(!******************************************************
   CP Example Problems
   ===================

   file b4seq2_ka.mos
   ``````````````````
   Sequencing jobs on a bottleneck machine
   (See "Applications of optimization with Xpress-MP",
        Section 7.4 Sequencing jobs on a bottleneck machine)
   - Alternative formulation using disjunctions -

   *** This model cannot be run with a Community Licence 
       for the provided data instance ***

   (c) 2008 Artelys S.A. and Fair Isaac Corporation
       
*******************************************************!)

model "B-4 Sequencing (CP)"
 uses "kalis"

 forward procedure print_sol
 forward procedure print_sol3
 
 declarations   
  NJ = 7                          ! Number of jobs
  JOBS=1..NJ

  REL: array(JOBS) of integer     ! Release dates of jobs
  DUR: array(JOBS) of integer     ! Durations of jobs
  DUE: array(JOBS) of integer     ! Due dates of jobs
  DURS: array(set of cpvar) of integer  ! Dur.s indexed by start variables

  start: array(JOBS) of cpvar     ! Start time of jobs
  comp: array(JOBS) of cpvar      ! Completion time of jobs
  finish: cpvar                   ! Completion time of the entire schedule
  Disj: set of cpctr              ! Disjunction constraints
  Strategy: array(range) of cpbranching  ! Branching strategy
 end-declarations
 
 initializations from 'Data/b4seq.dat'
  DUR REL DUE
 end-initializations

 MAXTIME:= max(j in JOBS) REL(j) + sum(j in JOBS) DUR(j)

 forall(j in JOBS) do
  0 <= start(j); start(j) <= MAXTIME 
  0 <= comp(j); comp(j) <= MAXTIME
 end-do 

! Disjunctions between jobs
 forall(j in JOBS) DURS(start(j)):= DUR(j)
 disjunctive(union(j in JOBS) {start(j)}, DURS, Disj, 1)

! Start times
 forall(j in JOBS) start(j) >= REL(j)

! Completion times
 forall(j in JOBS) comp(j) = start(j) + DUR(j)

!**** Objective function 1: minimize latest completion time ****
 finish = maximum(comp)

 Strategy(1):= settle_disjunction(Disj)
 Strategy(2):= split_domain(KALIS_LARGEST_MAX, KALIS_MIN_TO_MAX)
 cp_set_branching(Strategy)
 
 if cp_minimize(finish) then
  print_sol
 end-if


!**** Objective function 2: minimize average completion time ****
 declarations   
  totComp: cpvar
 end-declarations

 totComp = sum(k in JOBS) comp(k)

 if cp_minimize(totComp) then
  print_sol
 end-if


!**** Objective function 3: minimize total tardiness ****
 declarations   
  late: array(JOBS) of cpvar      ! Lateness of jobs
  totLate: cpvar
 end-declarations

 forall(k in JOBS) do
  0 <= late(k); late(k) <= MAXTIME
 end-do 
 
! Late jobs: completion time exceeds the due date
 forall(j in JOBS) late(j) >= comp(j) - DUE(j) 

 totLate = sum(k in JOBS) late(k)
 if cp_minimize(totLate) then
  writeln("Tardiness: ", getsol(totLate))
  print_sol
  print_sol3
 end-if

!-----------------------------------------------------------------

! Solution printing
 procedure print_sol
  writeln("Completion time: ", getsol(finish) ,
          "  average: ", getsol(sum(j in JOBS) comp(j)))
  write("Rel\t")
  forall(j in JOBS) write(strfmt(REL(j),4))
  write("\nDur\t")
  forall(j in JOBS) write(strfmt(DUR(j),4))
  write("\nStart\t")
  forall(j in JOBS) write(strfmt(getsol(start(j)),4))
  write("\nEnd\t")
  forall(j in JOBS) write(strfmt(getsol(comp(j)),4))
  writeln
 end-procedure

 procedure print_sol3
  write("Due\t")
  forall(j in JOBS) write(strfmt(DUE(j),4))
  write("\nLate\t")
  forall(j in JOBS) write(strfmt(getsol(late(j)),4))
  writeln
 end-procedure 
 
end-model