运筹学实验报告lingo软件的使用习题代码Word格式文档下载.docx
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运筹学实验报告lingo软件的使用习题代码Word格式文档下载.docx
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9*x1+8*x2<
=12;
7*x1+11*x2<
=24;
9*x1+11*x2<
=13;
x1>
=0;
x2>
(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
5
55
A2
3
8
47
A3
1
42
A4
52
A5
41
A6
32
销量
60
51
43
38
(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
473.0000
Infeasibilities:
0.000000
9
ModelClass:
LP
Totalvariables:
48
Nonlinearvariables:
0
Integervariables:
Totalconstraints:
15
Nonlinearconstraints:
Totalnonzeros:
144
Nonlinearnonzeros:
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
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
服务员最少数目
10
11
13
time/x1..x8/:
required,start;
每天所需的最少职员数;
required=10891113853;
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));
结果
23.00000
3
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
123.00000-1.000000
20.000000-1.000000
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。
15
12
17
14
5个工人,5个工作的分配问题;
workers/w1..w5/;
jobs/j1..j5/;
links(workers,jobs):
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):
cost=4871512
79171410
691287
6714610
6912106;
Globaloptimalsolutionfound.
34.00000
10
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(
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