How to call the same index in each of 2 dimensions in a GAMS variable? - indexing

Question

I am running a model in GAMS with a number of variables with 2 dimensions, calling the indexes i and j respectively. I have a few constraints relating to just the "diagonal" entries, so I coded them something like "d(i,i)", but GAMS gives error 171 when I do this, for example the first error comes on equation e3. How do I express this in GAMS? Code follows:
Set
i 'Origin' / 1*20 /
j 'Destination' / 1*20 /;
Table A(i,j)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 0 4 2 574 481 440 408 633 573 1066 486 1926 1537 183 334 374 107 509 378 499
2 4 0 2 573 480 438 412 632 572 1064 484 1924 1535 182 332 372 111 508 377 498
3 3 2 0 572 479 437 411 631 571 1063 484 1923 1534 181 332 371 109 507 376 497
4 574 572 572 0 93 249 135 1188 1128 1620 1040 2480 2091 737 888 928 683 498 367 488
5 481 480 479 93 0 156 228 1095 1035 1527 948 2387 1998 645 796 836 591 406 275 396
6 440 438 437 249 156 0 384 1053 993 1485 906 2345 1956 603 754 794 549 364 233 354
7 409 412 411 135 228 384 0 1044 984 1476 897 2336 1947 594 745 785 302 633 502 623
8 633 632 631 1188 1095 1053 1044 0 532 1024 623 1246 792 450 300 403 742 560 992 668
9 573 572 571 1128 1035 993 984 532 0 494 326 879 424 392 385 207 682 1063 932 1053
10 1066 1064 1063 1620 1527 1485 1476 1024 494 0 820 1979 823 885 878 699 1175 1555 1424 1545
11 486 484 484 1040 948 906 897 623 326 820 0 724 270 359 477 223 595 975 844 966
12 1926 1924 1923 2480 2387 2345 2336 1246 878 1979 724 0 454 1943 1099 846 2035 2415 2284 2405
13 1537 1535 1534 2091 1998 1956 1947 792 424 823 270 454 0 1554 645 392 1646 2026 1895 2016
14 183 182 181 738 645 603 594 450 392 884 359 1943 1554 0 151 192 292 672 542 663
15 334 332 332 888 796 754 745 300 385 878 477 1099 645 151 0 257 443 261 692 369
16 373 372 371 928 835 793 784 403 207 699 223 846 392 192 256 0 482 863 732 853
17 107 111 109 683 591 549 302 742 683 1175 595 2035 1646 292 443 483 0 618 487 608
18 509 507 507 498 406 364 633 560 1063 1555 975 2415 2026 672 261 863 618 0 134 180
19 378 377 376 367 275 233 502 992 932 1424 844 2284 1895 542 692 732 487 134 0 122
20 500 498 497 489 396 354 624 668 1053 1545 966 2405 2016 663 369 854 609 180 122 0
;
Positive variable c(i,j) 'cost direct';
Positive variable cstar(i,j) 'cost routing';
Positive variable z 'objective';
Binary variable d(i,j) 'decision direct';
Binary variable dstar(i,j) 'decision routing';
Binary variable p(i,j) 'd(i,i)*dstar(i,j)';
Binary variable q(i,j) 'd(i,j)*p(i,j)';
Binary variable x(i,j) 'd(j,j)*dstar(i,j)';
Binary variable y(i,j) 'd(i,j)*x(i,j)';
Binary variable f(i,j) 'd(i,i)*d(j,j)';
Binary variable g(i,j) 'f(i,j)*dstar(i,j)';
Integer variable h(i) 'd(i,i)*u(i)';
Integer variable k(i,j) 'd(i,i)*u(j)';
Integer variable m(i,j) 'f(i,j)*u(i)';
Integer variable u(i) 'ordering of tours';
