运筹学实验报告-lingo软件地使用-习题代码

1、WORD格式运 筹 学实验报告*：学号：班级：专业资料整理WORD格式相关问题说明：一、 实验性质和教学目的本实验是运筹学课内安排的上机操作实验。目的在于了解、熟悉计算机Lingo 软件在运筹学模型求解中的作用，激发学习兴趣，提高学习效果，增强自身的动手能力，提高实际应用能力。二、 实验根本要求要求学生：1. 实验前认真做好理论准备，仔细阅读实验指导书；2. 遵从教师指导，认真完成实验任务，按时按质提交实验报告。三、 主要参考资料1 LINGO软件2. LINGO8.0及其在环境系统优化中的应用，*大学，20053. 优化建模与 LINDO/LINGO软件，清华大学， 20054运筹学编写组主

2、编，运筹学修订版，清华大学，19905蓝伯雄主编，管理数学下运筹学，清华大学，19976胡运权主编，运筹学习题集修订版，清华大学，19957胡运权主编，运筹学教程第二版，清华大学，2003专业资料整理WORD格式实验内容1、线性规划问题：max z8 x16x2专业资料整理WORD格式s.t.9x18 x2127 x111 x2249x111x213x1 , x20专业资料整理WORD格式(1) 给出原始代码； (2) 计算结果 (包括灵敏度分析，求解结果粘贴 )；(3) 答复以下问题 (手写 )：a) 最优解及最优目标函数值是多少；b) 资源的对偶价格各为多少，并说明对偶价格的含义；c) 为

3、了使目标函数值增加最多， 让你选择一个约束条件，将它的常数项增加一个单位，你将选择哪一个约束条件？这时目标函数值将是多少？d) 对 x2的目标函数系数进展灵敏度分析；e) 对第 2 个约束的约束右端项进展灵敏度分析；f ) 结合此题的结果解释“ Reduced Cost的含义。对偶价格就是说约束方程右端变量增加1 对目标函数值的影响答案： 1代码max =8*x1+6*x2;9*x1+8*x2<=12;7*x1+11*x2<=24;9*x1+11*x2<=13;x1>=0;x2>=0; 2计算结果Global optimal solution found.Obje

4、ctive value:10.66667Total solver iterations:2VariableValueReduced CostX11.3333330.000000X20.0000001.111111RowSlack or SurplusDual Price110.666671.00000020.0000000.8888889314.666670.00000041.0000000.00000051.3333330.00000060.0000000.000000专业资料整理WORD格式 1专业资料整理WORD格式Ranges in which the basis is unchang

5、ed:Objective Coefficient RangesCurrentAllowableAllowableVariableCoefficientIncreaseDecreaseX18.000000INFINITY1.250000X26.0000001.111111INFINITYRighthand Side RangesRowCurrentAllowableAllowableRHSIncreaseDecrease212.000001.00000012.00000324.00000INFINITY14.66667413.00000INFINITY1.00000050.01.333333IN

6、FINITY60.00.0INFINITY(3)a)b)c)d)e)f)2、运输问题： 6 个发点 8 个收点的最小费用运输问题。产销量及单位运价如下表。销地cijBBBBBBBB产12345678量产地A 16297425955A 24553853247A 35213748342A 47679927152A 52365726541A 65922814332销量6055514341524338(1) 给出原始代码； (2) 计算结果 (决策变量求解结果粘贴 )6 8Min Z =Cij Xij6 i 1 j 1Xij <=bjj=1.8销量约束i1专业资料整理WORD格式 2专业资料整理

7、WORD格式8Xij = ai i=1.6产量约束j1Xij 0 i=1.6；j=1.8代码：model:!6 发点 8 model :!6 发点 8收点运输问题;sets :warehouses/wh1.wh6/: capacity;vendors/v1.v8/: demand;links(warehouses,vendors): cost, volume;endsetsmin=sum(links: cost*volume);! 目标函数 ;for(vendors(J):sum(warehouses(I): volume(I,J)<=demand(J);! 需求约束 ;for(ware

