Intervals functions¶

Intervals functions define interval-typed variables (typically used to model tasks or activities with a duration) and the constraints that can be defined among them.

The following functions are available:

interval¶

Declares an interval variable, representing the integer time range of a task or event. If Argument 1 is 0, the interval is optional, default to 1. Argument 2 and Argument 3 are the start and the end of the interval and they could be either integer variables or integer constants. Argument 4 is the duration of the interval and it could be either an integer variable or an integer constant.

Parameters

Parameter	Description	Requirement
Argument 1	boolean	Optional
Argument 2	integer	Optional
Argument 3	integer	Optional
Argument 4	integer	Optional

noOverlap¶

Returns 1 if a given set of intervals do not overlap, and 0 otherwise

Parameters

Signature (dimension of Argument 1: 0)

Parameter	Description	Requirement
Argument 1	interval	Mandatory
Argument >= 2	Additional intervals. They all together form the array of intervals to be checked for overlaps.	Optional

Signature (dimension of Argument 1: 1)

Parameter	Description	Requirement
Argument 1	interval	Mandatory

cumulative¶

Returns 1 if the resource constraint, where the sum of the demands of the overlapping intervals must not exceed the capacity of the resource, is satisfied, and 0 otherwise. The first argument is an array of intervals, the second argument is the weight in capacity for each interval, and the third argument is the capacity of the resource.

Parameters

Parameter	Description	Requirement
Argument 1	interval (dimension 1)	Mandatory
Argument 2	array of integers of dimension 1	Mandatory
Argument 3	integer (dimension 0)	Mandatory

reservoir¶

Returns 1 if the reservoir constraint is satisfied, and 0 otherwise. The reservoir constraint guaranties a certain quantity not overcome a supposed maximum and does not become lower of a supposed minimum. It is configured with 4 arguments. The Argument 1 is an array of moments in which a change in the studied quantity occurs, the Argument 2 is an array of the changes in the quantity at each moment, the Argument 3 is the minimum value of the quantity and the Argument 4 is the maximum value of the quantity. The last argument is an array of boolean values that indicates if the change should be considered or not. If the last argument is not provided, all changes are considered.

Parameters

Parameter	Description	Requirement
Argument 1	numeric (dimension 1)	Mandatory
Argument 2	numeric array (dimension 1)	Mandatory
Argument 3	numeric (dimension 0)	Optional
Argument 4	numeric (dimension 0)	Optional
Argument 5	boolean	Optional