After LINGO generates a model, it checks all the nonzero coefficients in the model and computes the ratio of the largest to smallest coefficients.  This ratio is an indicator of how well the model is scaled.  When the ratio gets to be too high, scaling is considered to be poor, and numerical difficulties may result during the solution phase.  If the scaling ratio exceeds the value of the SCALEW parameter, LINGO will display this error message  The default value for SCALEW is 1e9.  Instead of simply increasing the SCALEW setting to eliminate error 205, we strongly suggest that you attempt to rescale the units of your model so as to reduce the largest-to-smallest coefficient ratio.

In some instances, changing the units of measure can be an easy way to improve a model’s scaling.  For instance, suppose we have a model with the following budget constraint in dollar units:

 1000000 * X + 2200000 * Y + 2900000 * Z <= 5000000;

This constraint introduces several large coefficients into the model.   If we rewrote the constraint so that it is in units of millions of dollars, then we would have:

 X + 2.2 * Y + 2.9 * Z <= 5;

The coefficients in this new constraint are much less likely to present a problem.

As part of this error message, LINGO reports the values of the largest and smallest coefficients, as well as where they appear in the model.  This information should help in tracking down the problem.  You may also run the Solver|Generate command to track down other extreme coefficients.  This Generate command displays the full, generated model and specifically lists all the coefficients.