數(shù)學(xué)建模中選址問題(Lingo程序)

1、精選優(yōu)質(zhì)文檔-傾情為你奉上P94，例3.4 選址問題目錄題目6個(gè)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(gè)臨時(shí)料場，日儲(chǔ)量各有20t，如何安排運(yùn)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(yùn)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(需求點(diǎn)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(diǎn)）;endinit!Objective function（目標(biāo)）;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); );END運(yùn)行可得到全局最優(yōu)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，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

5、/1.2/:x,y,e; link(demand,supply):c;endsetsdata:!locations for the demand(需求點(diǎn)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（初始點(diǎn)）;!x,y=5,1,2,7;endinit!Objective function（目標(biāo)）;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、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. 0. X( 2) 7. -0.E-05 Y( 1) 4. 0. Y( 2) 7. -0.E-05如果不要初始數(shù)據(jù)，可能計(jì)算時(shí)間更長，本例的結(jié)果更優(yōu)：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如果想求全局最優(yōu)解，結(jié)果將會(huì)出現(xiàn)如下錯(cuò)誤版本限制，但會(huì)得到一個(gè)的局部最優(yōu)解，結(jié)果與不要初始數(shù)據(jù)時(shí)算出的結(jié)果一樣。 Local optimal solution found. Objective value: 85.26604 Extended solver steps: 18 Total solver iterations: