运筹学实验报告
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运筹学实验报告
专业：
班级：
姓名：
学号:
指导教师：
数学与应用数学专业
2015-12-18
实验目录
一、实验目的 (3)
二、实验要求 (3)
三、实验容 (3)
1、线性规划 (3)
2、整数规划 (6)
3、非线性规划 (13)
4、动态规划 (114)
5、排队论 (19)
四、需用仪器设备 (26)
五、MATLAB优化工具箱使用方法简介 (26)
六、LINGO优化软件简介 (26)
七、实验总结 (27)
一、实验目的
1、会利用适当的方法建立相关实际问题的数学模型；
2、会用数学规划思想及方法解决实际问题；
3、会用排队论思想及方法解决实际问题；
4、会用决策论思想及方法解决实际问题；
5、掌握MATLAB、LINGO等数学软件的应用；
二、实验要求
1、七人一组每人至少完成一项实验容；
2、每组上交一份实验报告；
3、每人进行1~2分钟实验演示；
4、实验成绩比例：
出勤：40%
课堂提问：20%
实验报告：30%
实验演示：10%。
三、实验容
1、线性规划
例运筹学74页14题
Min z=-2x
-x2
s.t. 2x1+5x2≤60
x1+x2≤18
3x1+x2≤44
X2≤10
X1,x2≥0
用matlab运行后得到以下结果:
the program is with the linear programming
Please input the constraints number of the linear programming m=6
m =
6
Please input the variant number of the linear programming n=2
n =
2
Please input cost array of the objective function c(n)_T=[-2,-1]'
c =
-2
-1
Please input the coefficient matrix of the constraints A(m,n)=[2,5;1,1;3,1;0,1;-1,0;0,-1]
A =
2 5
1 1
3 1
0 1
-1 0
0 -1
Please input the resource array of the program b(m)_T=[60,18,44,10,0,0]'
b =
60
18
44
10
Optimization terminated.
The optimization solution of the programming is:
x =
13.0000
5.0000
The optimization value of the programming is:
opt_value =
-31.0000
LINDO程序
在命令窗口键入以下容:
max -2x-y
subject to
2x+5y<=60
x+y<=18
3x+y<=44
y<=10
end
按solve键在reports window出现:
Global optimal solution found.
Objective value: 0.000000
Total solver iterations: 0
Variable Value Reduced Cost X 0.000000 2.000000
Y 0.000000 1.000000
Row Slack or Surplus Dual Price
1 0.000000 1.000000
2 60.00000 0.000000
3 18.00000 0.000000
4 44.00000 0.000000
5 10.00000 0.000000 2、整数规划
课本第二章79页1题
Max z=100x1+180x2+70x3
s.t. 40x1+50x2+60x3≤10000
3 x1+6x2+ 2x3≤600
x1≤130
X2≤80
x3≤200
x1 x2 x3≥0
程序运行及结果：
biprogram
the program is with the binary linear programming
Please input the constraints number of the programming m=5
m =
5
Please input the variant number of the programming n=5
n =
5
Please input cost array of the objective function c(n)_T=[100,180 ,70]'
c =
100
180
70
Please input the coefficient matrix of the constraints A(m,n)=[40 ,50,60;3,6,2;1,0,0;0,1,0;0,0,1]
A =
40 50 60
3 6 2
1 0 0
0 1 0
0 0 1
Please input the resource array of the program b(m)_T=[10000;600; 130;80;200]
b =
10000
600
130
80
200
Optimization terminated.
The optimization solution of the programming is:
x =
The optimization value of the programming is:
opt_value =
程序名：intprogram b程序说明：
% the programm is with the integer linear programming use branc h and bound method!
%这个程序是用分支定界法解决整数规划问题
% please input the parameters in the main function in the comm and winows
%请在命令窗口输入这个主要定义函数的参数
function [x,f]=ILp(c,A,b,vlb,vub,x0,neqcstr,pre)
% min f=c'*x,s.t. A*x<=b,vlb<=x<=vub
% f的最小值等于c的转置乘以x，A乘以x小于等于b,x大于等于vlb小于等于vub % the vectors of x is required as integers as whole
% x是整个的整数需要
% x0 is the initialization,'[]' is also ok
% x0是初始值,"[]"也可以是。
% neqcstr is the number of equational constraints,when 0 can be delete
% neqcstr是平均约束条件的数目，当0能删除时
% pre is the concise rate
% pre是简明率
% x is the integer optimization and f is the optimal value
% x是整数规划，f 是最优值
%%%%%%%%%%%%%%%%