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

   file i3school.mos
   `````````````````
   Determine a timetable for 2 classes

   A weekly timetable for two classes must be determined.
   The classes have the same teachers, except for mathematics
   and sport. The duration of a lesson, the slots to schedule
   courses, and specific requirements on days and slots to
   assign some courses are given. All students of a course must
   attend exactly the same courses. What teachers should be
   assigned to each class in each time slot?

   This IP model minimizes the number of 'holes' in the class
   timetables, formulated indirectly via the number of courses
   scheduled in the first or last time slots per day. Although 
   most of constraints are implemented in a generic way, some  
   specific requirements are implemented as explicit constraints.

   (c) 2008-2022 Fair Isaac Corporation
       author: S. Heipcke, Mar. 2002, rev. Mar. 2022
*******************************************************!)

model "I-3 School timetable"
 uses "mmxprs"

 declarations
  TEACHERS: set of string         ! Set of teachers
  CLASS = 1..2                    ! Set of classes
  NP = 4                          ! Number of time periods for courses
  ND = 5                          ! Days per week
  SLOTS=1..NP*ND                  ! Set of time slots for the entire week
  
  COURSE: array(TEACHERS,CLASS) of integer ! Lessons per teacher and class
 end-declarations

 initializations from 'i3school.dat'
  COURSE
 end-initializations

 declarations
  teach: array(TEACHERS,CLASS,SLOTS) of mpvar 
                                  ! teach(t,c,l) = 1 if teacher t gives a
                                  ! lesson to class c during time period l
 end-declarations

! Objective: number of "holes" in the class timetables
 Hole:= 
  sum(t in TEACHERS, c in CLASS, d in 0..ND-1) (teach(t,c,d*NP+1) + 
      teach(t,c,(d+1)*NP))

! Plan all courses
 forall(t in TEACHERS, c in CLASS) sum(l in SLOTS) teach(t,c,l) = COURSE(t,c)

! For every class, one course at a time
 forall(c in CLASS, l in SLOTS) sum(t in TEACHERS) teach(t,c,l) <= 1

! Teacher teaches one course at a time
 forall(t in TEACHERS, l in SLOTS) sum(c in CLASS) teach(t,c,l) <= 1

! Every subject only once per day
 forall(t in TEACHERS, c in CLASS, d in 0..ND-1) 
  sum(l in d*NP+1..(d+1)*NP) teach(t,c,l) <= 1
 
! Sport Thursday afternoon (slot 15)
 teach("Mr Muscle",1,15) = 1
 teach("Mrs Biceps",2,15) = 1
 
! No course during first period of Monday morning
 forall(t in TEACHERS, c in CLASS) teach(t,c,1) = 0

! No course by Mr Effofecks Monday morning
 forall(l in 1..2) teach("Mr Effofecks",2,l) = 0
 
! No Biology on Wednesday
 forall(c in CLASS, l in 2*NP+1..3*NP) teach("Mrs Insulin",c,l) = 0 

 forall(t in TEACHERS, c in CLASS, l in SLOTS) teach(t,c,l) is_binary
 
! Solve the problem
 minimize(Hole)
 
! Solution printing
 declarations
  DAYS=1..ND
  NAMES: array(DAYS) of string
 end-declarations
 
 initializations from 'i3school.dat'
  NAMES
 end-initializations

 writeln("Courses at begin or end of day: ", getobjval)
 forall(c in CLASS) do
  writeln("Class ",c)
  forall(d in DAYS) do
   write(NAMES(d), ":  ")
   forall(l in (d-1)*NP+1..d*NP)
    if (getsol(sum(t in TEACHERS) teach(t,c,l))>0) then
     forall(t in TEACHERS | getsol(teach(t,c,l))>0) write(strfmt(t,-14))
    else
     write(strfmt("",14))
    end-if     
   writeln 
  end-do
 end-do 

end-model