A poorly scaled model is one in which the typical values of the objective and constraint functions differ by several orders of magnitude. A classic example is a financial model with some dollar amounts in millions, and other rate of return figures in percent. Poorly scaled models often cause difficulty for both linear and nonlinear Solver algorithms; the effect is often more severe for the nonlinear GRG Solver.

#### Poor Scaling and its Effect on Solutions

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.

#### Poor Scaling and Assume Linear Model

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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