Problems with Poorly Scaled Models
Problems due to poor scaling in a large,
complex optimization model can be difficult to identify and resolve.
It can cause Solver engines to return messages such as "Solver
could not find a feasible solution" or "Solver could not
improve the current solution," with results that are suboptimal
or otherwise very different from your expectations.
For example, suppose you decide to make a simple
change in your portfolio optimization model: Instead of using percentages
for the stock allocations, you'd rather see the actual dollars
to be invested, in your $1 billion institutional portfolio. So you
change the constraint TotalPortfolio = 1 (or 100%) to be
TotalPortfolio = 1000000000. When you click Solve, you are surprised
to find that the Solver reports it cannot find a feasible solution
(click the worksheet to see it full size):
You get this result whether or not you check the
Use Automatic Scaling box in the LP/Quadratic Solver Options
dialog. You've read about the effects of poor scaling, but how
do you find the poorly scaled formulas In a large, complex
optimization model? The Polymorphic
Spreadsheet Interpreter in the Premium Solver Platform can help
-- just select the Scaling Report in the Solver Results
dialog above, to obtain a report like the one below, inserted as a
new worksheet in your workbook:
The report indicates that there are scaling
problems with the formulas at H6, I14 and I16. You can click on the
cell references to jump to the actual cells containing these
formulas. You see that the calculation of the Portfolio
Variance involves adding a very small value and a very
large one (the Stock 5 variance times 1 billion squared) which
leads to a loss of significant digits.
Helping you find scaling problems in a large model
is just another way that the Premium Solver Platform can save you
hours of time, and enable you to find better solutions.
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