博客

嵌套@for或嵌套@sum

对集合中的i单独求和，例如集合Xij，求Xi1+Xi2+Xi3…+Xin

sets:
r/1..5:y;
c/1..5/:;
link(r,c):x;
endsets
@for(r(i):y(i)=@sum(c(j):x(i,j)));

for instance

model:

sets:
fac/1..65/:y;
plant/1..65/:b,p;
coo(fac,plant):d,x;
endsets

data:
p=10,12,18,6,10,15,4,8,7,11,13,11,16,11,8,9,22,14,8,7,10,15,28,18,13,12,23,29,13,15,16,27,6,3,4,8,9,13,12,13,15,8,15,8,5,11,16,15,13,6,9,7,20,12,5,7,9,12,15,23,7,9,14,15,12;
d=0,23,24,64,32,50,40,82,41,50,73,49,61,56,71,35,69,18,35,30,60,35,28,50,3,42,52,56,55,64,75,73,41,59,59,31,22,48,13,26,17,13,17,16,27,37,47,53,59,55,63,45,63,42,15,55,31,42,30,33,74,51,49,60,26
23,0,27,49,24,27,18,67,18,35,51,27,39,41,53,47,61,41,31,15,52,12,17,32,26,50,48,48,47,56,54,55,23,41,41,13,7,30,10,18,33,36,40,39,50,60,63,58,51,63,48,27,41,34,14,33,8,38,53,25,56,33,31,38,38
24,27,0,40,51,30,16,58,29,26,49,25,37,32,74,20,45,19,11,42,36,15,44,53,27,30,28,32,31,40,51,56,44,62,62,40,34,51,37,45,41,37,34,40,41,42,43,38,35,43,39,54,39,18,39,31,19,18,27,9,77,47,52,36,11
64,49,40,0,73,52,31,18,51,14,26,22,14,8,46,47,25,59,37,64,33,37,66,58,67,49,47,36,28,35,11,20,52,34,49,62,56,59,59,67,81,77,74,80,68,69,62,57,38,62,22,65,36,22,63,32,41,37,54,31,38,48,44,33,51
32,24,51,73,0,47,42,82,37,59,68,51,63,65,66,67,85,50,55,20,76,36,41,45,35,74,72,72,71,80,77,68,36,54,54,26,17,41,19,6,21,45,49,48,59,69,79,82,75,87,72,35,65,58,38,57,32,62,62,49,69,46,44,62,58
50,27,30,52,47,0,21,70,10,38,50,30,42,44,55,50,64,49,34,38,55,15,44,34,53,53,51,51,50,59,57,57,25,43,43,21,30,32,37,41,56,63,64,66,71,72,66,61,54,66,51,35,43,37,41,35,19,41,57,28,58,28,33,41,41
40,18,16,31,42,21,0,49,20,17,33,9,21,23,65,30,43,35,13,33,34,6,35,44,43,32,30,30,29,38,36,40,35,53,53,31,25,42,28,36,51,53,50,56,51,52,45,40,33,45,30,45,23,16,32,15,10,20,37,7,68,38,43,20,27
82,67,58,18,82,70,49,0,61,32,22,40,32,26,40,65,43,77,55,73,51,55,84,52,85,67,65,54,46,53,24,15,46,28,43,56,65,53,74,76,91,95,92,98,86,87,80,75,56,80,40,59,33,40,81,41,59,55,72,49,20,44,38,36,69
41,18,29,51,37,10,20,61,0,37,40,29,41,43,45,49,63,48,33,28,54,14,35,24,44,52,50,50,49,58,56,47,15,33,33,11,20,22,28,31,46,54,58,57,68,71,65,60,53,65,50,25,33,36,32,25,10,40,56,27,48,18,23,36,40
50,35,26,14,59,38,17,32,37,0,24,8,12,6,57,33,26,45,23,50,19,23,52,60,53,35,33,22,14,23,25,31,51,45,60,48,42,58,45,53,67,63,60,66,54,55,48,43,24,48,13,62,22,8,49,18,27,23,40,17,52,41,49,19,37
73,51,49,26,68,50,33,22,40,24,0,24,12,18,33,57,38,68,46,59,43,39,68,41,76,59,57,46,38,47,16,7,32,21,36,42,51,39,60,62,77,86,83,89,78,79,72,67,48,72,32,45,11,32,65,19,43,47,64,40,36,22,30,14,60
49,27,25,22,51,30,9,40,29,8,24,0,12,14,57,39,34,44,22,42,27,15,44,52,52,41,39,30,22,31,27,31,43,45,60,40,34,50,37,45,60,62,59,65,60,61,54,49,32,54,21,54,14,16,41,10,19,29,46,16,60,33,41,11,36
