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

   file j3elect.mos
   ````````````````
   Grouping quarters to election districts

   For elections, a capital is divided into zones called
   quarters. For each quarter, we know the forecasted number
   of favorable votes for a particular candidate and the total
   number of electors. An electoral district is formed by
   several adjacent quarters that must have between a minimum
   and a maximum number of voters. Determine a partitioning
   into five electoral districts that maximizes the number
   of seats for the candidate.

   This partitioning problem asks for a subset of electoral
   districts such that every quarter appears in a single chosen
   electoral district. The Mosel implementation is divided into
   the data preprocessing and the model itself. After data arrays
   declaration, the included file j3elect_calc.mos generates the data
   in the form required for the model. Function 'getprobstat'
   is used to test the optimization status.

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

model "J-3 Rigging elections"
 uses "mmxprs"

 parameters
  REQD = 6                            ! Required number of districts
 end-parameters

 declarations
  QUARTERS = 1..14                    ! Number of quarters
  RDIST: range                        ! Set of election districts
  
  MAJ: array(RDIST) of integer        ! 1 if majority of votes, 0 otherwise
  DISTR: array(RDIST,QUARTERS) of integer  ! 1 if quarter is in district,
                                           ! 0 otherwise
 end-declarations

 include "j3elect_calc.mos"

 declarations
  choose: array(RDIST) of mpvar      ! 1 if district chosen, 0 otherwise
 end-declarations

! Objective: number of votes
 Votes:= sum(d in RDIST) MAJ(d)*choose(d)

! Partitioning
 forall(q in QUARTERS) sum(d in RDIST) DISTR(d,q)*choose(d) = 1
 
! Desired number of districts
 sum(d in RDIST) choose(d) = REQD

 forall(d in RDIST) choose(d) is_binary

! Solve the problem
 maximize(Votes)
 
! Solution printing
 if(getprobstat<>XPRS_OPT) then
  writeln("Problem is infeasible")
 else 
  writeln("Total number of votes: ", getobjval)
  forall(r in RDIST | getsol(choose(r))>0) do
   write(r, ": ")
   forall(q in QUARTERS | DISTR(r,q)>0) write(" ", q)
   writeln(" (", MAJ(r), ")") 
  end-do
 end-if
  
end-model