/*

  Scheduling in Picat.

  Example from SICStus Prolog:
  http://www.sics.se/sicstus/docs/latest/html/sicstus/Cumulative-Scheduling.html#Cumulative%20Scheduling

  """
  Cumulative Scheduling

  This example is a very small scheduling problem. We consider seven
  tasks where each task has a fixed duration and a fixed amount of used
  resource:

  Task Duration Resource
   t1    16       2
   t2     6       9
   t3    13       3
   t4     7       7
   t5     5      10
   t6    18       1
   t7     4      11

  The goal is to find a schedule that minimizes the completion time for
  the schedule while not exceeding the capacity 13 of the resource. The
  resource constraint is succinctly captured by a cumulative/4
  constraint. Branch-and-bound search is used to find the minimal
  completion time. 

  This example was adapted from [Beldiceanu & Contejean 94]. 
  """

  Model created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.

go =>
   Capacity = 13,
   schedule1(Ss, End, Capacity),
   writeln(capacity= Capacity),
   writeln([Ss, End]).

schedule1(Ss, End,Capacity) =>

   Ds = [16, 6,13, 7, 5,18, 4],
   Ss = new_list(Ds.length),
   Ss :: 1..30,

   Rs = [ 2, 9, 3, 7,10, 1,11],
   End :: 1..50,

   after(Ss, Ds, End),
   cumulative(Ss, Ds, Rs, Capacity),

   Vars = Ss ++ [End],

   solve([$min(End)],Vars).


after([], [], _) => true.
after([S|Ss], [D|Ds], E) => E #>= S+D, after(Ss, Ds, E).