运筹学实验报告lingo软件的使用习题代码.docx
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运筹学实验报告lingo软件的使用习题代码
运筹学
实验报告
姓名:
学号:
班级:
相关问题说明:
一、实验性质和教学目的
本实验是运筹学课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、实验基本要求
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,2005
3.优化建模与LINDO/LINGO软件,清华大学,2005
4.运筹学编写组主编,运筹学(修订版),清华大学,1990
5.蓝伯雄主编,管理数学(下)—运筹学,清华大学,1997
6.胡运权主编,运筹学习题集(修订版),清华大学,1995
7.胡运权主编,运筹学教程(第二版),清华大学,2003
实验容
1、线性规划问题:
(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)回答下列问题(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的目标函数系数进行灵敏度分析;
e)对第2个约束的约束右端项进行灵敏度分析;
f)结合本题的结果解释“ReducedCost”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
Globaloptimalsolutionfound.
Objectivevalue:
10.66667
Totalsolveriterations:
2
VariableValueReducedCost
X11.3333330.000000
X20.0000001.111111
RowSlackorSurplusDualPrice
110.666671.000000
20.0000000.8888889
314.666670.000000
41.0000000.000000
51.3333330.000000
60.0000000.000000
Rangesinwhichthebasisisunchanged:
ObjectiveCoefficientRanges
CurrentAllowableAllowable
VariableCoefficientIncreaseDecrease
X18.000000INFINITY1.250000
X26.0000001.111111INFINITY
RighthandSideRanges
RowCurrentAllowableAllowable
RHSIncreaseDecrease
212.000001.00000012.00000
324.00000INFINITY14.66667
413.00000INFINITY1.000000
50.01.333333INFINITY
60.00.0INFINITY
(3)a)
b)
c)
d)
e)
f)
2、运输问题:
已知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
cij
产地
B1
B2
B3
B4
B5
B6
B7
B8
产量
A1
6
2
9
7
4
2
5
9
55
A2
4
5
5
3
8
5
3
2
47
A3
5
2
1
3
7
4
8
3
42
A4
7
6
7
9
9
2
7
1
52
A5
2
3
6
5
7
2
6
5
41
A6
5
9
2
2
8
1
4
3
32
销量
60
55
51
43
41
52
43
38
(1)给出原始代码;
(2)计算结果(决策变量求解结果粘贴)
MinZ=CijXij
Xij<=bj(j=1...8)销量约束
Xij=ai(i=1...6)产量约束
Xij≥0(i=1...6;j=1...8)
代码:
model:
!
6发点8model:
!
6发点8收点运输问题;
sets:
warehouses/wh1..wh6/:
capacity;
vendors/v1..v8/:
demand;
links(warehouses,vendors):
cost,volume;
endsets
min=sum(links:
cost*volume);!
目标函数;
for(vendors(J):
sum(warehouses(I):
volume(I,J))<=demand(J));!
需求约束;
for(warehouses(I):
sum(vendors(J):
volume(I,J))=capacity(I));!
产量约束;
!
这里是数据;
data:
capacity=554742524132;
demand=6055514341524338;
cost=62974259
45538532
52137483
76799271
23657265
59228143;
enddata
end
答案
Globaloptimalsolutionfound.
