运筹学2.docx

1、运筹学2 运筹学 姓名：李思 班级：应数1001 学号：13041008092012年 5 月 9日 案例C.9市场分配 应数1001 李思 学号：1304100809（一）问题的提出某大型公司有 D1 和 D2 两个分公司，该公司向零售商供应油和酒： 公司打算将每位零售商分配给分公司 D1 或分公司 D2，由分公司向零售商供应货物。这种分配应尽可能使分公司 D1 控制 40%销售量， D2 控制其余 60%销售量。零售商的编号 见下面给出的 M1 至 M23。每位零售商有个预计的油和酒的销售量。编号 M1 至 M8 的零售 商在 1 区，编号 M9 至 M18 在 2 区，编号 M19 至

2、M23 的在 3 区。被认为有发展前途的一 些零售商分在 A 组，其余的分在 B 组，每位零售商有如表所示给出的一些供应点，希望将 如下各项按 40/60 的比例分给 D1 和 D21.有销售量的控制 2.零售商的控制 3.供应点的总数4.酒销售量的控制 5.1 区油销售量的控制 6.2 区油销售量的控制7.3 区油销售量的控制 8.A 组零售商总数 9.B 组零售商总数 这里有某些灵活性，任何分配可以变化+5%（包括零售商人数）。简单的说，每种分配可在35/65 至 45/55 之间变动。而目标是保持百分偏差之和为最小。 试建立模型，并确定此问题有无可行解。如有则求出最优解。数据如下表所示，

3、其中销售量 单位是（106）公升 表区位零售商油销量供应点酒销量类型1区M191134AM21347411AM3144482AM41725157BM518105AM61926183AM7232614BM82154215B2区M9918102BM10115121AM11172054BM12181050BM131876BM14171696BM152234118AM1624100112BM173650535BM1843218B3区M1961153BM20151928AM21151469BM22251065BM23391127B（二）模型分析因为目标是保持百分偏差之和为最小，所以在设计模型的时候，考虑

4、到尽可能使分公司 D1 控制 40%销售量， D2 控制其余 60%销售量。可将其列成整数规划模型， 在模型中，23 个零售商中每一位均用一个 01 变量 xi 来代表。若 xi=1，则把零售商 i 分 配 到 分 公 司 D1, 否 则 就 把 他 分 配 到 分 公 司 D2 。 可 在 约 束 条 件 上 引 入 n1,n2,n3,n4,n5,n6,n7,n8,n9 负偏差，p1,p2,p3,p4,p5,p6,p7,p8,p9 正偏差，以提供所需 目标，其中 n1,n2,n3,n4,n5,n6,n7,n8,n9 相当于松弛变量，p1,p2,p3,p4,p5,p6,p7,p8,p9 相当于

5、剩余变量。 n1,n2,n3,n4,n5,n6,n7,n8,n9，p1,p2,p3,p4,p5,p6,p7,p8,p9 的上界为 总量与 5%的乘积目标就是使期望按比值 40/60 使“目标”所造成的绝对偏差之和为 最小。（三） 模型建立目标规划如下min=n1+n2+n3+n4+n5+n6+n7+n8+n9+p1+p2+p3+p4+p5+p6+p7+p8+p9s.t.9x1+13x2+14x3+17x4+18x5+19x6+23x7+21x8+9x9+11x10+17x11+18x12+18x13+17x14+22x15+24x16+36x17+43x18+6x19+15x20+15x21+

6、25x22+39x23+n1p1=179.6x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13+x14+x15+x16+x17+x18+x19+x20+x21+x22+x23+n2p2=9.211x1+47x2+44x3+25x4+10x5+26x6+26x7+54x8+18x9+51x10+20x11+105x12+7x13+16x14+34x15+100x16+50x17+21x18+11x19+19x20+14x21+10x22+11x23+n3p3=29234x1+411x2+82x3+157x4+5x5+183x6+14x7+215x8+102x9+

7、21x10+54x11+0x12+6x13+96x14+118x15+112x16+535x17+8x18+53x19+28x20+69x21+65x22+27x23+n4p4=9589x1+13x2+14x3+17x4+18x5+19x6+23x7+21x8+n5p5=53.69x9+11x10+17x11+18x12+18x13+17x14+22x15+24x16+36x17+43x18+n6p6=866x19+15x20+15x21+25x22+39x23+n7p7=40 x1+x2+x3+x5+x6+x10+x15+x20+n8p8=3.2 x4+x7+x8+x9+x11+x12+x1

8、3+x14+x16+x17+x18+x19+x21+x22+x23+n9p9=6 xi=0，1（i=1，2，23）（四）模型求解1. 在软件上输入如下：min obj s.t.9x1+13x2+14x3+17x4+18x5+19x6+23x7+21x8+9x9+11x10+17x11+18x12+18x13+17x14+22x15+24x16+36x17+43x18+6x19+15x20+15x21+25x22+39x23+n1p1=179.6x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13+x14+x15+x16+x17+x18+x19+x20+x21+x