61,39,37,14,63,42,21,32,41,12,12,12,0,6,45,45,26,56,34,54,31,27,56,53,64,47,45,34,26,35,15,19,44,33,48,52,46,51,49,57,72,74,71,77,66,67,60,55,36,60,20,57,23,20,53,22,31,35,52,28,48,34,42,23,48
56,41,32,8,65,44,23,26,43,6,18,14,6,0,51,39,20,51,29,56,25,29,58,59,59,41,39,28,20,29,19,25,50,39,54,54,48,57,51,59,73,69,66,72,60,61,54,49,30,54,14,63,28,14,55,24,33,29,46,23,46,40,48,25,43
71,53,74,46,66,55,65,40,45,57,33,57,45,51,0,90,71,89,78,57,76,59,70,28,74,92,90,79,71,80,35,26,30,12,27,40,49,37,58,60,75,84,88,87,98,108,105,100,81,105,65,43,44,65,67,52,55,80,97,72,27,30,22,47,85
35,47,20,47,67,50,30,65,49,33,57,39,45,39,90,0,46,17,17,62,43,35,63,73,32,10,20,33,38,47,58,64,64,78,82,60,54,71,48,61,52,42,31,39,21,22,23,21,42,23,46,74,53,25,50,45,39,10,7,23,85,67,72,50,9
74,61,50,25,85,64,43,43,63,26,38,34,26,20,71,57,0,69,47,76,24,49,78,79,77,59,57,39,19,10,36,45,70,59,74,74,68,77,71,79,91,87,84,90,78,79,72,67,29,72,25,83,48,32,75,44,53,47,64,41,63,60,68,45,61
18,41,19,59,50,49,35,77,48,45,68,44,56,51,89,17,63,0,30,48,55,34,46,68,15,24,37,50,50,59,70,75,59,77,77,49,40,66,31,44,35,25,15,23,25,27,37,35,54,37,58,63,58,37,33,50,38,27,12,28,92,66,67,55,8
35,31,11,37,55,34,13,55,33,23,46,22,34,29,78,17,42,30,0,46,33,19,48,57,38,19,17,29,28,37,48,53,48,66,66,44,38,55,41,49,52,48,45,51,38,39,32,27,32,32,36,58,36,15,45,28,23,7,24,6,75,51,56,33,22
30,15,42,64,20,38,33,73,28,50,59,42,54,56,57,62,76,48,46,0,67,27,32,36,33,65,63,63,62,71,68,59,27,45,45,17,8,21,17,19,34,43,47,46,57,67,77,73,66,78,63,15,56,49,29,48,23,53,60,40,60,37,35,53,53
60,52,36,33,76,55,34,51,54,19,43,27,31,25,76,43,24,55,33,67,0,40,69,78,63,45,43,25,5,14,44,50,69,64,79,65,59,76,62,70,77,73,70,76,64,65,58,53,15,58,29,79,41,18,66,37,44,33,50,27,71,60,68,38,47
35,12,15,37,36,15,6,55,14,23,39,15,27,29,59,35,49,34,19,27,40,0,29,38,38,38,36,36,35,44,42,46,29,47,47,25,19,36,22,30,45,48,49,51,56,57,51,46,39,51,36,39,29,22,26,21,4,26,42,13,62,32,37,26,26
28,17,44,66,41,44,35,84,35,52,68,44,56,58,70,63,78,46,48,32,69,29,0,49,31,67,65,65,64,73,71,72,40,58,58,30,24,47,27,35,45,41,45,44,55,65,75,75,68,80,65,44,58,51,13,50,25,55,58,42,73,50,48,55,54
50,32,53,58,45,34,44,52,24,60,41,52,53,59,28,73,79,68,57,36,78,38,49,0,53,76,74,74,73,82,47,38,9,24,9,19,28,16,37,39,54,63,67,66,77,87,89,84,77,89,73,22,38,60,46,46,34,64,80,51,39,19,17,41,64
3,26,27,67,35,53,43,85,44,53,76,52,64,59,74,32,72,15,38,33,63,38,31,53,0,39,52,59,58,67,78,76,44,62,62,34,25,51,16,29,20,10,14,13,24,34,44,50,62,52,66,48,66,45,18,58,34,42,27,36,77,54,52,63,23
