How big should the constant M be in the equation, where Y(J) are binary variables:

 
 YBIN(J).. SUM(I,X(I,J)) =L= M*Y(J);

I said in my model:

 SCALAR M /10000000000/ 

but that causes problems.

In general the answer should be as small as possible. Your model with the M of 1.0E10 could not be solved by any of the MIP solvers we tried out. It causes enormous scaling problems. However further on in your model you have

   CAP(J).. SUM(I,X(I,J)) =L= MAXCAP;

We can combine these two equations in one:

   YBIN(J).. SUM(I,X(I,J)) =L= MAXCAP*Y(J);

Which both sets M to the smallest possible value and reduces the number of constraints.

We have seen MIP models fail miserably when using a real big M.