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.