(!****************************************************************
   CP example problems
   ===================
   
   file b1stadium_main.mos
   ```````````````````````
   Construction of a stadium
   (See "Applications of optimization with Xpress-MP",
        Section 7.1 Construction of a stadium)

   1. Calculate the earliest completion time with the given
      durations of the operations.
   2. Reduce the completion time of the project such that the total 
      profit calculated as
        BONUS_per_week_finished_earlier - COST_of_finishing_earlier
      is maximized.
   
   The first problem is solved merely by posting the precedence
   constraints in a CP model. Since there are no side-constraints, the 
   earliest possible completion time is the earliest start of the last, 
   fictitiuous task N. We get it for free (i.e. without enumeration) 
   thanks to the propagation of constraints.
   
   For the formulation of the second problem the definition of the
   CP model is changed: durations are turned into variables and start 
   times are bounded by the previously calculated earliest completion 
   time. The feasible start time intervals are again determined by 
   constraint propagation. 
   The complete problem is then formulated and solved as an LP problem, 
   taking the lower bounds on start times from the CP model. Doing so
   we may switch off the preprocessing of the LP model - the CP constraint
   propagation is used as preprocessor.
   
   (c) 2008 Fair Isaac Corporation
       author: S. Heipcke, March 2005, rev. Jul. 2017
*****************************************************************!)
model "B-1 Stadium construction (CP + LP) main model"
 uses "mmxprs", "mmjobs"

 forward procedure print_CP_solution(num: integer)

 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
  BONUS: integer                      ! Bonus per week finished earlier
  MAXW: array(TASKS) of integer       ! Max. reduction of tasks (in weeks)
  COST: array(TASKS) of real          ! Cost of reducing tasks by a week 
  lbstart,ubstart: array(TASKS) of integer  ! Bounds on start dates of tasks
  HORIZON: integer                    ! Time horizon 
  bestend: integer                    ! CP solution value

  CPmodel: Model                      ! Reference to the CP model
  msg: Event                          ! Termination message sent by submodel
 end-declarations

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

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

! **** First CP model ****

 res:= compile("b1stadium_sub.mos")   ! Compile the CP model
 load(CPmodel, "b1stadium_sub.bim")   ! Load the CP model
 setworkdir(CPmodel, ".")
 run(CPmodel, "MODE=1,HORIZON=" + HORIZON)  ! Solve first version of CP model
 wait                                 ! Wait until subproblem finishes
 msg:= getnextevent                   ! Get the termination event message
 if getclass(msg)<>EVENT_END then     ! Check message type
  writeln("Submodel 1 is infeasible")
  exit(1)
 end-if
 
 initializations from "raw:"
  lbstart as "shmem:lbstart" ubstart as "shmem:ubstart"
 end-initializations

 bestend:= lbstart(N)
 print_CP_solution(1)

! **** Second CP model ****

 run(CPmodel, "MODE=2,HORIZON=" + bestend)  ! Solve second version of CP model
 wait                                 ! Wait until subproblem finishes
 msg:= getnextevent                   ! Get the termination event message
 if getclass(msg)<>EVENT_END then     ! Check message type
  writeln("Submodel 2 is infeasible")
  exit(2)
 end-if
 
 ! Retrieve solution from memory
 initializations from "raw:"
  lbstart as "shmem:lbstart" ubstart as "shmem:ubstart"
 end-initializations

 print_CP_solution(2)
  
! **** LP model for second problem ****
 declarations
  start: array(TASKS) of mpvar        ! Start times of tasks
  save: array(TASKS) of mpvar         ! Number of weeks finished early
 end-declarations 

! Objective function: total profit
 Profit:= BONUS*save(N) - sum(i in 1..N-1) COST(i)*save(i)

! Precedence relations between tasks
 forall(i,j in TASKS | exists(ARC(i,j)))  
  Precm(i,j):= start(i) + DUR(i) - save(i) <= start(j)

! Total duration
 start(N) + save(N) = bestend

! Limit on number of weeks that may be saved
 forall(i in 1..N-1) save(i) <= MAXW(i)

! Bounds on start times deduced by constraint propagation
 forall(i in 1..N-1) do
  lbstart(i) <= start(i); start(i) <= ubstart(i)
 end-do

! Solve the second problem: maximize the total profit
 setparam("XPRS_VERBOSE", true)
 setparam("XPRS_PRESOLVE", 0)   ! We use constraint propagation as preprocessor
 maximize(Profit) 
 
! Solution printing
 writeln("Total profit: ", getsol(Profit))
 writeln("Total duration: ", getsol(start(N)), " weeks")
 forall(i in 1..N-1)
  write(strfmt(i,2), ": ", strfmt(getsol(start(i)),-3),
   if(i mod 6 = 0,"\n",""))
 writeln

!*********************************************************************
 procedure print_CP_solution(num: integer)
  writeln("CP solution (version ", num, "):")
  writeln("Earliest possible completion time: ", lbstart(N), " weeks")
  forall(i in 1..N-1) 
   write(i, ": ", lbstart(i), if(lbstart(i)<ubstart(i), "-"+ubstart(i), ""),
        if(i mod 6 = 0, "\n", ", "))
 end-procedure
  
end-model