数学模型：平板车结果

先看看一般的线性规划,即变量看作为实数.结果为
LP OPTIMUM FOUND AT STEP 6
OBJECTIVE FUNCTION VALUE
1) 2040.000
VARIABLE VALUE REDUCED COST
X11 0.000000 -0.000001
X21 8.000000 0.000000
X12 7.000000 0.000000
X22 0.000000 0.000000
X13 9.000000 0.000000
X23 0.000000 0.000001
X14 1.448611 0.000000
X24 4.551389 0.000000
X15 0.000000 0.000000
X25 0.000000 0.000000
X16 0.000000 0.000000
X26 0.000000 0.000000
X17 0.000000 0.000000
X27 4.729688 0.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 48.700001
3) 0.000000 52.000000
4) 0.000000 61.299999
5) 0.000000 72.000000
6) 6.000000 0.000000
7) 4.000000 0.000000
8) 3.270313 0.000000
9) 0.000000 0.000000
10) 0.000000 0.000000
11) 9.275695 0.000000
12) 16.994617 0.000000
13) 0.000000 1.000000
NO,ITERATIONS= 6
RANGES IN WHICH THE BASIS IS UNCHANGED,
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X11 48.700001 0.000000 INFINITY
X21 48.700001 INFINITY 0.000000
X12 52.000000 INFINITY 0.000000
X22 52.000000 0.000000 INFINITY
X13 61.299999 INFINITY 0.000000
X23 61.299999 0.000000 INFINITY
X14 72.000000 0.000000 0.000000
X24 72.000000 0.000000 0.000000
X15 48.700001 0.000000 INFINITY
X25 48.700001 0.000000 INFINITY
X16 52.000000 0.000000 INFINITY
X26 52.000000 0.000000 INFINITY
X17 64.000000 0.000000 INFINITY
X27 64.000000 INFINITY 0.000000
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 8.000000 0.000000 2.141684
3 7.000000 0.000000 7.000000
4 9.000000 0.000000 9.000000
5 6.000000 0.000000 1.448611
6 6.000000 INFINITY 6.000000
7 4.000000 INFINITY 4.000000
8 8.000000 INFINITY 3.270313
9 1020.000000 INFINITY 0.000000
10 1020.000000 104.300003 0.000000
11 40.000000 INFINITY 9.275695
12 40.000000 INFINITY 16.994617
13 302.700012 0.000000 104.300003
基于分析,删掉第七组变量后,修改后运行时间10秒
max
48.7x11+48.7x21+52x12+52x22+61.3x13+61.3x23+72x14+72x24+48.7x15+48.7x25+52x16+52
x26
st
x11+x21<8
x12+x22<7
x13+x23<9
x14+x24<6
x15+x25<6
x16+x26<4
48.7 x11+52 x12+61.3 x13+72 x14+48.7 x15+52 x16<1020
48.7 x21+52 x22+61.3 x23+72 x24+48.7 x25+52 x26<1020
2 x11+3 x12+ x13+0.5 x14+4 x15+2 x16<40
2 x21+3 x22+ x23+0.5 x24+4 x25+2 x26<40
48.7x15+48.7x25+52x16+52x26<302.7
end
gin 12
运行结果为
OBJECTIVE FUNCTION VALUE
1) 2039.400
VARIABLE VALUE REDUCED COST
X11 4.000000 -48.700001
X21 4.000000 -48.700001
X12 7.000000 -52.000000
X22 0.000000 -52.000000
X13 4.000000 -61.299999
X23 5.000000 -61.299999
X14 3.000000 -72.000000
X24 3.000000 -72.000000
X15 0.000000 -48.700001
X25 3.000000 -48.700001
X16 0.000000 -52.000000
X26 3.000000 -52.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 0.000000
3) 0.000000 0.000000
4) 0.000000 0.000000
5) 0.000000 0.000000
6) 3.000000 0.000000
7) 1.000000 0.000000
8) 0.000000 0.000000
9) 0.599998 0.000000
10) 5.500000 0.000000
11) 7.500000 0.000000
12) 0.599998 0.000000
NO,ITERATIONS= 17314
BRANCHES= 4471 DETERM.= 1.000E 0
第二次运行,时间为7秒,结果为
OBJECTIVE FUNCTION VALUE
1) 2039.400
VARIABLE VALUE REDUCED COST
X11 4.000000 -48.700001
X21 4.000000 -48.700001
X12 7.000000 -52.000000
X22 0.000000 -52.000000
X13 4.000000 -61.299999
X23 5.000000 -61.299999
X14 3.000000 -72.000000
X24 3.000000 -72.000000
X15 0.000000 -48.700001
X25 3.000000 -48.700001
X16 0.000000 -52.000000
