【Lingo】运输网络流 1stTest

最新推荐文章于 2022-05-02 12:04:57 发布

糖果天王

最新推荐文章于 2022-05-02 12:04:57 发布

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CC 4.0 BY-SA版权

本文链接：https://blog.youkuaiyun.com/okcd00/article/details/17265957

本文探讨了一种解决地点分配问题的优化算法，通过最小化需求与供应之间的距离来实现全局最优解。分析了需求与供应的量，确定了各点的位置限制，并通过数学模型实现了目标函数和约束条件的设定。最终，通过求解过程找到了最优位置，显著减少了需求与供应之间的距离。

MODEL:
Title Location Problem;
sets:
	demand/1..6/:a,b,d;
	supply/1..2/:x,y,e;
	link(demand,supply):c;  !'()' Not '{}' 
! 'link' is a combination of two or more sets;
endsets

data:
!locations for the demand();
a=1.25,8.75,0.5 ,5.75,3   ,7.25;
b=1.25,0.75,4.75,5   ,6.5 ,7.75;
!quantities of the demand and supply;
d=3, 5, 4, 7, 6, 11; e=20, 20;
enddata

init:
!initial locations for the supply;
x,y=5,1,2,7; ! P(5,1)	Q(2,7);
endinit	!give values by column;

!Objective function;
[OBJ] min=@sum(link(i,j):c(i,j)*((x(j)-a(i))^2+(y(j)-b(i))^2)^(1/2));
!Demand limit(constraints);
@for(demand(i):[DEMAND_CON] @sum(supply(j):c(i,j))=d(i);); ![DEMAND_CON]为添加关注名，在LingoSolveReport里将专门列出数据;
!Supply limit(constraints);
@for(supply(i):[SUPPLY_CON] @sum(demand(j):c(j,i))<=e(i););
@for(supply:@bnd(0.5,X,8.75); @bnd(0.75,Y,7.75););  !bnd represent range 0.5<=x<=8.75;
END

Solve 全局最优解：

  Local optimal solution found.
  Objective value:                              85.26604
  Infeasibilities:                              0.000000
  Total solver iterations:                            61


  Model Title: Location Problem

                       Variable           Value        Reduced Cost
                          A( 1)        1.250000            0.000000
                          A( 2)        8.750000            0.000000
                          A( 3)       0.5000000            0.000000
                          A( 4)        5.750000            0.000000
                          A( 5)        3.000000            0.000000
                          A( 6)        7.250000            0.000000
                          B( 1)        1.250000            0.000000
                          B( 2)       0.7500000            0.000000
                          B( 3)        4.750000            0.000000
                          B( 4)        5.000000            0.000000
                          B( 5)        6.500000            0.000000
                          B( 6)        7.750000            0.000000
                          D( 1)        3.000000            0.000000
                          D( 2)        5.000000            0.000000
                          D( 3)        4.000000            0.000000
                          D( 4)        7.000000            0.000000
                          D( 5)        6.000000            0.000000
                          D( 6)        11.00000            0.000000
                          X( 1)        3.254883            0.000000
                          X( 2)        7.250000           0.6335133E-06
                          Y( 1)        5.652332            0.000000
                          Y( 2)        7.750000           0.5438639E-06
                          E( 1)        20.00000            0.000000
                          E( 2)        20.00000            0.000000
                       C( 1, 1)        3.000000            0.000000
                       C( 1, 2)        0.000000            4.008540
                       C( 2, 1)        0.000000           0.2051358
                       C( 2, 2)        5.000000            0.000000
                       C( 3, 1)        4.000000            0.000000
                       C( 3, 2)        0.000000            4.487750
                       C( 4, 1)        7.000000            0.000000
                       C( 4, 2)        0.000000           0.5535090
                       C( 5, 1)        6.000000            0.000000
                       C( 5, 2)        0.000000            3.544853
                       C( 6, 1)        0.000000            4.512336
                       C( 6, 2)        11.00000            0.000000

                            Row    Slack or Surplus      Dual Price
                            OBJ        85.26604           -1.000000
                 DEMAND_CON( 1)        0.000000           -4.837363
                 DEMAND_CON( 2)        0.000000           -7.158911
                 DEMAND_CON( 3)        0.000000           -2.898893
                 DEMAND_CON( 4)        0.000000           -2.578982
                 DEMAND_CON( 5)        0.000000          -0.8851584
                 DEMAND_CON( 6)        0.000000            0.000000
                 SUPPLY_CON( 1)        0.000000            0.000000
                 SUPPLY_CON( 2)        4.000000            0.000000