Multiplicative Equality Constraint

Overview

The Multiplicative Equality Constraint ensures that one variable is the product of multiple other variables within the dataset. This constraint is crucial in scenarios where interdependent variables need to synchronize multiplicatively to reflect accurate relationships in real-world models.

Application

This type of constraint is particularly useful in operational contexts where output is the product of several input factors. For example, the total work output could be a product of the number of employees and the number of hours they are scheduled to work.

Parameters

• left_variable: The name of the column that will be set equal to the product of the other columns specified. This column represents the resulting variable that is being optimized or constrained.

• right_variables: A list of column names whose values will be multiplied together. There must be at least two variables to form a product.

Example

Here’s an example of how to set up a Multiplicative Equality Constraint in YAML format:

yamlCopy codenb_workers_today:
  constraint_type: multiplicative_equality
  left_variable: employees_working
  right_variables:
    - nb_workers
    - scheduled_today

How it works

According to the YAML example above, the constraint enforces that for each row selected:

employees_working = nb_workers × scheduled_today

Here's how Verteego applies this constraint:

• Per Row Basis: The constraint is enforced on each row individually, ensuring that the calculated output matches the expected product for that particular data entry.

• Multiple Variables: While the example shows a product of two variables, the constraint can extend to any number of factors as needed for the model.

Best Practices

• Ensure the selected variables are appropriate for multiplication and reflect a meaningful relationship within your model.

• Verify that no variable involved in the product is likely to be zero, as this would nullify the product and may not be suitable for the intended application.