X26 3.000000 -52.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 0.000000
3) 0.000000 0.000000
4) 0.000000 0.000000
5) 0.000000 0.000000
6) 3.000000 0.000000
7) 1.000000 0.000000
8) 0.000000 0.000000
9) 0.599998 0.000000
10) 5.500000 0.000000
11) 7.500000 0.000000
12) 0.599998 0.000000
NO,ITERATIONS= 34517
BRANCHES= 8905 DETERM.= 1.000E 0
再改进,令x13<4
第一次运行,时间为11秒,结果为
OBJECTIVE FUNCTION VALUE
1) 2039.400
VARIABLE VALUE REDUCED COST
X11 4.000000 -48.700001
X21 4.000000 -48.700001
X12 4.000000 -52.000000
X22 3.000000 -52.000000
X13 4.000000 -61.299999
X23 5.000000 -61.299999
X14 3.000000 -72.000000
X24 3.000000 -72.000000
X15 0.000000 -48.700001
X25 3.000000 -48.700001
X16 3.000000 -52.000000
X26 0.000000 -52.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 0.000000
3) 0.000000 0.000000
4) 0.000000 0.000000
5) 0.000000 0.000000
6) 3.000000 0.000000
7) 1.000000 0.000000
8) 0.000000 0.000000
9) 0.599998 0.000000
10) 8.500000 0.000000
11) 4.500000 0.000000
12) 0.599998 0.000000
13) 0.000000 0.000000
NO,ITERATIONS= 19624
BRANCHES= 4700 DETERM.= 1.000E 0
第二次运行,时间为7秒,结果为
OBJECTIVE FUNCTION VALUE
1) 2039.400
VARIABLE VALUE REDUCED COST
X11 4.000000 -48.700001
X21 4.000000 -48.700001
X12 5.000000 -52.000000
X22 2.000000 -52.000000
X13 4.000000 -61.299999
X23 5.000000 -61.299999
X14 3.000000 -72.000000
X24 3.000000 -72.000000
X15 0.000000 -48.700001
X25 3.000000 -48.700001
X16 2.000000 -52.000000
X26 1.000000 -52.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 0.000000
3) 0.000000 0.000000
4) 0.000000 0.000000
5) 0.000000 0.000000
6) 3.000000 0.000000
7) 1.000000 0.000000
8) 0.000000 0.000000
9) 0.599998 0.000000
10) 7.500000 0.000000
11) 5.500000 0.000000
12) 0.599998 0.000000
13) 0.000000 0.000000
第三次运行,时间为6秒,结果为
OBJECTIVE FUNCTION VALUE
1) 2039.400
VARIABLE VALUE REDUCED COST
X11 8.000000 -48.700001
X21 0.000000 -48.700001
X12 1.000000 -52.000000
X22 6.000000 -52.000000
X13 0.000000 -61.299999
X23 9.000000 -61.299999
X14 6.000000 -72.000000
X24 0.000000 -72.000000
X15 3.000000 -48.700001
X25 0.000000 -48.700001
X16 0.000000 -52.000000
X26 3.000000 -52.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 0.000000
3) 0.000000 0.000000
4) 0.000000 0.000000
5) 0.000000 0.000000
6) 3.000000 0.000000
7) 1.000000 0.000000
8) 0.299992 0.000000
9) 0.300007 0.000000
10) 6.000000 0.000000
11) 7.000000 0.000000
12) 0.599998 0.000000
13) 4.000000 0.000000
NO,ITERATIONS= 50704
BRANCHES=11942 DETERM.= 1.000E 0
第四次运行,时间为7秒,结果为
OBJECTIVE FUNCTION VALUE
1) 2039.400
VARIABLE VALUE REDUCED COST
X11 4.000000 -48.700001
X21 4.000000 -48.700001
X12 5.000000 -52.000000
X22 2.000000 -52.000000
X13 4.000000 -61.299999
X23 5.000000 -61.299999
X14 3.000000 -72.000000
X24 3.000000 -72.000000
X15 0.000000 -48.700001
X25 3.000000 -48.700001
X16 2.000000 -52.000000
X26 1.000000 -52.000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 0.000000 0.000000
3) 0.000000 0.000000
4) 0.000000 0.000000
5) 0.000000 0.000000
6) 3.000000 0.000000
7) 1.000000 0.000000
8) 0.000000 0.000000
9) 0.599998 0.000000
10) 7.500000 0.000000
11) 5.500000 0.000000
12) 0.599998 0.000000
13) 0.000000 0.000000
NO,ITERATIONS= 67795
BRANCHES=15943 DETERM.= 1.000E 0