
cumulative_optional(+StartTimes, +Durations, +Usages, +ResourceLimit, +Scheduled)

   Single resource cumulative constraint on scheduling optional tasks.

Arguments
   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 or integer, array notation accepted)
   Scheduled           Collection of N scheduled booleans for task (0/1 domain variables or integers)

Type
   library(gfd)

Description

   A cumulative scheduling constraint. StartTimes, Durations, Usages and 
   Scheduled are collections (a la collection_to_list/2) of equal size N,
   representing N task. Durations must be non-negative, Usages and 
   ResourceLimit must be strictly positive, and Scheduled are booleans 
   (values of 0/1). 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 task would not be scheduled 
   if its Scheduled boolean is 0, and must be scheduled if 1.
/P>
   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.



See Also
   disjunctive / 2, disjunctive_optional / 3, cumulative / 4, 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
