运筹学例题Word文件下载.docx
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运筹学例题Word文件下载.docx
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Globaloptimalsolutionfound.
Objectivevalue:
272.0000
Totalsolveriterations:
2
Variable
Value
ReducedCost
DESKS
0.000000
6.000000
TABLES
1.600000
0.000000
CHAIRS
11.20000
Row
SlackorSurplus
DualPrice
1
272.0000
1.000000
2
25.20000
3
12.00000
4
4.000000
5
3.400000
运输规划
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
8
2
6
7
4
5
9
80
A2
3
55
A3
1
57
A4
11
43
A5
41
A6
52
销量
35
37
25
32
36
38
使用LINGO软件,编制程序如下:
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
638.0000
16
CAPACITY(WH1)
80.00000
CAPACITY(WH2)
55.00000
CAPACITY(WH3)
57.00000
CAPACITY(WH4)
43.00000
CAPACITY(WH5)
41.00000
CAPACITY(WH6)
52.00000
DEMAND(V1)
35.00000
DEMAND(V2)
37.00000
DEMAND(V3)
25.00000
DEMAND(V4)
32.00000
DEMAND(V5)
DEMAND(V6)
36.00000
DEMAND(V7)
DEMAND(V8)
38.00000
COST(WH1,V1)
8.000000
COST(WH1,V2)
2.000000
COST(WH1,V3)
6.000000
COST(WH1,V4)
7.000000
COST(WH1,V5)
4.000000
COST(WH1,V6)
COST(WH1,V7)
9.000000
COST(WH1,V8)
5.000000
COST(WH2,V1)
COST(WH2,V2)
COST(WH2,V3)
COST(WH2,V4)
3.000000
COST(WH2,V5)
COST(WH2,V6)
COST(WH2,V7)
COST(WH2,V8)
COST(WH3,V1)
COST(WH3,V2)
COST(WH3,V3)
1.000000
COST(WH3,V4)
COST(WH3,V5)
COST(WH3,V6)
COST(WH3,V7)
COST(WH3,V8)
COST(WH4,V1)
COST(WH4,V2)
COST(WH4,V3)
COST(WH4,V4)
COST(WH4,V5)
11.00000
COST(WH4,V6)
COST(WH4,V7)
COST(WH4,V8)
COST(WH5,V1)
COST(WH5,V2)
COST(WH5,V3)
COST(WH5,V4)
COST(WH5,V5)
COST(WH5,V6)
COST(WH5,V7)
COST(WH5,V8)
COST(WH6,V1)
COST(WH6,V2)
COST(WH6,V3)
COST(WH6,V4)
COST(WH6,V5)
COST(WH6,V6)
COST(WH6,V7)
COST(WH6,V8)
VOLUME(WH1,V1)
VOLUME(WH1,V2)
VOLUME(WH1,V3)
3.000000
VOLUME(WH1,V4)
VOLUME(WH1,V5)
VOLUME(WH1,V6)
VOLUME(WH1,V7)
VOLUME(WH1,V8)
VOLUME(WH2,V1)
2.000000
VOLUME(WH2,V2)
7.000000
VOLUME(WH2,V3)
VOLUME(WH2,V4)
14.00000
VOLUME(WH2,V5)
VOLUME(WH2,V6)
VOLUME(WH2,V7)
VOLUME(WH2,V8)
VOLUME(WH3,V1)
5.000000
VOLUME(WH3,V2)
VOLUME(WH3,V3)
VOLUME(WH3,V4)
8.000000
VOLUME(WH3,V5)
VOLUME(WH3,V6)
VOLUME(WH3,V7)
VOLUME(WH3,V8)
VOLUME(WH4,V1)
VOLUME(WH4,V2)
VOLUME(WH4,V3)
VOLUME(WH4,V4)
VOLUME(WH4,V5)
VOLUME(WH4,V6)
VOLUME(WH4,V7)
VOLUME(WH4,V8)
VOLUME(WH5,V1)
VOLUME(WH5,V2)
VOLUME(WH5,V3)
VOLUME(WH5,V4)
VOLUME(WH5,V5)
VOLUME(WH5,V6)
VOLUME(WH5,V7)
VOLUME(WH5,V8)
VOLUME(WH6,V1)
VOLUME(WH6,V2)
VOLUME(WH6,V3)
VOLUME(WH6,V4)
13.00000
VOLUME(WH6,V5)
VOLUME(WH6,V6)
28.00000
VOLUME(WH6,V7)
VOLUME(WH6,V8)
638.0000
-1.000000
-2.000000
-3.000000
6
-4.000000
7
8
-5.000000
9
10
11
12
13
14
15
整数规划
整数规划篮球比赛问题
在高校篮球联赛中,我校男子篮球队要从8名队员中选择平均身高最高的出场阵容,队员的号码、身高及擅长的位置如右表3:
同时,要求出场阵容满足以下条件:
(1)中锋最多只能上场一个;
(2)至少有一名后卫;
(3)如果1号队员和4号队员都上场,则6号队员不能出场;
(4)2号队员和6号队员必须保留一个不出场,问应当选择哪5名队员上场,才能使出场队员平均身高最高?
表3
队员
身高(m)
位置
1.92
中锋
1.90
1.88
前锋
1.86
1.85
1.83
后卫
1.80
1.78
试写出上述问题的数学模型,并求解。
解:
(1)
模型建立
设
表示第
号队员上场,
号队员不上场,其中,
,其中,
号队员的身高,
。
则该问题的数学模型为:
其中,
MAX=(1.92*X1+1.90*X2+1.88*X3+1.86*X4+1.85*X5+1.83*X6+1.80*X7+1.78*X8)/5;
X1+X2+X3+X4+X5+X6+X7+X8=5;
X1+X2<
=1;
X6+X7+X8>
X1+X4+X6<
=2;
X2+X6<
@BIN(X1);
@BIN(X2);
@BIN(X3);
@BIN(X4);
@BIN(X5);
@BIN(X6);
@BIN(X7);
@BIN(X8);
END
1.862000
Objectivebound:
Infeasibilities:
Extendedsolversteps:
0
X1
-0.3840000
X2
-0.3800000
X3
-0.3760000
X4
-0.3720000
X5
-0.3700000
X6
-0.3660000
X7
-0.3600000
X8
-0.3560000
1.862000
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