數(shù)學(xué)建模中選址問題Lingo程序

1、P94，例3.4 選址問題目錄題目1第一步，舊址基礎(chǔ)上只求運量的程序1第二步，舊址基礎(chǔ)上選擇新址的NLP程序2題目6個工地的地址(坐標(biāo)表示，距離單位KM)及水泥用量(單位：噸)如下表，而在P(5,1)及Q(2,7)處有兩個臨時料場，日儲量各有20t，如何安排運輸，可使總的噸公里數(shù)最小?新料場應(yīng)選何處？能節(jié)約多少噸公里數(shù)？123456A1.258.750.55.7537.25B1.250.754.7556.57.75D3547611第一步，舊址基礎(chǔ)上只求運量的程序MODEL:Title Location Problem;sets: demand/1.6/:a,b,d; supply/1.2/:x

2、,y,e; link(demand,supply):c;endsetsdata:!locations for the demand(需求點的位置);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（初始點）;endinit!Objective function（目標(biāo)）;OBJ min=su

3、m(link(i,j): c(i,j)*(x(j)-a(i)2+(y(j)-b(i)2)(1/2) );!demand constraints（需求約束）;for(demand(i):DEMAND_CON sum(supply(j):c(i,j) =d(i););!supply constraints（供應(yīng)約束）;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); )

4、;END運行可得到全局最優(yōu)解 Global optimal solution found. Objective value: 136.2275 Total solver iterations: 1 Model Title: Location Problem Variable Value Reduced Cost X( 1) 5.000000 0.000000 X( 2) 2.000000 0.000000 Y( 1) 1.000000 0.000000 Y( 2) 7.000000 0.000000 E( 1) 20.00000 0.000000 E( 2) 20.00000 0.000000

5、第二步，舊址基礎(chǔ)上選擇新址的NLP程序!選新址的程序;MODEL:Title Location Problem;sets: demand/1.6/:a,b,d; supply/1.2/:x,y,e; link(demand,supply):c;endsetsdata:!locations for the demand(需求點的位置);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;enddataini

6、t:!initial locations for the supply（初始點）;!x,y=5,1,2,7;endinit!Objective function（目標(biāo)）;OBJ min=sum(link(i,j): c(i,j)*(x(j)-a(i)2+(y(j)-b(i)2)(1/2) );!demand constraints（需求約束）;for(demand(i):DEMAND_CON sum(supply(j):c(i,j) =d(i););!supply constraints（供應(yīng)約束）;for(supply(i):SUPPLY_CON sum(demand(j):c(j,i) &

7、lt;=e(i); );!for(supply: free(x); !free(Y); !);for(supply: bnd(0.5,X,8.75); bnd(0.75,Y,7.75); );END求解結(jié)果只得到局部最優(yōu)解 Local optimal solution found. Objective value: 89.88347 Total solver iterations: 67 Model Title: Location Problem Variable Value Reduced Cost X( 1) 5.695966 0.000000 X( 2) 7.250000 -0.3212

8、138E-05 Y( 1) 4.928558 0.000000 Y( 2) 7.750000 -0.1009767E-05如果不要初始數(shù)據(jù)，可能計算時間更長，本例的結(jié)果更優(yōu)：Local optimal solution found. Objective value: 85.26604 Total solver iterations: 29 Model Title: Location Problem Variable Value Reduced Cost X( 1) 3.254883 0.000000 X( 2) 7.250000 -0.2958858E-05 Y( 1) 5.652332 0.000000 Y( 2) 7.750000 -0.1114154E-05如果想求全局最優(yōu)解，結(jié)果將會出現(xiàn)如下錯誤版本限制，但會得到一個的局部最優(yōu)解，結(jié)果與不要初始數(shù)據(jù)時算出的結(jié)果一樣。 Local optimal solution found. Objective value: 85.26604 Extended solver steps: 18 Total solver iterations: 16121 Model Title: Location Pro