Counting Elements in a Set using AIMMS

In AIMMS, counting elements within a set is a fundamental operation used for data validation, calculating averages, or defining constraints. While there are multiple ways to achieve this, the two most common programmatic approaches are using the sum operator and the count operator.

Using the Sum Operator

The sum operator is the most flexible aggregation tool in AIMMS. To use it for counting, you effectively sum the value “1” for every element that meets your criteria.

For example, if you have a set Products with index p and you want to count how many products have a stock level below 10:

p_LowStockCount := sum( p | p_StockLevel(p) < 10, 1 );

  • Pros: Highly familiar to those used to mathematical modeling; easy to pivot from a count to a total (by changing the “1” to a parameter).

  • Cons: Slightly more verbose than dedicated counting functions.

Using the Count Operator

The count operator is a specialized version of the sum operator. It is designed specifically for tallying elements, making the code more readable and expressive.

For example, using the same product scenario, the code becomes cleaner:

p_LowStockCount := count( p | p_StockLevel(p) < 10 );

  • Pros: Improved readability; explicitly states the intent of the code (counting).

  • Cons: Only used for counting; cannot be used to aggregate non-unit values.

Using the Card Operator

If you do not need to apply a condition and simply want the total size of a set, the Card (cardinality) function is the most efficient method:

p_TotalSize := Card(Products);

Conclusion

  • Use sum if you are performing complex math or might change the logic to a total later.

  • Use count for better readability when the goal is a simple tally.

  • Use Card for the total size of a set without filters.