8、houses(I):sum(vendors(J): volume(I,J)=capacity(I);! 产量约束 ;! 这里是数据 ;data :capacity=55 47 42 52 41 32;demand=60 55 51 43 41 52 43 38;cost=6 2 9 7 4 2 5 94553853252137483767992712365726559228143;enddataend答案Global optimal solution found.Objective value:473.0000Infeasibilities:0.000000Total solver itera

9、tions:9Model Class:LPTotal variables:48Nonlinear variables:0Integer variables:0专业资料整理WORD格式 3专业资料整理WORD格式Total constraints:15Nonlinear constraints:0Total nonzeros:144Nonlinear nonzeros:0VariableValueReduced CostCAPACITY( WH1)55.000000.000000CAPACITY( WH2)47.000000.000000CAPACITY( WH3)42.000000.00000

10、0CAPACITY( WH4)52.000000.000000CAPACITY( WH5)41.000000.000000CAPACITY( WH6)32.000000.000000DEMAND( V1)60.000000.000000DEMAND( V2)55.000000.000000DEMAND( V3)51.000000.000000DEMAND( V4)43.000000.000000DEMAND( V5)41.000000.000000DEMAND( V6)52.000000.000000DEMAND( V7)43.000000.000000DEMAND( V8)38.000000

11、.000000COST( WH1, V1)6.0000000.000000COST( WH1, V2)2.0000000.000000COST( WH1, V3)9.0000000.000000COST( WH1, V4)7.0000000.000000COST( WH1, V5)4.0000000.000000COST( WH1, V6)2.0000000.000000COST( WH1, V7)5.0000000.000000COST( WH1, V8)9.0000000.000000COST( WH2, V1)4.0000000.000000COST( WH2, V2)5.0000000

12、.000000COST( WH2, V3)5.0000000.000000COST( WH2, V4)3.0000000.000000COST( WH2, V5)8.0000000.000000COST( WH2, V6)5.0000000.000000COST( WH2, V7)3.0000000.000000COST( WH2, V8)2.0000000.000000COST( WH3, V1)5.0000000.000000COST( WH3, V2)2.0000000.000000COST( WH3, V3)1.0000000.000000COST( WH3, V4)3.0000000

13、.000000COST( WH3, V5)7.0000000.000000COST( WH3, V6)4.0000000.000000COST( WH3, V7)8.0000000.000000专业资料整理WORD格式 4专业资料整理WORD格式COST( WH3, V8)3.0000000.000000COST( WH4, V1)7.0000000.000000COST( WH4, V2)6.0000000.000000COST( WH4, V3)7.0000000.000000COST( WH4, V4)9.0000000.000000COST( WH4, V5)9.0000000.000

14、000COST( WH4, V6)2.0000000.000000COST( WH4, V7)7.0000000.000000COST( WH4, V8)1.0000000.000000COST( WH5, V1)2.0000000.000000COST( WH5, V2)3.0000000.000000COST( WH5, V3)6.0000000.000000COST( WH5, V4)5.0000000.000000COST( WH5, V5)7.0000000.000000COST( WH5, V6)2.0000000.000000COST( WH5, V7)6.0000000.000

15、000COST( WH5, V8)5.0000000.000000COST( WH6, V1)5.0000000.000000COST( WH6, V2)9.0000000.000000COST( WH6, V3)2.0000000.000000COST( WH6, V4)2.0000000.000000COST( WH6, V5)8.0000000.000000COST( WH6, V6)1.0000000.000000COST( WH6, V7)4.0000000.000000COST( WH6, V8)3.0000000.000000VOLUME( WH1, V1)0.0000004.0

16、00000VOLUME( WH1, V2)55.000000.000000VOLUME( WH1, V3)0.0000007.000000VOLUME( WH1, V4)0.0000005.000000VOLUME( WH1, V5)0.0000002.000000VOLUME( WH1, V6)0.0000000.000000VOLUME( WH1, V7)0.0000003.000000VOLUME( WH1, V8)0.0000008.000000VOLUME( WH2, V1)0.0000001.000000VOLUME( WH2, V2)0.0000002.000000VOLUME(