9、22+x23+n2p2=9.211x1+47x2+44x3+25x4+10x5+26x6+26x7+54x8+18x9+51x10+20x11+105x12+7x13+16x14+34x15+100x16+50x17+21x18+11x19+19x20+14x21+10x22+11x23+n3p3=29234x1+411x2+82x3+157x4+5x5+183x6+14x7+215x8+102x9+21x10+54x11+0x12+6x13+96x14+118x15+112x16+535x17+8x18+53x19+28x20+69x21+65x22+27x23+n4p4=9589x1+13

10、x2+14x3+17x4+18x5+19x6+23x7+21x8+n5p5=53.69x9+11x10+17x11+18x12+18x13+17x14+22x15+24x16+36x17+43x18+n6p6=866x19+15x20+15x21+25x22+39x23+n7p7=40x1+x2+x3+x5+x6+x10+x15+x20+n8p8=3.2x4+x7+x8+x9+x11+x12+x13+x14+x16+x17+x18+x19+x21+x22+x23+n9p9=6objn1p1n2p2n3p3n4p4n5p5n6p6n7p7n8p8n9p9=0end int x1 int x2 i

11、nt x3 int x4 int x5 int x6 int x7 int x8 int x9int x10 int x11 int x12 int x13 int x14 int x15 int x16 int x17 int x18 int x19 int x20 int x21 int x22 int x23sub n1 22.45 sub n2 1.15 sub n3 36.5 sub n4 119.75 sub n5 6.7sub n6 10.75sub n7 5sub n8 0.4 sub n9 0.75 sub p1 22.45 sub p2 1.15 sub p3 36.5 s

12、ub p4 119.75sub p5 6.7 sub p6 10.75 sub p7 5sub p8 0.4sub p9 0.752. 在软件 lindo 上运行结果人如下：LP OPTIMUM FOUND AT STEP 27OBJECTIVE VALUE = 0.888178420E15DELETE X22 AT LEVEL 15DELETE X11 AT LEVEL 14DELETE X1 AT LEVEL 13FLIP X15 TO = 1 AT 13, BND= 10.92 TWIN=0.1000E+31 30951SET X14 TO = 1 AT 14, BND= 10.92 T

13、WIN=0.1000E+31 30951SET X10 TO = 1 AT 15, BND= 11.73 TWIN= 40.03 30973SET X22 TO = 1 AT 16, BND= 11.73 TWIN=0.1000E+31 30973SET X16 TO = 1 AT 17, BND= 27.15 TWIN=0.1000E+31 30999DELETE X16 AT LEVEL 17DELETE X22 AT LEVEL 16DELETE X10 AT LEVEL 15DELETE X14 AT LEVEL 14DELETE X11 AT LEVEL 13DELETE X15 A

14、T LEVEL 12DELETE X13 AT LEVEL 11DELETE X9 AT LEVEL 10DELETE X3 AT LEVEL 9FLIP X12 TO = 1 AT 8 WITH BND= 8.3263254SET X10 TO = 0 AT 9, BND= 8.326 TWIN=0.1000E+31 30999SET X16 TO = 1 AT 11, BND= 8.326 TWIN=0.1000E+31 30999SET X15 TO = 1 AT 12, BND= 12.38 TWIN= 27.61 31075SET X3 TO = 1 AT 14, BND= 12.3

15、8 TWIN=0.1000E+31 31075SET X21 TO = 1 AT 15, BND= 13.37 TWIN= 16.11 31128SET X19 TO = 0 AT 16, BND= 13.37 TWIN=0.1000E+31 31128SET X14 TO = 1 AT 18, BND= 16.04 TWIN=0.1000E+31 31149SET X20 TO = 0 AT 19, BND= 16.04 TWIN=0.1000E+31 31149DELETE X9 AT LEVEL 20DELETE X20 AT LEVEL 19DELETE X11 AT LEVEL 18

16、DELETE X14 AT LEVEL 17DELETE X19 AT LEVEL 16FLIP X21 TO = 0 AT 15 WITH BND= 16.106396SET X1 TO = 0 AT 16, BND= 16.11 TWIN=0.1000E+31 31172SET X19 TO = 0 AT 17, BND= 16.11 TWIN=0.1000E+31 31172SET X9 TO = 1 AT 5 WITH BND= 2.3200004SET X6 TO = 1 AT 6, BND= 2.320 TWIN= 2.369 31232SET X15 TO = 1 AT 7, B

17、ND= 2.320 TWIN= 2.400 31246SET X16 TO = 1 AT 9, BND= 2.472 TWIN= 5.640 31360SET X14 TO = 1 AT 10, BND= 3.591 TWIN= 5.588 31406SET X5 TO = 1 AT 13, BND= 3.591 TWIN=0.1000E+31 31406SET X10 TO = 0 AT 13, BND= 3.591 TWIN=0.1000E+31 31406SET X3 TO = 0 AT 14, BND= 7.430 TWIN=0.1000E+31 31442SET X4 TO = 1

