Hi,

this is the problem 18 in Model Building by H. Paul Williams

https://www.amazon.fr/Model-Building-Mathematical-Programming-Williams/dp/1118443330?cm_mc_uid=56329990040415039023459&cm_mc_sid_50200000=1507305800&cm_mc_sid_52640000=

let me address this in a naive and simple way, without ceiling and roofing but relying on presolve.

.mod

int n=...;

{int} s=asSet(1..n);

// computing all the subsets
range r=1.. ftoi(pow(2,card(s)));
{int} s2 [k in r] = {i | i in s: ((k div (ftoi(pow(2,(ord(s,i))))) mod 2) == 1)};
 
// initial constraint
int coef[s]=...;
int rhs=...;

// result constraint
dvar int coef2[i in s] in ((coef[i]>=0)?0:-maxint)..((coef[i]>=0)?maxint:0);
dvar int rhs2;

minimize abs(rhs2);
subject to
{
forall(i in r)
 (sum(j in s2[i]) coef2[j]<=rhs2)
 ==
 (sum(j in s2[i]) coef[j]<=rhs);
}

execute display
{
for(var i in s)
{
  write(coef2[i],"x",i);
  if (i!=n) if (coef2[i+1]>=0) write("+");
}
writeln("<=",rhs2);
}

.dat

n=8;
coef=[9,13,-14,17,13,-19,23,21];
rhs=37;

which gives

6x1+9x2-10x3+12x4+9x5-13x6+16x7+14x8<=25

regards