Equation
e1
e2(i,j)
e3
e4(j)
e5(i,j)
e6(i,j)
e7(i)
e8(j)
e9(i)
e10(i,j)
e11(i,j)
e12(i,j)
e13(i,j)
e14(i,j)
e15(i,j)
e16(i,j)
e17(i,j)
e18(i,j)
e19(i,j)
e20(i,j)
e21(i,j)
e22(i,j)
e23(i,j)
e24(i,j)
e25(i,j)
e26(i,j)
e27(i,j)
e28(i)
e29(i)
e30(i)
e31(i,j)
e32(i,j)
e33(i,j)
e34(i,j)
e35(i,j)
e36(i,j)
e37(i,j)
e38(i,j)
e39(i)
e40(i)
e41(i)
e42(i)
e43(i,j)
e44(i,j)
e45(i,j)
e46(i,j)
e47(i,j)
e48(i,j)
e49(i,j)
e50(i,j)
e51(i,j);
e1 .. z =e= sum((i,j),c(i,j))+sum((i,j),cstar(i,j));
e2(i,j) .. c(i,j) =e= A(i,j)*d(i,j);
e3 .. sum((i),d(i,i)) =e= 2;
e4(j) .. sum((i),d(i,j)) =e= 1;
e5(i,j) .. d(i,j)-d(i,i) =l= 0;
e6(i,j) .. cstar(i,j) =e= A(i,j)*dstar(i,j);
e7(i) .. dstar(i,i) =e= 0;
e8(j) .. sum((i),dstar(i,j)) =e= 1;
e9(i) .. sum((j),dstar(i,j)) =e= 1;
e10(i,j) .. p(i,j) =l= d(i,i);
e11(i,j) .. p(i,j) =l= dstar(i,j);
e12(i,j) .. p(i,j) =g= d(i,i)+dstar(i,j)-1;
e13(i,j) .. p(i,j) =g= 0;
e14(i,j) .. q(i,j) =l= d(i,j);
e15(i,j) .. q(i,j) =l= p(i,j);
e16(i,j) .. q(i,j) =g= d(i,j)+p(i,j)-1;
e17(i,j) .. q(i,j) =g= 0;
e18(i,j) .. p(i,j)-q(i,j) =e= 0;
e19(i,j) .. x(i,j) =l= d(j,j);
e20(i,j) .. x(i,j) =l= dstar(i,j);
e21(i,j) .. x(i,j) =g= d(j,j)+dstar(i,j)-1;
e22(i,j) .. x(i,j) =g= 0;
e23(i,j) .. y(i,j) =l= d(i,j);
e24(i,j) .. y(i,j) =l= x(i,j);
e25(i,j) .. y(i,j) =g= d(i,j)+x(i,j)-1;
e26(i,j) .. y(i,j) =g= 0;
e27(i,j) .. x(i,j)-y(i,j) =e= 0;
e28(i) .. u(i) =l= 20;
e29(i) .. 1000*(1-d(i,i)) =g= u(i)-1;
e30(i) .. 2-d(i,i) =l= u(i);
e31(i,j) .. f(i,j) =l= d(i,i);
e32(i,j) .. f(i,j) =l= dstar(j,j);
e33(i,j) .. f(i,j) =g= d(i,i)+dstar(j,j)-1;
e34(i,j) .. f(i,j) =g= 0;
e35(i,j) .. g(i,j) =l= f(i,j);
e36(i,j) .. g(i,j) =l= dstar(i,j);
e37(i,j) .. g(i,j) =g= f(i,j)+dtar(i,j)-1;
e38(i,j) .. g(i,j) =g= 0;
e39(i) .. 0 =l= h(i);
e40(i) .. h(i) =l= 1000*d(i,i);
e41(i) .. u(i)-1000*(1-d(i,i)) =l= h(i);
e42(i) .. h(i) =l= u(i);
e43(i,j) .. 0 =l= k(i,j);
e44(i,j) .. k(i,j) =l= 1000*d(i,i);
e45(i,j) .. u(j)-1000*(1-d(i,i)) =l= k(i,j);
e46(i,j) .. k(i,j) =l= u(j);
e47(i,j) .. 0 =l= m(i,j);
e48(i,j) .. m(i,j) =l= 1000*f(i,j);
e49(i,j) .. u(i)-1000*(1-f(i,j)) =l= m(i,j);
e50(i,j) .. m(i,j) =l= u(i);
e51(i,j) .. u(i)-u(j)+1-h(i)+k(i,j)-d(i,i)-k(j,i)+h(j)-d(j,j)-m(i,j)+m(j,i)-f(i,j) =l= 19*(1-d(i,i)-d(j,j)-f(i,j)-dstar(i,j)+p(i,j)+x(i,j)+g(i,j));
Model transport / all /;
solve transport using mip minimizing z;
display d.l, dstar.l;

Answer 1

The problem is, that you declared d (and other symbols) with domain (i,j) but try to access it as (i,i). Therefore, you get a domain violation since you declared i and j as different sets. Is that really wanted? Or are they really the same (i.e., is each origin also a destination)? Looking at table A that seems to be the case. So, instead of declaring j as a new set, you should define it as Alias to j. The start of your model would look like this then:
Set
i 'Origin' / 1*20 /;
Alias(i,j);
The rest stays the same.