18、AT 16, BND= 7.430 TWIN=0.1000E+31 31442SET X13 TO = 1 AT 17, BND= 7.430 TWIN=0.1000E+31 31442SET X19 TO = 0 AT 18, BND= 7.430 TWIN=0.1000E+31 31442SET X21 TO = 0 AT 19, BND= 7.430 TWIN=0.1000E+31 31442SET X22 TO = 0 AT 20, BND= 7.430 TWIN=0.1000E+31 31442SET X11 TO = 0 AT 21, BND= 7.693 TWIN=0.1000E

19、+31 31452SET X1 TO = 0 AT 22, BND= 7.693 TWIN=0.1000E+31 31452SET X20 TO = 0 AT 23, BND= 9.400 TWIN=0.1000E+31 31461NEW INTEGER SOLUTION OF 9.39999962 AT BRANCH 832 PIVOT31461BOUND ON OPTIMUM: 2.368894DELETE X20 AT LEVEL 23DELETE X1 AT LEVEL 22DELETE X11 AT LEVEL 21DELETE X22 AT LEVEL 20DELETE X21 A

20、T LEVEL 19DELETE X19 AT LEVEL 18DELETE X13 AT LEVEL 17DELETE X12 AT LEVEL 16DELETE X4 AT LEVEL 15DELETE X3 AT LEVEL 14DELETE X10 AT LEVEL 13DELETE X7 AT LEVEL 12DELETE X5 AT LEVEL 11FLIP X14 TO = 0 AT 10 WITH BND= 5.5878572SET X10 TO = 1 AT 12, BND= 5.588 TWIN=0.1000E+31 31461SET X3 TO = 1 AT 14, BN

21、D= 6.556 TWIN=0.1000E+31 31527SET X13 TO = 1 AT 15, BND= 6.556 TWIN=0.1000E+31 31527SET X20 TO = 0 AT 16, BND= 6.556 TWIN=0.1000E+31 31527SET X4 TO = 0 AT 17, BND= 13.27 TWIN= 113.0 31556DELETE X4 AT LEVEL 17DELETE X20 AT LEVEL 16DELETE X13 AT LEVEL 15DELETE X11 AT LEVEL 14DELETE X3 AT LEVEL 13DELET

22、E X12 AT LEVEL 12DELETE X10 AT LEVEL 11DELETE X14 AT LEVEL 10FLIP X9 TO = 0 AT 9 WITH BND= 5.6395464SET X1 TO = 0 AT 10, BND= 5.640 TWIN=0.1000E+31 31556SET X3 TO = 0 AT 11, BND= 5.640 TWIN=0.1000E+31 31556SET X5 TO = 0 AT 12, BND= 5.640 TWIN=0.1000E+31 31556SET X19 TO = 0 AT 13, BND= 5.640 TWIN=0.1

23、000E+31 31556SET X20 TO = 0 AT 14, BND= 5.640 TWIN=0.1000E+31 31556SET X21 TO = 0 AT 15, BND= 5.640 TWIN=0.1000E+31 31556SET X22 TO = 0 AT 16, BND= 5.640 TWIN=0.1000E+31 31556SET X4 TO = 1 AT 8 WITH BND= 7.5999956SET X3 TO = 0 AT 9, BND= 7.600 TWIN=0.1000E+31 31577SET X4 TO = 1 AT 11, BND= 7.600 TWI

24、N=0.1000E+31 31577SET X14 TO = 0 AT 12, BND= 7.600 TWIN=0.1000E+31 31577SET X20 TO = 0 AT 13, BND= 7.600 TWIN=0.1000E+31 31577SET X21 TO = 0 AT 14, BND= 7.600 TWIN=0.1000E+31 31577SET X9 TO = 0 AT 15, BND= 9.275 TWIN= 38.04 31603SET X5 TO = 0 AT 16, BND= 9.275 TWIN=0.1000E+31 31603SET X10 TO = 1 AT

25、18, BND= 9.275 TWIN=0.1000E+31 31603SET X22 TO = 0 AT 19, BND= 9.275 TWIN=0.1000E+31 31603SET X12 TO = 0 AT 20, BND= 25.76 TWIN=0.1000E+31 31625DELETE X12 AT LEVEL 20DELETE X22 AT LEVEL 19DELETE X11 AT LEVEL 18DELETE X10 AT LEVEL 17DELETE X5 AT LEVEL 16DELETE X9 AT LEVEL 15DELETE X21 AT LEVEL 14DELE

26、TE X20 AT LEVEL 13DELETE X14 AT LEVEL 12DELETE X13 AT LEVEL 11DELETE X4 AT LEVEL 10DELETE X3 AT LEVEL 9DELETE X16 AT LEVEL 8FLIP X15 TO = 0 AT 7 WITH BND= 2.4003751SET X4 TO = 1 AT 9, BND= 2.870 TWIN= 6.438 31743SET X16 TO = 1 AT 10, BND= 5.813 TWIN= 9.994 31813SET X1 TO = 0 AT 11, BND= 5.813 TWIN=0.1000E+31 31813SET X3 TO = 1 AT 13, BND= 5.813 TWIN=0.1000E+31 31813SET X11 TO = 1 AT 14, BND= 5.813 TWIN=0.1000E+31 31813SET X13 TO