运筹学 实验报告.docx
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运筹学 实验报告.docx
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运筹学实验报告
运筹学
实验报告
姓名:
系别:
学号:
班级:
指导老师:
注意事项:
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,天津大学出版社,2005
3.优化建模与LINDO/LINGO软件,清华大学出版社,2005
4.运筹学编写组主编,运筹学(修订版),清华大学出版社,1990
5.蓝伯雄主编,管理数学(下)—运筹学,清华大学出版社,1997
6.胡运权主编,运筹学习题集(修订版),清华大学出版社,1995
7.胡运权主编,运筹学教程(第二版),清华大学出版社,2003
四、实验内容
4.1线形规划问题:
4.1.1问题描述:
某工厂在计划期内要安排生产Ⅰ、Ⅱ两种产品,已知生产单位产品所需的设备台时及A、B两种原材料的消耗,如下表所示:
Ⅰ
Ⅱ
设备
1
2
8台时
原材料A
4
0
16kg
原材料B
0
4
12kg
4.1.2数学模型:
目标函数maxz=2x1+3x2
Stx1+2x2<=8
4x1<=16
4x2<=12
x1,x2>=0
4.1.3原始代码:
max=2*x1+3*x2
x1+2*x2<=8
4*x1<=16
4*x2<=12
4.1.4计算结果及分析(包括灵敏度分析):
Globaloptimalsolutionfound.
Objectivevalue:
14.00000
Totalsolveriterations:
2
VariableValueReducedCost
X14.0000000.000000
X22.0000000.000000
RowSlackorSurplusDualPrice
114.000001.000000
20.0000001.500000
30.0000000.1250000
44.0000000.000000
Rangesinwhichthebasisisunchanged:
ObjectiveCoefficientRanges
CurrentAllowableAllowable
VariableCoefficientIncreaseDecrease
X12.000000INFINITY0.5000000
X23.0000001.0000003.000000
RighthandSideRanges
RowCurrentAllowableAllowable
RHSIncreaseDecrease
28.0000002.0000004.000000
316.0000016.000008.000000
412.00000INFINITY4.000000
4.2运输问题:
4.2.1问题描述:
使用LINGO软件计算6个发点8个收点的最小费用运输问题。
产销单位运价如下表。
单
位销地
运
价
产地
B1
B2
B3
B4
B5
B6
B7
B8
产量
A1
6
2
6
7
4
2
5
9
60
A2
4
9
5
3
8
5
8
2
55
A3
5
2
1
9
7
4
3
3
51
A4
7
6
7
3
9
2
7
1
43
A5
2
3
9
5
7
2
6
5
41
A6
5
5
2
2
8
1
4
3
52
销量
35
37
22
32
41
32
43
38
4.2.2数学模型:
4.2.3原始代码:
model:
sets:
warehouses/wh1..wh6/:
capacity;
vendors/v1..v8/:
demand;
links(warehouses,vendors):
cost,volume;
endsets
min=@sum(links:
cost*volume);
@for(vendors(J):
@sum(warehouses(I):
volume(I,J))=demand(J));
@for(warehouses(I):
@sum(vendors(J):
volume(I,J))<=capacity(I));
data:
capacity=605551434152;
demand=3537223241324338;
cost=62674295
49538582
52197433
76739271
23957265
55228143;
enddata
end
4.2.4计算结果及分析:
Globaloptimalsolutionfound.
