lingo实验分析报告

1、lingo实验报告作者:日期:一、实验名称：推销员指派问题二、实验目的及任务：1、掌握Lingo软件的使用方法2、编写简单的Lin go程序3、解决Lingo中的最优指派问题三、实验内容1、问题描述一个公司要分派5个推销员去5个地区推销某种产品，5个推销员在各个地 区推销这种产品的预期利润如下表所示。若每个推销员只能去一个地区。应如何 分派这5个推销员才能使公司的利润为最大？地区推销贰ABCDE甲11821乙563)107丙3104HI3 'T77548 '戊426392、模型建立决策变量：设xij(i,j=1,2,3,4,5)1指派第i个人去第j个地区0不指派第i个人去第j个

2、地区目标函数：设总利润为z,第i个人去第j个地区的利润为A(i,j=1,2,3,4,5), 假设Aij为指派矩阵，则55Max zAj Xji 1 j 1约束条件：1第j个地区只有一个人去:5Xij 1(j=1,2,3,4,5)i 12.第i个人只去一个地区：5Xij 1(i=1,2,3,4,5)j 1由此得基本模型：S,t,Max5xiji 1Xij 1Xij5Aij xijj 1(j=1,2,3,4,5)(i=1,2,3,4,5)(i,j=1,2,3,4,5)3、Lingo 程序（一）常规程序Lingo输入：model : max=1*x11+8*x12+9*x13+2*x14+1*x15

3、+5*x21+6*x22+3*x23+10*x24+7*x25+ 3*x31+10*x32+4*x33+11*x34+3*x35+7*x41+7*x42+5*x43+4*x44+8*x45+4*x 51+2*x52+6*x53+3*x54+9*x55;x11+x12+x13+x14+x15=1;x21+x22+x23+x24+x25=1;x31+x32+x33+x34+x35=1;x41+x42+x43+x44+x45=1;x51+x52+x53+x54+x55=1;x11+x21+x31+x41+x51=1;x12+x22+x32+x42+x52=1;x13+x23+x33+x43+x53=

4、1;x14+x24+x34+x44+x54=1;x15+x25+x35+x45+x55=1;endLingo输出：Global optimal solution found.45.000000.000000Objective value:Infeasibilities:Total solver iterati ons:VariableValueReducedCostX110.0000007.000000X120.0000000.000000X131.0000000.000000X140.0000007.000000X150.0000008.000000X210.0000004.000000X2

5、20.0000003.000000X230.0000007.000000X241.0000000.000000X250.0000003.000000X310.0000007.000000X321.0000000.000000X330.0000007.000000X340.0000000.000000X350.0000008.000000X411.0000000.000000X420.0000000.000000X430.0000003.000000X440.0000004.000000X450.0000000.000000X510.0000004.000000X520.0000006.0000

6、00X533.000000X546.000000X550.000000Row Slack11.00000029.000000310.00000411.0000058.00000069.0000007-1.0000008-1.00000090.000000100.000000110.000000(二)集合函数程序Lingo输入：model :sets :pers on/1.5/;area/1.5/;assig n( pers on ,area):A,x; en dsetsdata :A=1,8,9,2,10.0000000.0000001.000000or Surplus DualPrice45

7、.000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000005,6,3,10,77,7,5,4,84,2,6,3,9;en ddatamax= sum(assig n: A*x);for (person(i):sum(area(j):x(i,j)=1);for (area(j):sum(person(i):x(i,j)=1);for (assign(i,j):bin (x(i,j);endLingo输出：Global optimal soluti on found.Objective

8、 value:45.00000Objective bou nd:45.00000In feasibilities:0.000000Exte nded solver steps:0Total solver iterati ons:0VariableValueReducedCostA(1,1)1.0000000.000000A(1,2)8.0000000.000000A(1,3)9.0000000.000000A(1,4)2.0000000.000000A(1,5)1.0000000.000000A(2,1)5.0000000.000000A(2,2)6.0000000.000000A(2,3)3

9、.0000000.000000A(2,4)10.000000.000000A(2,5)7.0000000.000000A(3,1)3.0000000.000000A(3,2)10.000000.000000A(3,3)4.000000A(3,0.000000A(3,0.000000A(4,0.000000A(4,0.000000A(4,0.000000A(4,0.000000A(4,0.000000A(5,0.000000A(5,0.000000A(5,0.000000A(5,0.000000A(5,0.000000X(1,-1.000000X(1,-8.000000X(1,-9.000000

10、X(1,-2.000000X(1,-1.000000X(2,-5.000000X(2,-6.000000X(2,-3.000000X(2,-10.00000X(2,0.00000011.000003.0000007.0000007.0000005.0000004.0000008.0000004.0000002.0000006.0000003.0000009.0000000.0000000.0000001.0000000.0000000.0000000.0000000.0000000.0000001.0000004)5)1)2)3)4)5)1)2)3)4)5)1)2)3)4)5)1)2)3)4)

11、5)-7.000000xc3,1)0.000000-3.000000X(3,2)1.000000-10.00000X(3,3)0.000000-4.000000X(3,4)0.000000-11.00000X(3,5)0.000000-3.000000X(4,1)1.000000-7.000000X(4,2)0.000000-7.000000X(4,3)0.000000-5.000000X(4,4)0.000000-4.000000X(4,5)0.000000-8.000000X(5,1)0.000000-4.000000X(5,2)0.000000-2.000000X(5,3)0.000000-6.000000X(5,4)0.000000-3.000000X(5,5)1.000000-9.000000or Surplus DualPrice45.000000.0000000.0000000.0000000.000000Row Slack11.00000020.00000030.00000040.00000050.00000060.00000070.0000000.00000080.0000000.00000090.0000