数学建模中选址问题(Lingo程序)

1、精选优质文档-倾情为你奉上P94，例3.4 选址问题目录题目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？123456A1.258.750.55.7537.25B1.250.754.7556.57.75D3547611第一步，旧址基础上只求运量的程序MODEL:Title Location Problem;sets: demand/1.6/:a,b,d; supply/1.2/:x,y,e; link(demand,supply):c

2、;endsetsdata:!locations for the demand(需求点的位置);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（供需量）;d=3,5,4,7,6,11; e=20,20;x,y=5,1,2,7;enddatainit:!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

3、(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(0.5,X,8.75); bnd(0.75,Y,7.75); );END运行可得到全局最优解 Global optim

4、al solution found. Objective value: 136.2275 Total solver iterations: 1 Model Title: Location Problem Variable Value Reduced Cost X( 1) 5. 0. X( 2) 2. 0. Y( 1) 1. 0. Y( 2) 7. 0. E( 1) 20.00000 0. E( 2) 20.00000 0.第二步，旧址基础上选择新址的NLP程序!选新址的程序;MODEL:Title Location Problem;sets: demand/1.6/:a,b,d; supply

5、/1.2/:x,y,e; link(demand,supply):c;endsetsdata:!locations for the demand(需求点的位置);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（供需量）;d=3,5,4,7,6,11; e=20,20;enddatainit:!initial locations for the supply（初始点）;!x,y=5,1,2,7;endinit!Objective function（目标）;OB

6、J 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(0.5,X,8.75); bnd(0.75,Y,

7、7.75); );END求解结果只得到局部最优解 Local optimal solution found. Objective value: 89.88347 Total solver iterations: 67 Model Title: Location Problem Variable Value Reduced Cost X( 1) 5. 0. X( 2) 7. -0.E-05 Y( 1) 4. 0. Y( 2) 7. -0.E-05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: 85.

8、26604 Total solver iterations: 29 Model Title: Location Problem Variable Value Reduced Cost X( 1) 3. 0. X( 2) 7. -0.E-05 Y( 1) 5. 0. Y( 2) 7. -0.E-05如果想求全局最优解，结果将会出现如下错误版本限制，但会得到一个的局部最优解，结果与不要初始数据时算出的结果一样。 Local optimal solution found. Objective value: 85.26604 Extended solver steps: 18 Total solver iterations: