30x54<=90
end
GIN 20
CORRIDA EN PROGRAMA LINDO
LP OPTIMUM FOUND AT STEP
9
OBJECTIVE VALUE = 32.3333321
SET
SET
SET
SET
X31 TO <=
X12 TO <=
X34 TO >=
X32 TO >=
0 AT
1 AT
6 AT
6 AT
1, BND=
2, BND=
3, BND=
4, BND=
32.33
32.33
32.33
32.00
NEW INTEGER SOLUTION OF 32.0000000
BOUND ON OPTIMUM: 32.33333
DELETE
X32 AT LEVEL 4
DELETE
X34 AT LEVEL 3
DELETE
X12 AT LEVEL 2
DELETE
X31 AT LEVEL 1
ENUMERATION COMPLETE. BRANCHES=
TWIN=
TWIN=
TWIN=
TWIN=
AT BRANCH
4 PIVOTS=
LAST INTEGER SOLUTION IS THE BEST FOUND
RE-INSTALLING BEST SOLUTION...
OBJECTIVE FUNCTION VALUE
1)
32.00000
32.33
32.33
32.33
32.33
12
15
19
25
4 PIVOT
25
25
VARIABLE
VALUE
X11
8.000000
X12
0.000000
X13
0.000000
X14
0.000000
X21
3.000000
X22
0.000000
X23
9.000000
X24
0.000000
X31
0.000000
X32
6.000000
X33
0.000000
X34
6.000000
X41
0.000000
X42
0.000000
X43
0.000000
X44
0.000000
X51
0.000000
X52
0.000000
X53
0.000000
X54
0.000000
REDUCED COST
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
ROW SLACK OR SURPLUS DUAL PRICES
2)
0.000000
0.000000
3)
1.000000
0.000000
4)
12.000000
0.000000
5)
13.000000
0.000000
6)
3.000000
0.000000
7)
0.000000
0.000000
8)
0.000000
0.000000
9)
0.000000
0.000000
10)
0.000000
0.000000
NO. ITERATIONS=
25
BRANCHES= 4 DETERM.= 1.000E
0
ACOMODO DE CAJONERAS
max
x11+x12+x13+x14+x21+x22+x23+x24+x31+x32+x33+x34+x41+x42+x43+x44+x51+x52+x53+x
54
subject to
x11+x12+x13+x14<=8
x21+x22+x23+x24<=13
x31+x32+x33+x34<=24
x41+x42+x43+x44<=13
x51+x52+x53+x54<=3
7.5x11+10x21+15x31+20x41+30x51<=90
7.5x12+10x22+15x32+20x42+30x52<=90
7.5x13+10x23+15x33+20x43+30x53<=90
7.5x14+10x24+15x34+20x44+30x54<=90
x11-x12=0
x12-x13=0
x13-x14=0
x21-x22=0
x22-x23=0
x23-x24=0
x31-x32=0
x32-x33=0
x33-x34=0
x41-x42=0
x42-x43=0
x43-x44=0
x51-x52=0
x52-x53=0
x53-x54=0
end
GIN 20
CORRIDA EN PROGRAMA LINDO
LP OPTIMUM FOUND AT STEP
7
OBJECTIVE VALUE = 32.3333321
FIX ALL VARS.( 1) WITH RC > 4.00000
SET
X24 TO <= 3 AT 1, BND= 32.00
NEW INTEGER SOLUTION OF 32.0000000
BOUND ON OPTIMUM: 32.00000
DELETE
X24 AT LEVEL 1
ENUMERATION COMPLETE. BRANCHES=
TWIN=-0.1000E+31
AT BRANCH
1 PIVOTS=
LAST INTEGER SOLUTION IS THE BEST FOUND
RE-INSTALLING BEST SOLUTION...
OBJECTIVE FUNCTION VALUE
1)
32.00000
VARIABLE
VALUE
X11
2.000000
X12
2.000000
X13
2.000000
X14
2.000000
X21
3.000000
X22
3.000000
X23
3.000000
X24
3.000000
X31
3.000000
X32
3.000000
X33
3.000000
REDUCED COST
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
10
1 PIVOT
10
10
X34
X41
X42
X43
X44
X51
X52
X53
X54
ROW
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
3.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
SLACK OR SURPLUS DUAL PRICES
0.000000
0.000000
1.000000
0.000000
12.000000
0.000000
13.000000
0.000000
3.000000
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
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
0.000000
0.000000
0.000000
0.000000
NO. ITERATIONS=
10
BRANCHES= 1 DETERM.= 1.000E
0
ACOMODO DE RESTO DE CAJONERAS
max
x11+x12+x13+x14+x15+x16+x21+x22+x23+x24+x25+x26+x31+x32+x33+x34+x35+x36+x41+x
42+x43+x44+x45+x46
subject to
x11+x12+x13+x14+x15+x16<=1
x21+x22+x23+x24+x25+x26<=12
x31+x32+x33+x34+x35+x36<=13
x41+x42+x43+x44+x45+x46<=3
10x11+15x21+20x31+30x41<=90
10x12+15x22+20x32+30x42<=90
10x13+15x23+20x33+30x43<=90
10x14+15x24+20x34+30x44<=90
10x15+15x25+20x35+30x45<=90
10x16+15x26+20x36+30x46<=90
end
GIN 24
CORRIDA EN PROGRAMA LINDO
LP OPTIMUM FOUND AT STEP 12
OBJECTIVE VALUE = 29.0000000
SET
SET
SET
SET
SET
SET
SET
X25 TO <=
X35 TO <=
X32 TO <=
X36 TO <=
X35 TO >=
X46 TO >=
X25 TO <=
2 AT
1 AT
1 AT
4 AT
1 AT
1 AT
0 AT
1, BND=
2, BND=
3, BND=
4, BND=
5, BND=
6, BND=
7, BND=
29.00
29.00
29.00
29.00
29.00
29.00
29.00
NEW INTEGER SOLUTION OF 29.0000000
BOUND ON OPTIMUM: 29.00000
DELETE
X25 AT LEVEL 7
DELETE
X46 AT LEVEL 6
DELETE
X35 AT LEVEL 5
DELETE
X36 AT LEVEL 4
DELETE
X32 AT LEVEL 3
DELETE
X35 AT LEVEL 2
DELETE
X25 AT LEVEL 1
ENUMERATION COMPLETE. BRANCHES=
TWIN= 29.00
34
TWIN= 29.00
37
TWIN= 29.00
39
TWIN=-0.1000E+31 39
TWIN= 29.00
48
TWIN= 29.00
52
TWIN= 29.00
56
AT BRANCH
6 PIVOTS=
LAST INTEGER SOLUTION IS THE BEST FOUND
RE-INSTALLING BEST SOLUTION...
OBJECTIVE FUNCTION VALUE
1)
29.00000
VARIABLE
VALUE
X11
0.000000
X12
0.000000
X13
0.000000
X14
0.000000
X15
1.000000
X16
0.000000
X21
2.000000
X22
6.000000
X23
2.000000
X24
2.000000
REDUCED COST
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
6 PIVOT
56
56
X25
X26
X31
X32
X33
X34
X35
X36
X41
X42
X43
X44
X45
X46
ROW
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
0.000000
0.000000
3.000000
0.000000
3.000000
3.000000
1.000000
3.000000
0.000000
0.000000
0.000000
0.000000
2.000000
1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
-1.000000
SLACK OR SURPLUS DUAL PRICES
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
0.000000
0.000000
NO. ITERATIONS=
56
BRANCHES= 6 DETERM.= 1.000E
0