数学建模中选址问题(Lingo程序)

P94，例选址问题

目录

题目......................................................... 错误!未定义书签。

第一步，旧址基础上只求运量的ＬＰ程序......................... 错误!未定义书签。

第二步，旧址基础上选择新址的NLP程序......................... 错误!未定义书签。题目

6个工地的地址(坐标表示，距离单位KM)及水泥用量(单位：吨)如下表，而在P(5,1)及Q(2,7)处有两个临时料场，日储量各有20t，如何安排运输，可使总的吨公里数最小？

新料场应选何处能节约多少吨公里数

第一步，旧址基础上只求运量的ＬＰ程序

MODEL:

Title Location Problem;

sets:

demand/1..6/:a,b,d;

supply/1..2/:x,y,e;

link(demand,supply):c;

endsets

data:

!locations for the demand(需求点的位置);

a=,,,,3,;

b=,,,5,,;

!quantities of the demand and supply（供需量）;

d=3,5,4,7,6,11; e=20,20;

x,y=5,1,2,7;

enddata

init:

!initial locations for the supply（初始点）;

endinit

!Objective function（目标）;

[OBJ] min=@sum(link(i,j): c(i,j)*((x(j)-a(i))^2+(y(j)-b(i))^2)^(1/2) );

!demand constraints（需求约束）;

@for(demand(i):[DEMAND_CON] @sum(supply(j):c(i,j)) =d(i););

!supply constraints（供应约束）;

@for(supply(i):[SUPPLY_CON] @sum(demand(j):c(j,i)) <=e(i); );

!@for(supply: @free(x);!@free(Y);!);

@for(supply: @bnd,X,; @bnd,Y,; );

END

运行可得到全局最优解

Global optimal solution found.

Objective value:

Total solver iterations: 1

Model Title: Location Problem

Variable Value Reduced Cost

X( 1)

X( 2)

Y( 1)

Y( 2)

E( 1)

E( 2)

第二步，旧址基础上选择新址的NLP程序

!选新址的ＮＬＰ程序;

MODEL:

Title Location Problem;

sets:

demand/1..6/:a,b,d;

supply/1..2/:x,y,e;

link(demand,supply):c;

endsets

data:

!locations for the demand(需求点的位置);

a=,,,,3,;

b=,,,5,,;

!quantities of the demand and supply（供需量）;

d=3,5,4,7,6,11; e=20,20;

enddata

init:

!initial locations for the supply（初始点）;

!x,y=5,1,2,7;

endinit

!Objective function（目标）;

[OBJ] min=@sum(link(i,j): c(i,j)*((x(j)-a(i))^2+(y(j)-b(i))^2)^(1/2) );

!demand constraints（需求约束）;

@for(demand(i):[DEMAND_CON] @sum(supply(j):c(i,j)) =d(i);); !supply constraints（供应约束）;

@for(supply(i):[SUPPLY_CON] @sum(demand(j):c(j,i)) <=e(i); );

!@for(supply: @free(x);!@free(Y);!);

@for(supply: @bnd,X,; @bnd,Y,; );

END

求解结果

只得到局部最优解

Local optimal solution found.

Objective value:

Total solver iterations: 67

Model Title: Location Problem

Variable Value Reduced Cost

X( 1)

X( 2)

Y( 1)

Y( 2)

如果不要初始数据，可能计算时间更长，本例的结果更优：

Local optimal solution found.

Objective value:

Total solver iterations: 29

Model Title: Location Problem

Variable Value Reduced Cost

X( 1)