17、 WH2, V3)0.0000002.000000VOLUME( WH2, V4)43.000000.000000VOLUME( WH2, V5)0.0000005.000000VOLUME( WH2, V6)0.0000002.000000VOLUME( WH2, V7)4.0000000.000000VOLUME( WH2, V8)0.0000000.000000VOLUME( WH3, V1)0.0000004.000000VOLUME( WH3, V2)0.0000001.000000VOLUME( WH3, V3)42.000000.000000VOLUME( WH3, V4)0.0

18、000002.000000专业资料整理WORD格式 5专业资料整理WORD格式VOLUME( WH3, V5)0.0000006.000000VOLUME( WH3, V6)0.0000003.000000VOLUME( WH3, V7)0.0000007.000000VOLUME( WH3, V8)0.0000003.000000VOLUME( WH4, V1)0.0000005.000000VOLUME( WH4, V2)0.0000004.000000VOLUME( WH4, V3)0.0000005.000000VOLUME( WH4, V4)0.0000007.000000VOLUM

19、E( WH4, V5)0.0000007.000000VOLUME( WH4, V6)14.000000.000000VOLUME( WH4, V7)0.0000005.000000VOLUME( WH4, V8)38.000000.000000VOLUME( WH5, V1)41.000000.000000VOLUME( WH5, V2)0.0000001.000000VOLUME( WH5, V3)0.0000004.000000VOLUME( WH5, V4)0.0000003.000000VOLUME( WH5, V5)0.0000005.000000VOLUME( WH5, V6)0

20、.0000000.000000VOLUME( WH5, V7)0.0000004.000000VOLUME( WH5, V8)0.0000004.000000VOLUME( WH6, V1)0.0000004.000000VOLUME( WH6, V2)0.0000008.000000VOLUME( WH6, V3)0.0000001.000000VOLUME( WH6, V4)0.0000001.000000VOLUME( WH6, V5)0.0000007.000000VOLUME( WH6, V6)32.000000.000000VOLUME( WH6, V7)0.0000003.000

21、000VOLUME( WH6, V8)0.0000003.000000RowSlack or SurplusDual Price1473.0000-1.000000219.000000.00000030.0000000.00000049.0000000.00000050.0000000.000000641.000000.00000076.0000000.000000839.000000.00000090.0000001.000000100.000000-2.000000110.000000-3.000000120.000000-1.000000130.000000-2.000000140.00

22、0000-2.000000150.000000-1.000000专业资料整理WORD格式 6专业资料整理WORD格式3、一般整数规划问题：某效劳部门各时段每 2h 为一时段需要的效劳员人数见下表。按规定，效劳员连续工作 8h即四个时段为一班。现要求安排效劳员的工作时间，使效劳部门效劳员总数最少。时 段12345678效劳员最少数目10891113853(1) 给出原始代码； (2) 计算结果 (决策变量求解结果粘贴 )model :sets :time/x1.x8/: required,start;endsetsdata :! 每天所需的最少职员数 ; required = 10 8 9 11

23、 13 8 5 3;enddata! 最小化每周所需职员数 ; min=sum(time: start); for(time (J):sum(time(I) | I #le# 4:start(wrap(J+I+2,8) >= required(J);end结果Global optimal solution found.Objective value:23.00000Total solver iterations:3VariableValueReduced CostREQUIRED( X1)10.000000.000000REQUIRED( X2)8.0000000.000000REQUI

24、RED( X3)9.0000000.000000REQUIRED( X4)11.000000.000000REQUIRED( X5)13.000000.000000REQUIRED( X6)8.0000000.000000REQUIRED( X7)5.0000000.000000REQUIRED( X8)3.0000000.000000START( X1)13.000000.000000START( X2)0.0000000.000000START( X3)0.0000000.000000START( X4)2.0000000.000000START( X5)8.0000000.000000S

