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

   file d5cutsh.mos
   ````````````````
   Cutting of sheet metal 
   (2-dimensional cutting patterns)
   
   A sheet metal shop cuts large pieces of sheet metal into
   4 smaller sizes. There are 16 possible patterns that a 
   large sheet can be cut into. How can the incoming order
   be met while using the smallest number of large sheets?
   
   This mathematical model (formulated as a covering problem)
   is very compact since the patterns have already been 
   pre-computed.

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

model "D-5 Sheet metal cutting"
 uses "mmxprs"

 declarations
  PATTERNS = 1..16                       ! Set of cutting patterns
  SIZES = 1..4                           ! Set of sheet sizes

  DEM: array(SIZES) of integer           ! Demands for the different sizes
  CUT: array(SIZES,PATTERNS) of integer  ! Cutting patterns
  
  use: array(PATTERNS) of mpvar          ! Use of cutting patterns
 end-declarations
 
 initializations from 'd5cutsh.dat'
  DEM CUT
 end-initializations

! Objective: total number of sheets used
 Sheets:= sum(p in PATTERNS) use(p)

! Satisfy demands
 forall(s in SIZES) sum(p in PATTERNS) CUT(s,p)*use(p) >= DEM(s)

 forall(p in PATTERNS) use(p) is_integer

! Solve the problem
 minimize(Sheets)
 
! Solution printing
  writeln("Total number of large sheets: ", getobjval)
  write("Cutting patterns used: ")
  forall(p in PATTERNS)
   write( if(getsol(use(p)) > 0 , " " + p + ":" + getsol(use(p)), "") )
  write("\nExemplaries of sheets sizes cut: ")
  forall(s in SIZES)
   write(s, ":", getsol(sum(p in PATTERNS) CUT(s,p)*use(p)), " ")
  writeln
      
end-model