Нахождение оптимальных планов производства продукции и их экономико-математический анализ [Отчет по лабораторной работе]
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1
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: CON-954 f/f
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..
1998
I. .
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1.2 :
- ;
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- ,
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1.3
9
. 1.3.1 .
,
(14,5+0,1N) ,
(1750+N) , (110+N) , (45+0,1N)
, (660+0,1N) (18+0,1N) .
: (, )
5-20%, ( , , )
15-35%, 35-60%, ( )
10-20%.
. N =8.
1.3.1 1
.
-
, 1,34 1,9 0,37 0,49 0,52 0,2 0,26 0,12 0,9
, 78 356 14 116 65 19 12 9 112
, 0,7 5,9 6,2 17,7 5,7 1,5 0,5 0,4 15
, 3,1 9,1 1 2,2 2,3 0,5 0,4 13 ---
, 4 2 5 45 15 15 --- --- ---
0,87 0,87 0,8 0,85 0,85 0,26 0,24 0,12 0,87
,
/ 0,43+
0,01N 0,65-
0,01N 0,05+
0,01N 0,25+
0,01N 0,3+
0,01N 0,8-
0,01N 0,15+
0,01N 0,14+
0,01N 0,75-
0,01N
2. LINDO
1. -
. xj(j=1,8)
. , ..
,
/, .
,
.
:
:
min Z = 0.51x1+0.57x2+0.13x3+0.33x4+0.38x5+0.72x6+0.23x7+0.22x8+0.67x9
:
1.34x1+ 1.9x2+0.37x3+0.49x4+0.52x5+ 0.2x6+0.26x7+0.12x8+ 0.9x9 >=15.3
78x1+ 356x2+ 14x3+ 116x4+ 65x5+ 19x6+ 12x7+ 9x8+ 112x9
>=1758
0.7x1+ 5.9x2+ 6.2x3+17.7x4+ 5.7x5+ 1.5x6+ 0.5x7+ 0.4x8+ 15x9
>=118
3.1x1+ 9.1x2+ x3+ 2.2x4+ 2.3x5+ 0.5x6+ 0.4x7+ 13x8
>=45.8
4x1+ 2x2+ 5x3+ 45x4+ 15x5+ 15x6
>=660.8
0.87x1+0.87x2+ 0.8x3+0.85x4+0.85x5+0.26x6+0.24x7+0.12x8+0.87x9 >=18.8
x1+ x2+
x9 >=5
x1+ x2+
x9 <=20
x3+ x4+ x5
>=15
x3+ x4+ x5
<=35
x6
>=35
x6
<=60
x7+ x8 >=10
x7+ x8 <=20
Xj >= 0
- ,
xj.
:
:
max F = 15.3y1+1758y2+118y3+45.8y4+660.8y5+18.8y6+5y7-20y8+15y9-35y10+
35y11-60y12+10y13-20y14
:
1.34y1+ 78y2+ 0.7y3+3.1y4+ 4y5+0.87y6+y7-y8
<=0.51
1.9y1+ 356y2+ 5.9y3+9.1y4+ 2y5+0.87y6+y7-y8
<=0.57
0.37y1+ 14y2 +6.2y3+ y4+ 5y5+ 0.8y6+ y9-y10
<=0.13
0.49y1+ 116y2+17.7y3+2.2y4+45y5+0.85y6+ y9-y10
<=0.33
0.52y1+ 65y2+ 5.7y3+2.3y4+15y5+0.85y6+ y9-y10
<=0.38
0.2y1+ 19y2+ 1.5y3+0.5y4+15y5+0.26y6+ y11-y12
<=0.72
0.26y1+ 12y2+ 0.5y3+0.4y4+ 0.24y6+
y13-y14 <=0.23
0.12y1+ 9y2+ 0.4y3+ 13y4+ 0.12y6+
y13-y14 <=0.22
0.9y1+112y2+ 15y3+ 0.87y6+y7-y8
<=0.67
.
,
.
3. LINDO.
: \LINDO.
lindo.exe.
F.
(:) max
. ST .
END.
LOOK ALL,
- LOOK < N >.
ALT < N >
(VAR), (RHS),
max min .
GO,
(?) Y.
GO
:
OBJECTIVE FUNCTION VALUE
32, 1779200
VARIABLE VALUE REDUCED COST
x1 3.943977 0
x2 1.056023 0
x3 13.927200 0
x4 1.072801 0
x5 0 0.193695
x6 35 0
x7 0 0.009258
x8 10 0
x9 0 0.169071
(N2)
ROW SLACK OF SURPLUS DUAL PRICES
2 5.870109 0
3 0 0.000247
4 52.828530 0
5 139.823500 0
6 0 0.004369
7 7.903641 0
8 0 0.473236
9 15 0
10 0 0.104691
11 20 0
12 0 0.649760
13 25 0
14 0 0.217775
15 10 0
N. ITERATIONS = 12
4. ,
,
32, 18 . :
min Z = 0.51*3,943977+0.57*1,056023+0.13*13,9272+0.33*1,072801+
+0.72*35+0.22*10=32,17792
:
= (3,943977; 1,056023; 13,927200; 1,072801; 0; 35; 0; 10; 0)
:
3,943977
1,056023
13,9272
1,072801
35
10
( , )
.
5. :
Y=(0; 0.000247; 0; 0; 0,004369; 0; 0,473236; 0; 0,104691; 0; 0,64976; 0;
0,217775; 0)
:
max F = 1758*0,000247+660.8*0,004369+5*0,473236+15*0,104691+
35*0,64976+10*0,217775=32,17792
,
:
Z(X)=F(Y)=32,17792
6. ,
Y
78*0.000247 +4*0.004369+1*0.473236 =0.5099 <=0.51
356*0.000247+2*0.004369+1*0.473236 =0.5699 <=0.57
14*0.000247 +5*0.004369+1*0.104691 =0.12999<=0.13
116*0.000247+45*0.004369+1*0.104691 =0.3299 <=0.33
65*0.000247 +15*0.004369+1*0.104691 =0.18628<=0.38
19*0.000247 +15*0.004369+1*0.64976 =0.71998<=0.72
12*0.000247 +1*0.217775 =0.2207 <=0.23
9*0.000247 +1*0.217775 =0.21999<=0.22
112*0.000247+1*0.473236 =0.5009 <=0.67
, ,
, .
7.
, . RANGE
YES. :
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES N3
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
x1 0.51 0.07 0.381798
x2 0.57 0.485098 0.07
x3 0.13 0.177986 0.093040
x4 0.33 0.761069 0.177986
x5 0.38 INFINITY 0.193695
x6 0.72 INFINITY 0.649760
x7 0.23 INFINITY 0.009258
x8 0.22 0.009258 0.217775
x9 0.67 INFINITY 0.169071
Cj Xj
:
0,128202 < C1 < 0,58
0,5 < C2 < 1,055098
0,03696 < C3 < 0,307986
0,152014 < C4 < 1,091069
0,186305 < C5 < INFINITY
0,07024 < C6 < INFINITY
0,220742 < C7 < INFINITY
0,002225 < C8 < 0,229258
0,500929 < C9 < INFINITY
, .
, .
N4
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 15.3 5.870109 INFINITY
3 1758 1116.54 298.960100
4 118 52.828530 INFINITY
5 45.8 139.823500 INFINITY
6 660.8 117.2392 43.69926
7 18.8 7.903641 INFINITY
8 5 4.409440 3.181932
9 20 INFINITY 15
10 15 8.567274 9.957481
11 35 INFINITY 20
12 35?????????????????????????????????????
:
.. , ..
" " ( ), ,
1995.