Implementation of question 1

Since there are no side constraints, the earliest possible completion time is the earliest start of the fictitious task N. We can obtain this value without enumeration thanks to the propagation of constraints. After posting the precedence constraints we retrieve the earliest completion time bestend and set this value as the upper bound on the last task. This fixes the start and completion times for the tasks on the critical path; for all other tasks the start and completion times are reduced to the feasible intervals:

model "B-1 Stadium construction (CP)"
 uses "kalis"

 declarations
  N = 19                              ! Number of tasks in the project
                                      ! (last = fictitious end task)
  TASKS = 1..N
  ARC: dynamic array(range,range) of integer  ! Matrix of the adjacency graph
  DUR: array(TASKS) of integer        ! Duration of tasks
  HORIZON : integer                   ! Time horizon

  start: array(TASKS) of cpvar        ! Start dates of tasks
  bestend: integer
 end-declarations

 initializations from 'Data/b1stadium.dat'
  DUR ARC
 end-initializations

 HORIZON:= sum(j in TASKS) DUR(j)

 forall(j in TASKS) do
  0 <= start(j); start(j) <= HORIZON
 end-do

! Task i precedes task j
 forall(i, j in TASKS | exists(ARC(i, j))) do
  Prec(i,j):= start(i) + DUR(i) <= start(j)
  if not cp_post(Prec(i,j)) then
   writeln("Posting precedence ", i, "-", j, " failed")
   exit(1)
  end-if
 end-do

! Since there are no side-constraints, the earliest possible completion
! time is the earliest start of the fictitiuous task N
 bestend:= getlb(start(N))
 start(N) <= bestend
 writeln("Earliest possible completion time: ", bestend)

! For tasks on the critical path the start/completion times have been fixed
! by setting the bound on the last task. For all other tasks the range of
! possible start/completion times gets displayed.
 forall(j in TASKS) writeln(j, ": ", start(j))

end-model