42,50,30,49,74,53,32,67,52,35,59,41,47,41,92,10,47,24,19,65,45,38,67,76,39,0,21,34,40,49,60,66,67,80,85,63,57,74,55,68,59,49,36,44,26,23,13,11,44,13,48,77,55,27,57,47,42,12,12,25,87,70,75,52,19
52,48,28,47,72,51,30,65,50,33,57,39,45,39,90,20,26,37,17,63,38,36,65,74,52,21,0,13,33,36,58,64,65,78,83,61,55,72,58,66,69,62,51,59,41,40,30,10,23,20,46,75,53,25,62,45,40,10,27,23,85,68,73,50,29
56,48,32,36,72,51,30,54,50,22,46,30,34,28,79,34,13,51,29,63,25,36,65,74,59,36,34,0,20,23,47,53,65,67,82,61,55,72,58,66,73,69,65,72,55,56,49,44,10,49,35,75,44,14,62,40,40,24,41,23,74,63,71,41,43
55,47,31,28,71,50,29,46,49,14,38,22,26,20,71,38,19,50,28,62,5,35,64,73,58,40,38,20,0,9,39,45,64,59,74,60,54,71,57,65,72,68,65,71,59,60,53,48,10,53,24,74,36,13,61,32,39,28,45,22,66,55,63,33,42
64,56,40,35,80,59,38,53,58,23,47,31,35,29,80,47,10,59,37,71,14,44,73,82,67,49,47,29,9,0,46,54,73,68,83,69,63,80,66,74,81,77,74,80,68,69,62,57,19,62,15,83,45,22,70,41,48,37,54,31,73,64,72,42,51
75,54,51,11,77,57,36,24,56,25,16,27,15,19,35,58,36,70,48,68,44,42,71,47,78,60,58,47,39,46,0,9,41,23,38,51,60,48,64,71,86,88,85,91,79,80,73,68,49,73,33,54,27,33,68,35,46,48,65,42,38,38,33,30,62
73,55,56,20,68,57,40,15,47,31,7,31,19,25,26,64,45,75,53,59,50,46,72,38,76,66,64,53,45,54,9,0,32,14,29,42,51,39,60,62,77,86,90,89,85,86,79,74,55,79,39,45,18,39,69,26,50,54,71,47,29,29,24,21,67
41,23,44,52,36,25,35,46,15,51,32,43,44,50,30,64,70,59,48,27,69,29,40,9,44,67,65,65,64,73,41,32,0,18,18,10,19,7,28,30,45,54,58,57,68,78,80,75,68,80,64,13,29,51,37,37,25,55,71,42,33,10,8,32,55
59,41,62,34,54,43,53,28,33,45,21,45,33,39,12,78,59,77,66,45,64,47,58,24,62,80,78,67,59,68,23,14,18,0,15,28,37,25,46,48,63,72,76,75,86,96,93,88,69,93,53,31,32,53,55,40,43,68,85,60,15,18,10,35,73
59,41,62,49,54,43,53,43,33,60,36,60,48,54,27,82,74,77,66,45,79,47,58,9,62,85,83,82,74,83,38,29,18,15,0,28,37,25,46,48,63,72,76,75,86,96,98,93,84,98,68,31,47,68,55,55,43,73,89,60,30,28,25,50,73
31,13,40,62,26,21,31,56,11,48,42,40,52,54,40,60,74,49,44,17,65,25,30,19,34,63,61,61,60,69,51,42,10,28,28,0,9,17,18,20,35,44,48,47,58,68,76,71,64,76,61,14,39,47,27,36,21,51,61,38,43,20,18,42,51
22,7,34,56,17,30,25,65,20,42,51,34,46,48,49,54,68,40,38,8,59,19,24,28,25,57,55,55,54,63,60,51,19,37,37,9,0,26,9,11,26,35,39,38,49,59,69,65,58,70,55,23,48,41,21,40,15,45,52,32,52,29,27,45,45
48,30,51,59,41,32,42,53,22,58,39,50,51,57,37,71,77,66,55,21,76,36,47,16,51,74,72,72,71,80,48,39,7,25,25,17,26,0,35,37,52,61,65,64,75,85,87,82,75,87,71,6,36,58,44,44,32,62,78,49,40,17,15,39,62
13,10,37,59,19,37,28,74,28,45,60,37,49,51,58,48,71,31,41,17,62,22,27,37,16,55,58,58,57,66,64,60,28,46,46,18,9,35,0,13,28,26,30,29,40,50,60,66,61,68,58,32,51,44,24,43,18,48,43,35,61,38,36,48,39
