(!******************************************************
   Mosel Example Problems
   ======================

   file b3jobshop3.mos
   ```````````````````
   Job shop production planning, 
   second, generic formulation.
   - Set/list version -
   
   Three types of wallpaper pass through three machines in
   different orders depending on the design. Processing times
   differ based on surface and design. What order should the
   paper be scheduled so that the order is completed as soon
   as possible.
   
   This second model formulation uses double indices so that
   'start' is now defined by machine AND job. The duration 
   array is also expanded to machine and job. The job sequence
   per machine is represented by an 'array of list' and the 
   set of disjunctive jobs per machine as an 'array of set'
   data structure.
   
   (c) 2008-2022 Fair Isaac Corporation
       author: S. Heipcke, Aug. 2006, rev. Mar. 2022
*******************************************************!)

model "B-3 Job shop (3)"
 uses "mmxprs"

 declarations   
  JOBS: range                         ! Set of jobs (wall paper types)
  MACH: range                         ! Set of machines (colors)

  DUR: array(MACH,JOBS) of integer    ! Durations per machine and paper
  SEQ: array(JOBS) of list of integer ! Machine sequence per job
  DISJ: array(MACH) of set of integer ! Sets of jobs per machine
 
  start: array(MACH,JOBS) of mpvar    ! Start times of tasks
  finish: mpvar                       ! Schedule completion time
  y: array(range) of mpvar            ! Disjunction variables
 end-declarations

 initializations from 'b3jobshop3.dat'
  DUR SEQ
 end-initializations

 forall(m in MACH, j in JOBS | DUR(m,j)>0 ) create(start(m,j))
 
 BIGM:=sum(m in MACH, j in JOBS) DUR(m,j)  ! Some (sufficiently) large value

! Precedence constraints
 forall(j in JOBS, jlast=SEQ(j).last) finish >= start(jlast,j) + DUR(jlast,j)
 forall(j in JOBS) do
  pred:= SEQ(j).first     ! Same as: SEQ(j)(1)
  forall(m in gettail(SEQ(j),-1)) do 
   start(pred,j)+DUR(pred,j) <= start(m,j)
   pred:=m
  end-do
 end-do

! Disjunctions
 forall(m in MACH) DISJ(m):= union(j in JOBS | findfirst(SEQ(j),m)<>0) {j}
 d:=1
 forall(m in MACH, i,j in DISJ(m) | i<j) do
  create(y(d))
  y(d) is_binary
  start(m,i) + DUR(m,i) <= start(m,j) + BIGM*y(d)
  start(m,j) + DUR(m,j) <= start(m,i) + BIGM*(1-y(d))
  d+=1
 end-do

! Bound on latest completion time
 finish <= BIGM

! Solve the problem: minimize latest completion time
 minimize(finish)

! Solution printing
 declarations
  COLOR: array(MACH) of string         ! Colors printed by the machines
 end-declarations

 initializations from 'b3jobshop3.dat'
  COLOR
 end-initializations

 writeln("Total completion time: ", getobjval)
 write("     ")
 forall(j in JOBS) write(strfmt(j,6))
 writeln
 forall(m in MACH) do
  write(strfmt(COLOR(m),-7))
  forall(j in JOBS)
   if(DUR(m,j)>0) then
    write(strfmt(getsol(start(m,j)),3), "-", getsol(start(m,j))+DUR(m,j))
   else
    write(strfmt(" ",6))
   end-if 
  writeln
 end-do
 
end-model