Objectivevalue:
473.0000
Infeasibilities:
0.000000
Totalsolveriterations:
9
ModelClass:
LP
Totalvariables:
48
Nonlinearvariables:
0
Integervariables:
0
Totalconstraints:
15
Nonlinearconstraints:
0
Totalnonzeros:
144
Nonlinearnonzeros:
0
VariableValueReducedCost
CAPACITY(WH1)55.000000.000000
CAPACITY(WH2)47.000000.000000
CAPACITY(WH3)42.000000.000000
CAPACITY(WH4)52.000000.000000
CAPACITY(WH5)41.000000.000000
CAPACITY(WH6)32.000000.000000
DEMAND(V1)60.000000.000000
DEMAND(V2)55.000000.000000
DEMAND(V3)51.000000.000000
DEMAND(V4)43.000000.000000
DEMAND(V5)41.000000.000000
DEMAND(V6)52.000000.000000
DEMAND(V7)43.000000.000000
DEMAND(V8)38.000000.000000
COST(WH1,V1)6.0000000.000000
COST(WH1,V2)2.0000000.000000
COST(WH1,V3)9.0000000.000000
COST(WH1,V4)7.0000000.000000
COST(WH1,V5)4.0000000.000000
COST(WH1,V6)2.0000000.000000
COST(WH1,V7)5.0000000.000000
COST(WH1,V8)9.0000000.000000
COST(WH2,V1)4.0000000.000000
COST(WH2,V2)5.0000000.000000
COST(WH2,V3)5.0000000.000000
COST(WH2,V4)3.0000000.000000
COST(WH2,V5)8.0000000.000000
COST(WH2,V6)5.0000000.000000
COST(WH2,V7)3.0000000.000000
COST(WH2,V8)2.0000000.000000
COST(WH3,V1)5.0000000.000000
COST(WH3,V2)2.0000000.000000
COST(WH3,V3)1.0000000.000000
COST(WH3,V4)3.0000000.000000
COST(WH3,V5)7.0000000.000000
COST(WH3,V6)4.0000000.000000
COST(WH3,V7)8.0000000.000000
COST(WH3,V8)3.0000000.000000
COST(WH4,V1)7.0000000.000000
COST(WH4,V2)6.0000000.000000
COST(WH4,V3)7.0000000.000000
COST(WH4,V4)9.0000000.000000
COST(WH4,V5)9.0000000.000000
COST(WH4,V6)2.0000000.000000
COST(WH4,V7)7.0000000.000000
COST(WH4,V8)1.0000000.000000
COST(WH5,V1)2.0000000.000000
COST(WH5,V2)3.0000000.000000
COST(WH5,V3)6.0000000.000000
COST(WH5,V4)5.0000000.000000
COST(WH5,V5)7.0000000.000000
COST(WH5,V6)2.0000000.000000
COST(WH5,V7)6.0000000.000000
COST(WH5,V8)5.0000000.000000
COST(WH6,V1)5.0000000.000000
COST(WH6,V2)9.0000000.000000
COST(WH6,V3)2.0000000.000000
COST(WH6,V4)2.0000000.000000
COST(WH6,V5)8.0000000.000000
COST(WH6,V6)1.0000000.000000
COST(WH6,V7)4.0000000.000000
COST(WH6,V8)3.0000000.000000
VOLUME(WH1,V1)0.0000004.000000
VOLUME(WH1,V2)55.000000.000000
VOLUME(WH1,V3)0.0000007.000000
VOLUME(WH1,V4)0.0000005.000000
VOLUME(WH1,V5)0.0000002.000000
VOLUME(WH1,V6)0.0000000.000000
VOLUME(WH1,V7)0.0000003.000000
VOLUME(WH1,V8)0.0000008.000000
VOLUME(WH2,V1)0.0000001.000000
VOLUME(WH2,V2)0.0000002.000000
VOLUME(WH2,V3)0.0000002.000000
VOLUME(WH2,V4)43.000000.000000
VOLUME(WH2,V5)0.0000005.000000
VOLUME(WH2,V6)0.0000002.000000
VOLUME(WH2,V7)4.0000000.000000
VOLUME(WH2,V8)0.0000000.000000
VOLUME(WH3,V1)0.0000004.000000
VOLUME(WH3,V2)0.0000001.000000
VOLUME(WH3,V3)42.000000.000000
VOLUME(WH3,V4)0.0000002.000000
VOLUME(WH3,V5)0.0000006.000000
VOLUME(WH3,V6)0.0000003.000000
VOLUME(WH3,V7)0.0000007.000000
VOLUME(WH3,V8)0.0000003.000000
VOLUME(WH4,V1)0.0000005.000000
VOLUME(WH4,V2)0.0000004.000000
VOLUME(WH4,V3)0.0000005.000000
