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# cumulative(+StartTimes, +Durations, +Usages, +ResourceLimit)

Single resource cumulative constraint on scheduling tasks.
*StartTimes*
- Collection of start times for tasks (integer variables or integers)
*Durations*
- Collection of duration for tasks (non-negative integer variables or integers)
*Usages*
- Collection of resource usages (positive integers)
*ResourceLimit*
- Maximum amount of resource available (domain variable, array notation accepted)

## Description

A cumulative scheduling constraint. StartTimes, Durations and Usages
are collections (a la collection_to_list/2) of equal size N representing
N tasks. Durations are non-negative, Usages and ResourceLimit are
strictly positive. The declarative meaning is:

The N tasks, each starting at a certain start time, having
a certain duration and consuming a certain (constant) amount of
resource, then the sum of resource usage of all the tasks does not
exceed ResourceLimit at any time.

A zero duration task both consume and release the resource it uses
at the same time-point, so effectively it does not consume any resources
at that time-point, but there must be sufficient resources available at
that time-point to allow the task to be scheduled.

Note that the constraint is implemented by different Gecode propagators,
depending on if Durations contains domain variables or not. If
Durations does have domain variables, the Gecode propagator requires
an extra End domain variable specifying the end time, and a constraint

End #= Start + Duration

for each task. These are posted as part of the constraint (the End
variables are not accessible by the user).
Any input variables which are not already domain variables are turned
into domain variables with default domain.

This constraint is also known as cumulative in the global constraint
catalog, but in the catalog, tasks with zero duration have a different
definition of overlap with other tasks. The constraint is implemented
using Gecode's cumulative constraint (with extra constraints on task
end-times if any task duration is a domain variable).

## Examples

% success (peak consumption is 7)
[eclipse 7]: cumulative([1,2,3,6,7], [3,9,10,6,2], [1,2,1,1,3], 8).
% fail (peak consumption is 7)
[eclipse 8]: cumulative([1,2,3,6,7], [3,9,10,6,2], [1,2,1,1,3], 6).

## See Also

disjunctive / 2, cumulative_optional / 5, cumulatives / 5, eclipse_6 : collection_to_list / 2, lists : collection_to_list / 2, ic_edge_finder : cumulative / 4, ic_edge_finder3 : cumulative / 4, edge_finder : cumulative / 4, edge_finder3 : cumulative / 4, cumulative : cumulative / 4, ic_cumulative : cumulative / 4