(!******************************************************
   Mosel Example Problems
   ======================
    
   file a2food.mos
   ```````````````
   Food production for farm animals
   
   Food must meet required content levels of nutritional 
   components (Proteins, Lipids, Fiber). Given the raw 
   materials available each day and daily demand to meet, 
   the objective is to determine how the Oat, Maize, 
   and Molasses should be blended to minimize the total cost.

   Simple linear programming blending problem formulation includes 
   data with string indices and string formatting for solution printout.

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

model "A-2 Animal Food Production"
 uses "mmxprs"
 
 declarations
  FOOD = 1..2                    ! Food types
  COMP = 1..3                    ! Nutritional components
  RAW  = {"oat", "maize", "molasses"}   ! Raw materials
  
  P: array(RAW,COMP) of real     ! Composition of raw materials (in percent)
  REQ: array(COMP) of real       ! Nutritional requirements
  AVAIL: array(RAW) of real      ! Raw material availabilities
  COST: array(RAW) of real       ! Raw material prices
  PCOST: array(set of string) of real  ! Cost of processing operations
  DEM: array(FOOD) of real       ! Demands for food types

  use: array(RAW,FOOD) of mpvar  ! Quantity of raw mat. used for a food type
  produce: array(FOOD) of mpvar  ! Quantity of food produced
 end-declarations

 initializations from 'a2food.dat'
  P REQ PCOST DEM
  [AVAIL, COST] as 'RAWMAT'
 end-initializations
 
! Objective function  
 Cost:= sum(r in RAW,f in FOOD) COST(r)*use(r,f) +
        sum(r in RAW,f in FOOD|r<>"molasses") PCOST("grinding")*use(r,f) +
        sum(r in RAW,f in FOOD) PCOST("blending")*use(r,f) +
        sum(r in RAW) PCOST("granulating")*use(r,1) +
        sum(r in RAW) PCOST("sieving")*use(r,2)

! Quantity of food produced corresponds to raw material used
 forall(f in FOOD) sum(r in RAW) use(r,f) = produce(f)

! Fulfill nutritional requirements
 forall(f in FOOD,c in 1..2) 
  sum(r in RAW) P(r,c)*use(r,f) >= REQ(c)*produce(f)
 forall(f in FOOD) sum(r in RAW) P(r,3)*use(r,f) <= REQ(3)*produce(f)

! Use raw materials within their limit of availability
 forall(r in RAW) sum(f in FOOD) use(r,f) <= AVAIL(r)

! Satisfy demands
 forall(f in FOOD) produce(f) >= DEM(f)

! Solve the problem
 minimize(Cost)

! Solution printing
 writeln("Total cost: ", getobjval)
 write("Food type"); forall(r in RAW) write(strfmt(r,9))
 writeln("  protein  lipid   fiber")
 forall(f in FOOD) do
  write(strfmt(f,-9))
  forall(r in RAW) write(strfmt(getsol(use(r,f)),9,2))     
  forall(c in COMP) write("   ", 
   strfmt(getsol(sum(r in RAW) P(r,c)*use(r,f))/getsol(produce(f)),3,2),"%")
  writeln
 end-do
 
end-model