In the previous sections, we presented some simple strategies to limit
the ranges of variable bounds, constraint right-hand sides, objective
values, and constraint matrix coefficients. However, it could happen
that by scaling constraints or variables, some constraint coefficients
become too small. Note that Gurobi will treat any constraint
coefficient with absolute value under as zero.
Consider the following example:
In this example, the matrix coefficients range in . If we multiply all coefficients by , and divide all coefficients in the second constraint by , we obtain:
where . The resulting matrix coefficients have a range in . Essentially the trick is to simultaneously scale a column and a row to achieve a smaller range in the coefficient matrix.
We recommend that you scale the matrix coefficients so that their range is contained in six orders of magnitude or less, and hopefully within .