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# 14.4. Efficient Surface

Applies to:
Evolver 7.x
@RISK 7.x, Industrial Edition (in RISKOptimizer)

Is Efficient Surface available in RISKOptimizer and Evolver?

The concept of "Efficient Surface" ("Efficient Frontier Surface", "Efficient Plane") generalizes the concept of Efficient Frontier to 3 dimensions.  It answers the question about the optimal value of one of the three quantities, given fixed bounds on the values of the two other quantities.

This functionality is not available out of the box, but it can be obtained using the programming interface of @RISK for Excel.  Say we start with a regular efficient frontier that analyzes the tradeoff between the standard deviation and the mean, except we add an additional constraint that skewness <= x1.  We get one efficient frontier curve.  Then we do the same with the constraint that skewness <= x2, getting another curve.  We repeat it and get a number of curves that define our efficient surface.  Using VBA, an Excel 3D graph can be generated to represent the surface.

Last edited: 2015-08-11