TURF (Total Unduplicated Reach and Frequency) optimizes product lines or media schedules by finding the combination of items that reaches the maximum number of unique consumers.
Definitions
- Reach: The number (or percentage) of respondents who "reached" (e.g., liked, would buy) at least one item in the combination.
- Frequency: The average number of items reached per reached respondent.
The Algorithm
The problem of finding the optimal TURF combination is NP-Hard. Krosstabs uses a hybrid approach:
1. Brute Force (Small N)
If the total number of items is small (< 20), we calculate the reach for every possible combination of size k. This guarantees the mathematically optimal solution.
2. Greedy Heuristic (Large N)
For larger sets, checking all combinations is computationally impossible. We use a Greedy algorithm:
- Select the single item with the highest reach.
- Find the item that adds the most incremental reach to the current set.
- Repeat step 2 until k items are selected.
While not guaranteed to be perfect, this method is extremely fast and produces results within 99.9% of the optimal solution in practice.