华东交通大学：《数学模型》课程教学资源（学习资料）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 2040.000 VARIABLE VALUE REDUCED COST 0.000000 0.000001 X21 8.000000 0.000000 X12 7.000000 0.000000 0.000000 0.000000 9.000000 0.000000 X23 0.000000 0.000001 14486l1 0.000000 4.551389 0.000000 X15 0.000000 0.000000 X25 0.000000 0.000000 X16 0.000000 0.000000 0.000000 X17 0.000000 0.000000 X27 4.729688 0.000000 ROW SLACK OR SURPLUS DUAL PRICES 0.000000 48.700001 0.000000 52.000000 61.299999 0.000000 72.000000 6.000000 0.000000 67890 4.000000 0.000000 3.270313 0.000000 0.000000 0.000000 0.000000 0.000000 9.275695 0.000000 16994617 0.000000 13) 0.000000 1.000000 NO ITERATIONS RANGES IN WHICH THE BASIS IS UNCHANGED

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 48.700001 INFINITY 0.000000 X12 52.000000 INFINITY 0.000000 52.000000 0.000000 INFINITY X13 INFINITY 0.000000 X23 61299999 0.000000 INFINITY Ⅹ14 72000000 0.000000 0.000000 X24 72.000000 0.000000 0.000000 Ⅹ15 48.700001 0.000000 INFINITY 48.70000 0.000000 INFINITY X16 0.000000 INFINITY 52.000000 0.000000 INFINITY X17 64.000000 0.000000 INFINITY 64.000000 INFINITY 0.000000 RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS NCREASE DECREASE 8.000000 0.000000 2.141684 7.000000 0.000000 7.000000 9.000000 0.000000 9.000000 6.000000 0.000000 1.44861 6.000000 INFINITY 6.000000 4.000000 INFINITY 4.000000 8 8.000000 INFINITY 3.270313 9 1020.000000 INFINITY 0.000000 101020.000000 104.300003 0.000000 40.000000 INFINITY 9.275695 40.000000 INFINITY 16.994617 02700012 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 48.7x11+48.7x21+52x12+52x22+61.3x13+61.3x23+72x14+72x24+48.7x15+48.7x25+52x16+52

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

xII+x21< 8 12+x22<7 x13+x23<9 14+x24<6 x15+x25<6 16+x26<4 48.7xll+52x12+61.3x13+72x14+48.7x15+52x16<1020 48.7x21+52x22+61.3x23+72x24+48.7x25+52x26<1020 2xl+3x12+x13+0.5x14+4x15+2x16<40 2x21+3x22+x23+0.5x24+4x25+2x26<40 48.7x15+48.7X25+52x16+52x26<302.7 gin 12 运行结果为 OBJECTIVE FUNCTION VALUE 2039.400 VARIABLE VALUE REDUCED COST 4.000000 -48.700001 X21 4.000000 -48.700001 X12 7.000000 52000000 0.000000 52000000 X13 4.000000 61.299999 X23 5.000000 -61.299999 3.000000 72.000000 3.000000 72000000 X15 0.000000 -48.700001 X25 3.000000 -48.700001 X16 0.000000 52000000 X26 3.000000 52000000 ROW SLACK OR SURPLUS DUAL PRICES 0.000000 0.000000 0.000000 0.000000

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

0.000000 0.000000 56 0.000000 0.000000 3.000000 0.000000 1000000 0.000000 0.000000 0.000000 0.000000 5.500000 0.000000 7.500000 0.000000 0.599998 0.000000 NO ITERATIONS= 17314 BRANCHES=4471 DETERM.= 1000E 0 第二次运行时间为7秒,结果为 OBJECTIVE FUNCTION VALUE 2039400 VARIABLE VALUE REDUCED COST X11 4.000000 -48.700001 4.000000 -48.700001 X12 -52.000000 X22 0.000000 52000000 X13 4.000000 -61.299999 X23 5.000000 -61.299999 X14 3.000000 72.000000 3.000000 72.000000 x3 0.000000 -48.70000 3.000000 48.700001 X16 0.000000 52000000 3.000000 52.000000 ROW SLACK OR SURPLUS DUAL PRICES 0.000000 0.0000 0.000000 0.000000 3456 0.000000 0.000000 0.000000 0.000000 3.000000 0.000000 1.000000 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 5.500000 0.000000 7500000 0.000000 0.599998 0.000000 NO ITERATIONS= 34517 BRANCHES=8905 DETERM= 1000E 0 再改进令x13<4 第一次运行,时间为11秒,结果为 OBJECTIVE FUNCTION VALUE 2039.400 VARIABLE VALUE REDUCED COST 4.000000 48.700001 4.000000 -48.700001 4.000000 52000000 3.000000 52000000 X13 4.000000 X23 5.000000 61.299999 X14 3.000000 72.000000 X24 3.000000 72000000 X15 0.000000 -48.700001 3.000000 -48.700001 3.000000 5200000 Ⅹ26 0.000000 -52.000000 ROW SLACK OR SURPLUS DUAL PRICES 0.000000 0.000000 0.000000 0.000000 3456789 0.000000 0.000000 0.000000 0.000000 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.599998 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

8.500000 0.000000 11 0.000000 0.000000 0.00000 0.000000 IO. ITERATIONS= 19624 BRANCHES= 4700 DETERM.= 1000E O 第二次运行,时间为7秒,结果为 OBJECTIVE FUNCTION VALUE VARIABLE VALUE REDUCED COST 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 Ⅹ14 3.000000 72.000000 3.000000 72.000000 X15 0.000000 -48.700001 X25 3.000000 -48.700001 X16 2.000000 52000000 X26 1.000000 52.000000 ROW SLACK OR SURPLUS DUAL PRICES 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 3.000000 0.000000 7) 1.000000 0.000000 0.000000 0.000000 0.000000 7.500000 0.000000 11) 5.500000 0.000000 0.000000 0.000000 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 2039400 VARIABLE VALUE REDUCED COST 8.000000 48.700001 X21 0.000000 -48.700001 X12 1.000000 52000000 6.000000 52000000 0.000000 61.299999 X23 9.000000 61.299999 6.000000 72.000000 0.000000 72.000000 X15 3.000000 -48.700001 X25 0.000000 -48.700001 X16 0.000000 -52.000000 X26 3.000000 52000000 ROW SLACK OR SURPLUS DUAL PRICES 0.000000 0.000000 3) 0.000000 0.000000 0.000000 0.000000 456 0.000000 0.000000 3.000000 0.000000 1.000000 )89 0.000000 0.299992 0.000000 0.300007 0.000000 6.000000 0.000000 0.000000 0.599998 0.000000 4.000000 0.000000 NO ITERATIONS= 50704 BRANCHES=11942 DETERM= 1000E 0 第四次运行,时间为7秒,结果为 OBJECTIVE FUNCTION VALUE

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

2039.400 VARIABLE VALUE REDUCED COST 4.000000 -48700001 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 3.000000 -48.700001 2.000000 -52.000000 X26 1.000000 52.000000 ROW SLACK OR SURPLUS DUAL PRICES 0.000000 0.000000 2345678 0.000000 0.000000 0.000000 0.000000 0.000000 3.000000 0.000000 1.000000 0.000000 0.000000 0.000000 9) 0.599998 0.000000 7500000 0.000000 5.500000 0.000000 0.599998 0.000000 0.000000 0.000000 NO ITERATIONS= 67795 BRANCHES=15943 DETERM= 1000E 0

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