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

   file c6assign.mos
   `````````````````
   Machine assignment for production batches
   
   10 batches must be produced in the upcoming period. There
   are 5 machines that can produce any given batch. However,
   processing time and cost depends on machine assignment.
   Each machine has a max production capacity. Determine the
   batch to machine assignment that minimizes the total cost
   of production.
   
   This is a generalized assignment problem and is a very
   compact mathematical model. Each batch must be assigned
   to only one machine and each machine must produce no more
   than its specified capacity. 

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

model "C-6 Machine assignment"
 uses "mmxprs"

 declarations   
  MACH = 1..5                        ! Set of machines
  PRODS = 1..10                      ! Set of production batches

  CAP: array(MACH) of integer        ! Machine capacities
  DUR: array(MACH,PRODS) of integer  ! Production durations
  COST: array(MACH,PRODS) of integer ! Production costs

  use: array(MACH,PRODS) of mpvar    ! 1 if machine assigned to batch, 
                                     ! 0 otherwise
 end-declarations

 initializations from 'c6assign.dat'
  DUR CAP COST
 end-initializations

! Objective: total production cost
 Cost:= sum(m in MACH, p in PRODS) COST(m,p)*use(m,p)

! Assign a single machine to every batch
 forall(p in PRODS) sum(m in MACH) use(m,p) = 1

! Limits on machine capacities
 forall(m in MACH) sum(p in PRODS) DUR(m,p)*use(m,p) <= CAP(m)

 forall(m in MACH, p in PRODS) use(m,p) is_binary

! Solve the problem
 minimize(Cost)
 
! Solution printing
 writeln("Total cost: ",getobjval)
 forall(m in MACH) do
  write("Machine ", m, ": ")
  forall(p in PRODS) 
   if (getsol(use(m,p))=1) then
    write(p, " ")
   end-if
  writeln(" (total duration: ", getsol(sum(p in PRODS) DUR(m,p)*use(m,p)), ")")
 end-do

end-model