25、TART( X6)0.0000000.000000START( X7)0.0000000.000000专业资料整理WORD格式 7专业资料整理WORD格式START( X8)0.0000000.000000RowSlack or SurplusDual Price123.00000-1.00000020.000000-1.00000030.0000000.00000044.0000000.00000052.0000000.00000060.000000-1.00000077.0000000.00000085.0000000.00000097.0000000.0000004、指派问题：如下效率矩

26、阵，求极大化指派问题。B1B2BBB534A 14871512A 279171410A 3691287A 46714610A 56912106(1) 给出原始代码； (2) 计算结果 (决策变量求解结果粘贴 )model :!5 个工人， 5 个工作的分配问题;sets :workers/w1.w5/;jobs/j1.j5/;links(workers,jobs): cost,volume;endsets! 目标函数 ;min=sum(links: cost*volume);! 每个工人只能有一份工作;for(workers(I):sum(jobs(J): volume(I,J)=1;);!

27、每份工作只能有一个工人;for(jobs(J):sum(workers(I): volume(I,J)=1;);data :cost= 4 8 7 15 127917141069128767146106912106；专业资料整理WORD格式 8专业资料整理WORD格式enddataend答案Global optimal solution found.Objective value:34.00000Total solver iterations:10VariableValueReduced CostCOST( W1, J1)4.0000000.000000COST( W1, J2)8.00000

28、00.000000COST( W1, J3)7.0000000.000000COST( W1, J4)15.000000.000000COST( W1, J5)12.000000.000000COST( W2, J1)7.0000000.000000COST( W2, J2)9.0000000.000000COST( W2, J3)17.000000.000000COST( W2, J4)14.000000.000000COST( W2, J5)10.000000.000000COST( W3, J1)6.0000000.000000COST( W3, J2)9.0000000.000000C

29、OST( W3, J3)12.000000.000000COST( W3, J4)8.0000000.000000COST( W3, J5)7.0000000.000000COST( W4, J1)6.0000000.000000COST( W4, J2)7.0000000.000000COST( W4, J3)14.000000.000000COST( W4, J4)6.0000000.000000COST( W4, J5)10.000000.000000COST( W5, J1)6.0000000.000000COST( W5, J2)9.0000000.000000COST( W5, J

30、3)12.000000.000000COST( W5, J4)10.000000.000000COST( W5, J5)6.0000000.000000VOLUME( W1, J1)0.0000003.000000VOLUME( W1, J2)0.0000005.000000VOLUME( W1, J3)1.0000000.000000VOLUME( W1, J4)0.00000013.00000VOLUME( W1, J5)0.00000011.00000VOLUME( W2, J1)0.0000000.000000VOLUME( W2, J2)1.0000000.000000VOLUME(

31、 W2, J3)0.0000004.000000VOLUME( W2, J4)0.0000006.000000VOLUME( W2, J5)0.0000003.000000专业资料整理WORD格式 9专业资料整理WORD格式VOLUME( W3, J1)1.0000000.000000VOLUME( W3, J2)0.0000001.000000VOLUME( W3, J3)0.0000000.000000VOLUME( W3, J4)0.0000001.000000VOLUME( W3, J5)0.0000001.000000VOLUME( W4, J1)0.0000001.000000VO

32、LUME( W4, J2)0.0000000.000000VOLUME( W4, J3)0.0000003.000000VOLUME( W4, J4)1.0000000.000000VOLUME( W4, J5)0.0000005.000000VOLUME( W5, J1)0.0000000.000000VOLUME( W5, J2)0.0000001.000000VOLUME( W5, J3)0.0000000.000000VOLUME( W5, J4)0.0000003.000000VOLUME( W5, J5)1.0000000.000000RowSlack or SurplusDual

33、 Price134.00000-1.00000020.000000-1.00000030.000000-7.00000040.000000-6.00000050.000000-5.00000060.000000-6.00000070.0000000.00000080.000000-2.00000090.000000-6.000000100.000000-1.000000110.0000000.0000005、一维资源分配问题：某工业部门根据国家方案的安排， 拟将某种高效率的设备五台， 分配给所属的甲、乙、丙三个工厂，各工厂假设获得这种设备之后，可以为国家提供的盈利如下表所示。问：这五台设备如何