26,18,45,67,6,41,36,76,31,53,62,45,57,59,60,61,79,44,49,19,70,30,35,39,29,68,66,66,65,74,71,62,30,48,48,20,11,37,13,0,15,39,43,42,53,63,73,76,69,81,66,34,59,52,32,51,26,56,56,43,63,40,38,56,52
17,33,41,81,21,56,51,91,46,67,77,60,72,73,75,52,86,35,52,34,77,45,45,54,20,59,69,73,72,81,86,77,45,63,63,35,26,52,28,15,0,30,34,33,44,54,64,70,76,72,80,49,74,59,32,66,41,59,47,50,78,55,53,71,43
13,36,37,77,45,63,53,95,54,63,86,62,74,69,84,42,82,25,48,43,73,48,41,63,10,49,62,69,68,77,88,86,54,72,72,44,35,61,26,39,30,0,24,23,34,44,54,60,72,62,76,58,76,55,28,68,44,52,37,46,87,64,62,73,33
17,40,34,74,49,64,50,92,58,60,83,59,71,66,88,31,77,15,45,47,70,49,45,67,14,36,51,64,65,74,85,90,58,76,76,48,39,65,30,43,34,24,0,8,10,20,30,47,69,40,73,62,73,52,32,65,48,41,24,43,91,68,66,70,23
16,39,40,80,48,66,56,98,57,66,89,65,77,72,87,39,85,23,51,46,76,51,44,66,13,44,59,72,71,80,91,89,57,75,75,47,38,64,29,42,33,23,8,0,18,28,38,55,75,48,79,61,79,58,31,71,47,49,32,49,90,67,65,76,31
27,50,41,68,59,71,51,86,68,54,78,60,66,60,98,21,67,25,38,57,64,56,55,77,24,26,41,54,59,68,79,85,68,86,86,58,49,75,40,53,44,34,10,18,0,10,20,37,63,30,67,72,74,46,42,66,58,31,14,44,101,78,76,71,30
37,60,42,69,69,72,52,87,71,55,79,61,67,61,108,22,66,27,39,67,65,57,65,87,34,23,40,53,60,69,80,86,78,96,96,68,59,85,50,63,54,44,20,28,10,0,10,30,63,20,68,82,75,47,52,67,61,32,15,45,107,88,86,72,31
47,63,43,62,79,66,45,80,65,48,72,54,60,54,105,23,56,37,32,77,58,51,75,89,44,13,30,43,53,62,73,79,80,93,98,76,69,87,60,73,64,54,30,38,20,10,0,20,53,10,61,90,68,40,62,60,55,25,25,38,100,83,88,65,32
53,58,38,57,82,61,40,75,60,43,67,49,55,49,100,21,36,35,27,73,48,46,75,84,50,11,10,23,43,46,68,74,75,88,93,71,65,82,66,76,70,60,47,55,37,30,20,0,33,10,56,85,63,35,68,55,50,20,23,33,95,78,83,60,30
59,51,35,38,75,54,33,56,53,24,48,32,36,30,81,42,23,54,32,66,15,39,68,77,62,44,42,10,10,19,49,55,68,69,84,64,58,75,61,69,76,72,69,75,63,64,57,52,0,57,34,78,46,17,65,42,43,32,49,26,76,65,73,43,46
55,63,43,62,87,66,45,80,65,48,72,54,60,54,105,23,46,37,32,78,58,51,80,89,52,13,20,33,53,56,73,79,80,93,98,76,70,87,68,81,72,62,40,48,30,20,10,10,43,0,61,90,68,40,70,60,55,25,25,38,100,83,88,65,32
63,48,39,22,72,51,30,40,50,13,32,21,20,14,65,46,25,58,36,63,29,36,65,73,66,48,46,35,24,15,33,39,64,53,68,61,55,71,58,66,80,76,73,79,67,68,61,56,34,61,0,75,35,21,62,31,40,36,53,30,60,54,62,32,50
45,27,54,65,35,35,45,59,25,62,45,54,57,63,43,74,83,63,58,15,79,39,44,22,48,77,75,75,74,83,54,45,13,31,31,14,23,6,32,34,49,58,62,61,72,82,90,85,78,90,75,0,42,61,41,50,35,65,75,52,46,23,21,45,65
63,41,39,36,65,43,23,33,33,22,11,14,23,28,44,53,48,58,36,56,41,29,58,38,66,55,53,44,36,45,27,18,29,32,47,39,48,36,51,59,74,76,73,79,74,75,68,63,46,68,35,42,0,30,55,8,33,43,60,30,47,19,27,3,50
