Scaling can also be done on equations. It again involves altering the units of model elements. For example, one might change the units of an equation from say acres to 1000 acres. To do that you would divide all associated coefficients by one thousand. In general equation scaling involves dividing very equation coefficient by the scaling factor (SR1) as follows:
where SR1 is a positive equation scaling factor.
Notes:
| • | The solutions to the problem before and after scaling have a mathematical relationship.http://agecon2.tamu.edu/people/faculty/mccarl-bruce/mccspr/new17.pdf show that such scaling divides the optimal slack variable (or equivalently equation level) by the scaling factor and multiplies the optimal shadow price or equation marginal by that scaling factor. |
| • | All coefficients for an equation have a common numerator (row resource units per variable unit) both before and after scaling, so every coefficient associated with the equation needs to be divided by the same scaling factor to maintain homogeneity of the numerator units in the equation. |