$ontext

    Alphametics, Simple formulation
    This does not work very well.

    Erwin Kalvelagen

              AN
  + ACCELERATING
   + INFERENTIAL
   + ENGINEERING
          + TALE
         + ELITE
         + GRANT
           + FEE
            + ET
        + CETERA =
   -------------
      ARTIFICIAL
  + INTELLIGENCE



$offtext

set i /A,N,C,E,L,R,T,I,G,F/;
alias (i,j);

set leading(i) /A,I,E,T,G,F,C/;

abort$(card(i) <> 10) "set i should have 10 elements";

parameter v(i); v(i) = ord(i)-1;

variables
     y(i) 'decision variables'
     x(i,j) 'auxiliary variables for uniqueness'
     z 'dummy objective variable'
;
binary variable x;

equation
     addition 'the actual problem'
     ydef(i) 'calculate y'
     xrow(i) 'row sums'
     xcol(j) 'column sums'
     dummy_objective
;

addition..
     10*y('A')+y('N')+
     1e11*y('A')+1e10*y('C')+1e9*y('C')+1e8*y('E')+1e7*y('L')+1e6*y('E')+1e5*y('R')+1e4*y('A')+1e3*y('T')+100*y('I')+10*y('N')+y('G')+
     1e10*y('I')+1e9*y('N')+1e8*y('F')+1e7*y('E')+1e6*y('R')+1e5*y('E')+1e4*y('N')+1e3*y('T')+100*y('I')+10*y('A')+y('L')+
     1e10*y('E')+1e9*y('N')+1e8*y('G')+1e7*y('I')+1e6*y('N')+1e5*y('E')+1e4*y('E')+1e3*y('R')+100*y('I')+10*y('N')+y('G')+
     1e3*y('T')+100*y('A')+10*y('L')+y('E')+
     1e4*y('E')+1e3*y('L')+100*y('I')+10*y('T')+y('E')+
     1e4*y('G')+1e3*y('R')+100*y('A')+10*y('N')+y('T')+
     100*y('F')+10*y('E')+y('E')+
     10*y('E')+y('T')+
     1e5*y('C')+1e4*y('E')+1e3*y('T')+100*y('E')+10*y('R')+y('A') =e=
     1e9*y('A')+1e8*y('R')+1e7*y('T')+1e6*y('I')+1e5*y('F')+1e4*y('I')+1e3*y('C')+100*y('I')+10*y('A')+y('L')+
     1e11*y('I')+1e10*y('N')+1e9*y('T')+1e8*y('E')+1e7*y('L')+1e6*y('L')+1e5*y('I')+1e4*y('G')+1e3*y('E')+100*y('N')+10*y('C')+y('E');


ydef(i).. y(i) =e= sum(j, x(i,j)*v(j));
xrow(i).. sum(j, x(i,j)) =e= 1;
xcol(j).. sum(i, x(i,j)) =e= 1;

*
* bounds on leading digits: they can not be 0
*
y.lo(leading) = 1;

dummy_objective.. z =e= sum(i, y(i));

model m /all/;
solve m using mip minimizing z;

option y:0;
display y.l;