## SAS Marketing Optimization: Scenario Modeling Tip #3

Started ‎09-14-2017 by
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Scenario Modeling Tip #3: Understand the role of ratio constraints in scenarios.

Common confusion: How does SAS Marketing Optimization interpret a ratio constraint? Remember that a ratio constraint is interpreted as a ratio of sums, not as a sum of ratios.

Example

The following expression represents a ratio constraint using the expected_profit and communication_unit_cost measures, where the sums are taken over all offers that are made.

Note that this is not the same as a sum of ratios, as in the following expression:

For the underlying marketing optimization problem, the ratio constraint is converted to the following linear constraint:

Σ (expected_profit – 0.3 x communication_unit_cost) ≥ 0.3

This transformation is valid only if the sum of the denominator measure (in this example, Σ communication_unit_cost) is positive. Therefore, use ratio constraints only when the values of the denominator measure are positive in order to guarantee that the sum is positive.

But is it feasible? Note that the zero solution is feasible for the linearized constraint even though it is undefined for the original ratio constraint. Therefore, for some scenarios, it might be better to not make any offers than to satisfy the ratio constraint. Then the Constraint Summary reports the ratio constraint as having a missing value. This situation is particularly common when the ratio constraint uses a communication filter or a customer filter, such that the solution still makes some offers, but not from the set of communications or customers that are included in the ratio constraint. Ratio constraints are interpreted as “if any offers are made, then they must satisfy this ratio.”

If you want to exclude the zero solution as a possibility (forcing offers to be made and forcing the ratio to be satisfied), include an additional constraint to require a minimum number of offers to be made, using the same communication filter and customer filter as in the ratio constraint.

Note: This post was adapted from Michelle Opp’s “Scenario Modeling Tips” document. For more information, see SAS Marketing Optimization User’s Guide.

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