Objectivevalue:
664.0000
Totalsolveriterations:
20
VariableValueReducedCost
CAPACITY(WH1)60.000000.000000
CAPACITY(WH2)55.000000.000000
CAPACITY(WH3)51.000000.000000
CAPACITY(WH4)43.000000.000000
CAPACITY(WH5)41.000000.000000
CAPACITY(WH6)52.000000.000000
DEMAND(V1)35.000000.000000
DEMAND(V2)37.000000.000000
DEMAND(V3)22.000000.000000
DEMAND(V4)32.000000.000000
DEMAND(V5)41.000000.000000
DEMAND(V6)32.000000.000000
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)6.0000000.000000
COST(WH1,V4)7.0000000.000000
COST(WH1,V5)4.0000000.000000
COST(WH1,V6)2.0000000.000000
COST(WH1,V7)9.0000000.000000
COST(WH1,V8)5.0000000.000000
COST(WH2,V1)4.0000000.000000
COST(WH2,V2)9.0000000.000000
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)8.0000000.000000
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)9.0000000.000000
COST(WH3,V5)7.0000000.000000
COST(WH3,V6)4.0000000.000000
COST(WH3,V7)3.0000000.000000
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)3.0000000.000000
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)9.0000000.000000
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)5.0000000.000000
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)0.0000005.000000
VOLUME(WH1,V2)19.000000.000000
VOLUME(WH1,V3)0.0000005.000000
VOLUME(WH1,V4)0.0000007.000000
VOLUME(WH1,V5)41.000000.000000
VOLUME(WH1,V6)0.0000002.000000
VOLUME(WH1,V7)0.0000006.000000
VOLUME(WH1,V8)0.0000006.000000
VOLUME(WH2,V1)1.0000000.000000
VOLUME(WH2,V2)0.0000004.000000
VOLUME(WH2,V3)0.0000001.000000
VOLUME(WH2,V4)32.000000.000000
VOLUME(WH2,V5)0.0000001.000000
VOLUME(WH2,V6)0.0000002.000000
VOLUME(WH2,V7)0.0000002.000000
VOLUME(WH2,V8)0.0000000.000000
VOLUME(WH3,V1)0.0000004.000000
VOLUME(WH3,V2)11.000000.000000
VOLUME(WH3,V3)0.0000000.000000
VOLUME(WH3,V4)0.0000009.000000
VOLUME(WH3,V5)0.0000003.000000
VOLUME(WH3,V6)0.0000004.000000
VOLUME(WH3,V7)40.000000.000000
VOLUME(WH3,V8)0.0000004.000000
VOLUME(WH4,V1)0.0000004.000000
VOLUME(WH4,V2)0.0000002.000000
VOLUME(WH4,V3)0.0000004.000000
VOLUME(WH4,V4)0.0000001.000000
VOLUME(WH4,V5)0.0000003.000000
VOLUME(WH4,V6)5.0000000.000000
VOLUME(WH4,V7)0.0000002.000000
VOLUME(WH4,V8)38.000000.000000
VOLUME(WH5,V1)34.000000.000000
VOLUME(WH5,V2)7.0000000.000000
VOLUME(WH5,V3)0.0000007.000000
VOLUME(WH5,V4)0.0000004.000000
VOLUME(WH5,V5)0.0000002.000000
VOLUME(WH5,V6)0.0000001.000000
VOLUME(WH5,V7)0.0000002.000000
VOLUME(WH5,V8)0.0000005.000000
VOLUME(WH6,V1)0.0000003.000000
VOLUME(WH6,V2)0.0000002.000000
VOLUME(WH6,V3)22.000000.000000
VOLUME(WH6,V4)0.0000001.000000
VOLUME(WH6,V5)0.0000003.000000
VOLUME(WH6,V6)27.000000.000000
VOLUME(WH6,V7)3.0000000.000000
VOLUME(WH6,V8)0.0000003.000000
RowSlackorSurplusDualPrice
1664.0000-1.000000
20.000000-4.000000
30.000000-5.000000
40.000000-4.000000
50.000000-3.000000
60.000000-7.000000