34、分配给各工厂，才能使国家得到的盈利最大。工厂设备台数甲 a乙 b丙 c000015542151526340404048060455907050(1) 给出原始代码； (2) 计算结果 (决策变量求解结果粘贴 )代码专业资料整理WORD格式 10专业资料整理WORD格式sets:R/1.6/:z;L/1.3/;c(R,L):x,y;endsetsdata:X=0005 5 415 15 2640 40 4080 60 4590 70 50;z=0 1 2 3 4 5;enddatamax = sum(c(i,j):X(i,j)*y(i,j);for(l(i):sum(c(j,k)|k#eq# 1

35、:y(j,k)=1);sum(c(i,j):y(i,j)*z(i)=5;for(c(i,j):B in(y(i,j);end答案Global optimal solution found.Objective value:90.00000Extended solver steps:0Total solver iterations:0VariableValueReduced CostZ( 1)0.0000000.000000Z( 2)1.0000000.000000Z( 3)2.0000000.000000Z( 4)3.0000000.000000Z( 5)4.0000000.000000Z( 6

36、)5.0000000.000000X( 1, 1)0.0000000.000000X( 1, 2)0.0000000.000000X( 1, 3)0.0000000.000000X( 2, 1)5.0000000.000000X( 2, 2)5.0000000.000000X( 2, 3)4.0000000.000000X( 3, 1)15.000000.000000X( 3, 2)15.000000.000000X( 3, 3)26.000000.000000X( 4, 1)40.000000.000000X( 4, 2)40.000000.000000X( 4, 3)40.000000.0

37、00000X( 5, 1)80.000000.000000专业资料整理WORD格式 11专业资料整理WORD格式X( 5, 2)60.000000.000000X( 5, 3)45.000000.000000X( 6, 1)90.000000.000000X( 6, 2)70.000000.000000X( 6, 3)50.000000.000000Y( 1, 1)0.0000000.000000Y( 1, 2)0.0000000.000000Y( 1, 3)0.0000000.000000Y( 2, 1)0.000000-5.000000Y( 2, 2)0.000000-5.000000Y(

38、 2, 3)0.000000-4.000000Y( 3, 1)0.000000-15.00000Y( 3, 2)0.000000-15.00000Y( 3, 3)0.000000-26.00000Y( 4, 1)0.000000-40.00000Y( 4, 2)0.000000-40.00000Y( 4, 3)0.000000-40.00000Y( 5, 1)0.000000-80.00000Y( 5, 2)0.000000-60.00000Y( 5, 3)0.000000-45.00000Y( 6, 1)1.000000-90.00000Y( 6, 2)0.000000-70.00000Y(

39、 6, 3)0.000000-50.00000RowSlack or SurplusDual Price190.000001.00000020.0000000.00000030.0000000.00000040.0000000.00000050.0000000.0000006、最短路问题：求从 V1至 V10的最短路。V4V7V 2V 5V 8V 1V 10V 9V3V6专业资料整理WORD格式 12专业资料整理WORD格式l 1,2=6,l1,3=5,l 2,4=3,l2,5=6,l 2,6=9,l3,4=7,l 3,5=5, l3,6=11, l4,7=9, l4,8=1,l 5,7=8,

40、l5,8=7,l 5,9=5,l6,8=4,l 6,9=10,l7,10=5,l 8,10=7, l 9,10=9 li,j表示 V i到 Vj之间的权重(1) 给出原始代码； (2) 计算结果 (决策变量求解结果粘贴 )! 最短路问题 ; model :data : n=10; enddata sets :cities/1.n/: F;!10 个城市 ;roads(cities,cities)/1,21,32,42,52,63,43,53,64,74,85,75,85,96,86,97,108,109,10/: D, P;endsetsdata :D=6536 975 119187 54 10579;enddataF(n)=0;for(c