$title Effect of aggregation on mip model solution time
set i /1*50/;
set j /1*250/;

option solprint=off, limrow=0, limcol=0;
option seed = 101;
parameter match(i,j);
match(i,j) = uniform(0,10);

binary variables build(i);
binary variables use(i,j) "use i for dealing with j";
variable profit;
equation defx, cons, obj;

* $ontext
defx(i)..
card(j)*build(i) =g= sum(j, use(i,j));
* $offtext

$ontext
defx(i,j)..
build(i) =g= use(i,j);
$offtext

cons..
  sum(i, build(i)) =l= card(i)/2;

obj..
profit =e= sum((i,j), match(i,j)*use(i,j));

model prob /all/;
solve prob using mip max profit;

display build.l;