VOLUME(WH4,V4)0.0000007.000000
VOLUME(WH4,V5)0.0000007.000000
VOLUME(WH4,V6)14.000000.000000
VOLUME(WH4,V7)0.0000005.000000
VOLUME(WH4,V8)38.000000.000000
VOLUME(WH5,V1)41.000000.000000
VOLUME(WH5,V2)0.0000001.000000
VOLUME(WH5,V3)0.0000004.000000
VOLUME(WH5,V4)0.0000003.000000
VOLUME(WH5,V5)0.0000005.000000
VOLUME(WH5,V6)0.0000000.000000
VOLUME(WH5,V7)0.0000004.000000
VOLUME(WH5,V8)0.0000004.000000
VOLUME(WH6,V1)0.0000004.000000
VOLUME(WH6,V2)0.0000008.000000
VOLUME(WH6,V3)0.0000001.000000
VOLUME(WH6,V4)0.0000001.000000
VOLUME(WH6,V5)0.0000007.000000
VOLUME(WH6,V6)32.000000.000000
VOLUME(WH6,V7)0.0000003.000000
VOLUME(WH6,V8)0.0000003.000000
RowSlackorSurplusDualPrice
1473.0000-1.000000
219.000000.000000
30.0000000.000000
49.0000000.000000
50.0000000.000000
641.000000.000000
76.0000000.000000
839.000000.000000
90.0000001.000000
100.000000-2.000000
110.000000-3.000000
120.000000-1.000000
130.000000-2.000000
140.000000-2.000000
150.000000-1.000000
3、一般整数规划问题:
某服务部门各时段(每2h为一时段)需要的服务员人数见下表。
按规定,服务员连续工作8h(即四个时段)为一班。
现要求安排服务员的工作时间,使服务部门服务员总数最少。
时段
1
2
3
4
5
6
7
8
服务员最少数目
10
8
9
11
13
8
5
3
(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;
endsets
data:
!
每天所需的最少职员数;
required=10891113853;
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
Globaloptimalsolutionfound.
Objectivevalue:
23.00000
Totalsolveriterations:
3
VariableValueReducedCost
REQUIRED(X1)10.000000.000000
REQUIRED(X2)8.0000000.000000
REQUIRED(X3)9.0000000.000000
REQUIRED(X4)11.000000.000000
REQUIRED(X5)13.000000.000000
REQUIRED(X6)8.0000000.000000
REQUIRED(X7)5.0000000.000000
REQUIRED(X8)3.0000000.000000
START(X1)13.000000.000000
START(X2)0.0000000.000000
START(X3)0.0000000.000000
START(X4)2.0000000.000000
START(X5)8.0000000.000000
START(X6)0.0000000.000000
START(X7)0.0000000.000000
START(X8)0.0000000.000000
RowSlackorSurplusDualPrice
123.00000-1.000000
20.000000-1.000000
30.0000000.000000
44.0000000.000000
52.0000000.000000
60.000000-1.000000
77.0000000.000000
85.0000000.000000
97.0000000.000000
4、指派问题:
已知如下效率矩阵,求极大化指派问题。
B1
B2
B3
B4
B5
A1
4
8
7
15
12
A2
7
9
17
14
10
A3
6
9
12
8
7
A4
6
7
14
6
10
A5
6
9
12
10
6
(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;
);
!
每份工作只能有一个工人;
for(jobs(J):
sum(workers(I):
volume(I,J))=1;
);
data:
cost=4871512
79171410
691287
6714610
6912106;
enddata
end
答案
Globaloptimalsolutionfound.
Objectivevalue:
34.00000
Totalsolveriterations:
10
VariableValueReducedCost
COST(W1,J1)4.0000000.000000
COST(W1,J2)8.0000000.000000
COST(W1,J3)7.0000000.000000
COST(W1,J4)15.000000.000000
COST(W1,J5)12.000000.000000
COST(W2,J1)7.0000000.000000
COST(W2,J2)9.0000000.000000
COST(W2,J3)17.000000.000000
COST(W2,J4)14.000000.000000
COST(W2,J5)10.000000.000000
COST(W3,J1)6.0000000.000000
COST(W3,J2)9.0000000.000000
COST(W3,J3)12.000000.000000
COST(W3,J4)8.0000000.000000
COST(W3,J5)7.0000000.000000
COST(W4,J1)6.0000000.000000
COST(W4,J2)7.0000000.000000
COST(W4,J3)