The Solver must perform many calculations where
quantities derived from the values of the objective and constraints
must be divided into and subtracted from one another. Because of the
finite precision of computer arithmetic, when these calculations are
performed with values of very different magnitudes, roundoff error
builds up to the point where the Solver can no longer reliably find
the optimal solution.
When the Use Automatic Scaling box in the
Solver Options dialog is checked, the Solver will attempt to scale
the values of the objective and constraint functions internally in
order to minimize the effects of a poorly scaled model. This
is usually, but not always, effective. Since automatic scaling
uses the initial values of the variables, problems may arise for the
nonlinear GRG Solver when the final values of the variables differ
from the initial values by several orders of magnitude.
By re-stating the quantities in your model
-- for example, by using variables expressed in units of thousand or
millions of dollars rather than dollars -- you can avoid problems
with poor scaling. Your goal should be to ensure that
quantities in your model are all within three or four orders of
magnitude of each other.
A model which is completely linear but poorly
scaled may cause sufficient roundoff error to make the Solver's
internal model inaccurate -- yielding the error message "The
conditions for Assume Linear Model are not satisfied." See the
Assume Linear Model option for further details.
As above, by re-stating the quantities in your
model so that they are all within three or four orders of
magnitude of each other, you can avoid this problem. As a
short-term fix, you may also "loosen" the Precision
setting, as described in Precision and Tolerance.
The Premium Solver products use advanced
automatic scaling methods and are less vulnerable to poorly scaled
models. Since no automatic scaling method will work in all
situations, we recommend that you take steps to ensure that the
model on your worksheet is reasonably well scaled.
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Diagnosing Solver Results
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