42,34,18,22,58,37,16,40,36,8,32,16,20,14,65,25,27,37,15,49,18,22,51,60,45,27,25,14,13,22,33,39,51,53,68,47,41,58,44,52,59,55,52,58,46,47,40,35,17,40,21,61,30,0,48,26,26,15,32,9,60,49,57,27,29
15,14,39,63,38,41,32,81,32,49,65,41,53,55,67,50,75,33,45,29,66,26,13,46,18,57,62,62,61,70,68,69,37,55,55,27,21,44,24,32,32,28,32,31,42,52,62,68,65,70,62,41,55,48,0,47,22,52,45,39,70,47,45,52,41
55,33,31,32,57,35,15,41,25,18,19,10,22,24,52,45,44,50,28,48,37,21,50,46,58,47,45,40,32,41,35,26,37,40,55,36,40,44,43,51,66,68,65,71,66,67,60,55,42,60,31,50,8,26,47,0,25,35,52,22,55,27,35,11,42
31,8,19,41,32,19,10,59,10,27,43,19,31,33,55,39,53,38,23,23,44,4,25,34,34,42,40,40,39,48,46,50,25,43,43,21,15,32,18,26,41,44,48,47,58,61,55,50,43,55,40,35,33,26,22,25,0,30,46,17,58,28,33,30,30
42,38,18,37,62,41,20,55,40,23,47,29,35,29,80,10,36,27,7,53,33,26,55,64,42,12,10,23,28,37,48,54,55,68,73,51,45,62,48,56,59,52,41,49,31,32,25,20,32,25,36,65,43,15,52,35,30,0,17,13,75,58,63,40,19
30,53,27,54,62,57,37,72,56,40,64,46,52,46,97,7,53,12,24,60,50,42,58,80,27,12,27,40,45,54,65,71,71,85,89,61,52,78,43,56,47,37,24,32,14,15,25,23,49,25,53,75,60,32,45,52,46,17,0,30,92,74,79,57,16
33,25,9,31,49,28,7,49,27,17,40,16,28,23,72,23,36,28,6,40,27,13,42,51,36,25,23,23,22,31,42,47,42,60,60,38,32,49,35,43,50,46,43,49,44,45,38,33,26,38,30,52,30,9,39,22,17,13,30,0,69,45,50,27,20
74,56,77,38,69,58,68,20,48,52,36,60,48,46,27,85,63,92,75,60,71,62,73,39,77,87,85,74,66,73,38,29,33,15,30,43,52,40,61,63,78,87,91,90,101,107,100,95,76,100,60,46,47,60,70,55,58,75,92,69,0,33,25,50,88
51,33,47,48,46,28,38,44,18,41,22,33,34,40,30,67,60,66,51,37,60,32,50,19,54,70,68,63,55,64,38,29,10,18,28,20,29,17,38,40,55,64,68,67,78,88,83,78,65,83,54,23,19,49,47,27,28,58,74,45,33,0,8,22,58
49,31,52,44,44,33,43,38,23,49,30,41,42,48,22,72,68,67,56,35,68,37,48,17,52,75,73,71,63,72,33,24,8,10,25,18,27,15,36,38,53,62,66,65,76,86,88,83,73,88,62,21,27,57,45,35,33,63,79,50,25,8,0,30,63
60,38,36,33,62,41,20,36,36,19,14,11,23,25,47,50,45,55,33,53,38,26,55,41,63,52,50,41,33,42,30,21,32,35,50,42,45,39,48,56,71,73,70,76,71,72,65,60,43,65,32,45,3,27,52,11,30,40,57,27,50,22,30,0,47
26,38,11,51,58,41,27,69,40,37,60,36,48,43,85,9,55,8,22,53,47,26,54,64,23,19,29,42,42,51,62,67,55,73,73,51,45,62,39,52,43,33,23,31,30,31,32,30,46,32,50,65,50,29,41,42,30,19,16,20,88,58,63,47,0;

enddata

min=@sum(coo(i,j):p(j)*d(i,j)*x(i,j));
@sum(fac(i):y(i))=3;
@for(plant(j):@sum(coo(i,j):x(i,j))=1);
@sum(coo(i,j):x(i,j))>=65;
@for(coo(i,j):x(i,j)<=y(i));
@for(fac(i):@bin(y));
@for(coo(i,j):@bin(x));

end

其中，

@for(plant(j):@sum(coo(i,j):x(i,j))=1);

就是典型的for中嵌套sum的算法，这在概率统计中很常见