70.000000-3.000000
80.000000-6.000000
90.000000-2.000000
100.0000003.000000
1122.000000.000000
120.0000003.000000
130.0000001.000000
140.0000002.000000
150.0000002.000000
Rangesinwhichthebasisisunchanged:
ObjectiveCoefficientRanges
CurrentAllowableAllowable
VariableCoefficientIncreaseDecrease
VOLUME(WH1,V1)6.000000INFINITY5.000000
VOLUME(WH1,V2)2.0000002.0000001.000000
VOLUME(WH1,V3)6.000000INFINITY5.000000
VOLUME(WH1,V4)7.000000INFINITY7.000000
VOLUME(WH1,V5)4.0000001.000000INFINITY
VOLUME(WH1,V6)2.000000INFINITY2.000000
VOLUME(WH1,V7)9.000000INFINITY6.000000
VOLUME(WH1,V8)5.000000INFINITY6.000000
VOLUME(WH2,V1)4.0000000.01.000000
VOLUME(WH2,V2)9.000000INFINITY4.000000
VOLUME(WH2,V3)5.000000INFINITY1.000000
VOLUME(WH2,V4)3.0000001.000000INFINITY
VOLUME(WH2,V5)8.000000INFINITY1.000000
VOLUME(WH2,V6)5.000000INFINITY2.000000
VOLUME(WH2,V7)8.000000INFINITY2.000000
VOLUME(WH2,V8)2.000000INFINITY0.0
VOLUME(WH3,V1)5.000000INFINITY4.000000
VOLUME(WH3,V2)2.0000001.0000000.0
VOLUME(WH3,V3)1.000000INFINITY0.0
VOLUME(WH3,V4)9.000000INFINITY9.000000
VOLUME(WH3,V5)7.000000INFINITY3.000000
VOLUME(WH3,V6)4.000000INFINITY4.000000
VOLUME(WH3,V7)3.0000000.01.000000
VOLUME(WH3,V8)3.000000INFINITY4.000000
VOLUME(WH4,V1)7.000000INFINITY4.000000
VOLUME(WH4,V2)6.000000INFINITY2.000000
VOLUME(WH4,V3)7.000000INFINITY4.000000
VOLUME(WH4,V4)3.000000INFINITY1.000000
VOLUME(WH4,V5)9.000000INFINITY3.000000
VOLUME(WH4,V6)2.0000001.0000000.0
VOLUME(WH4,V7)7.000000INFINITY2.000000
VOLUME(WH4,V8)1.0000000.0INFINITY
VOLUME(WH5,V1)2.0000001.0000000.0
VOLUME(WH5,V2)3.0000000.01.000000
VOLUME(WH5,V3)9.000000INFINITY7.000000
VOLUME(WH5,V4)5.000000INFINITY4.000000
VOLUME(WH5,V5)7.000000INFINITY2.000000
VOLUME(WH5,V6)2.000000INFINITY1.000000
VOLUME(WH5,V7)6.000000INFINITY2.000000
VOLUME(WH5,V8)5.000000INFINITY5.000000
VOLUME(WH6,V1)5.000000INFINITY3.000000
VOLUME(WH6,V2)5.000000INFINITY2.000000
VOLUME(WH6,V3)2.0000000.0INFINITY
VOLUME(WH6,V4)2.000000INFINITY1.000000
VOLUME(WH6,V5)8.000000INFINITY3.000000
VOLUME(WH6,V6)1.0000000.01.000000
VOLUME(WH6,V7)4.0000001.0000000.0
VOLUME(WH6,V8)3.000000INFINITY3.000000
RighthandSideRanges
RowCurrentAllowableAllowable
RHSIncreaseDecrease
235.0000022.000001.000000
337.0000022.000001.000000
422.000003.0000001.000000
532.0000022.0000032.00000
641.0000019.000001.000000
732.000003.0000001.000000
843.0000011.000001.000000
938.000003.0000001.000000
1060.000001.00000019.00000
1155.00000INFINITY22.00000
1251.000001.00000011.00000
1343.000001.0000003.000000
1441.000001.00000022.00000
1552.000001.0000003.000000
4.3一般整数规划问题:
4.3.1问题描述:
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
4.3.2数学模型:
目标函数minz=x1+x2+x3+x4+x5+x6+x7+x8
Stx6+x7+x8+x1>=10
x7+x8+x1+x2>=8
x8+x1+x2+x3>=9
x1+x2+x3+x4>=11
x2+x3+x4+x5>=13
x3+x4+x
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