Order Constraint

Overview

Order Constraints in Verteego ensure that variables within a dataset follow a specified order. This type of constraint is critical for operations where the sequence of values must adhere to a logical or business rule-defined order.

Applications

Order Constraints are typically applied to scenarios such as pricing models where items must escalate in cost based on size, quality, or other factors. They ensure that products or services are correctly sequenced, such as ensuring that heavier products are priced higher than lighter ones within the same category.

Parameters

• where: Optional. Filters rows based on specified conditions.

  • Example: where={"month": [1, 2, 3], "year": 2022} applies the constraint only to the first trimester of 2022.

• variable_column: Specifies the column containing the variable to be ordered (e.g., "price", "qty_to_buy").

• order_by: Identifies the column used to determine the order.

• ordering: Optional. Specifies custom ordering, overriding natural order. Unspecified values are ignored.

  • Example: ordering=["Citadine Manuel", "Citadine Auto", "Citadine Sport"] enforces an order only for listed car types.

• operator: Determines the direction of the order comparison (asc for ascending, desc for descending). Defaults to asc.

• left_column_weight/right_column_weight: Optional weights applied to the variable before ordering.

• factor: Multiplicative factor used in comparisons, defaults to 1.

• delta: Additive factor used in comparisons, defaults to 0.

• group_by: Optional. Specifies columns that define unique groups for ordering.

  • Example: group_by="duration" orders prices separately for each rental duration.

• relax: Whether the constraint can be relaxed with a penalty, defaults to false.

• allow_aggregation: Specifies if aggregation is permitted in cases where multiple variables share the same order value, useful for select variables.

Examples

To illustrate with a simple example, with this configuration:

Parameter	Value
variable_column	price
order_by	duration
ordering	[“1J”, “7J”, “30J”]
operator	desc
delta	1
groupby	category, rate

order_constraints:
  - constraint_type: order
    variable_column: price
    order_by: duration
    ordering: ["1J", "7J", "30J"]
    operator: desc
    delta: 1
    group_by: [category, rate]

For a given category and rate, the price variable in the row with duration=1J, must be less than price - 1 in the row with duration=7J. Likewise for the rows with durations 7J and 30J.

that is, for each category and rate:

$$price("1J") >= price("7J") + 1 price("7J") >= price("30J") + 1$$

For instance, with a minimum price of 1, an objective to minimize, and an order constraint with delta=-1, order_by=ord_col, group_by=group, operator=asc:

var_col	ord_col	group
NA	1	1
NA	4	1
NA	3	2
NA	4	2
NA	7	2

could get solved as:

var_col	ord_col	group
1	1	1
2	4	1
1	3	2
2	4	2
3	7	2