1、P94，例3.4 选址问题目录题目1第一步，旧址基础上只求运量的程序1第二步，旧址基础上选择新址的NLP程序2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
2、,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;x,y=5,1,2,7;enddatainit:!initial locations for the supply（初始点）;endinit!Objective function（目标）;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
4、运行可得到全局最优解 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第二步，
5、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/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:!i
6、nitial 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)
7、; );!for(supply: free(x); !free(Y); !);for(supply: bnd(0.5,X,8.75); bnd(0.75,Y,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) 5.695966 0.000000 X( 2) 7.250000 -0.3212138E-05
8、Y( 1) 4.928558 0.000000 Y( 2) 7.750000 -0.1009767E-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: 85.26604 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
9、( 2) 7.750000 -0.1114154E-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: 16121 Model Title: Location Problem Variable Value Reduced Cost X( 1) 3.254883 0.000000 X( 2) 7.250000 0.8084079E-07 Y( 1) 5.652332 0.000000 Y( 2) 7.750000 0.2675276E-06
