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

   file e5combine.mos
   ``````````````````
   Combining different modes of transport

   A large load needs to be transported through 5 cities via 
   3 possible transportation modes. Transportation type can
   be changed in any of the three intermediate cities. How
   should this load be transported so that the total cost of
   transportation and changing modes is minimized?

   This problem introduces triple indices for the variable 
   'change' since this is the change from mode m to mode n
   for leg l.
   
   (c) 2008-2022 Fair Isaac Corporation
       author: S. Heipcke, Mar. 2002, rev. Mar. 2022
*******************************************************!)

model "E-5 Combined transport"
 uses "mmxprs"

 declarations
  NL = 4
  LEGS = 1..NL                          ! Legs of the transport
  MODES: set of string                  ! Modes of transport

  CTRANS: array(MODES,LEGS) of integer  ! Transport cost
  CCHG: array(MODES,MODES) of integer   ! Cost of changing mode of transport
 end-declarations

 initializations from 'e5combine.dat'
  CTRANS CCHG
 end-initializations

 declarations
  use: array(MODES,LEGS) of mpvar        ! 1 if a mode is used, 0 otherwise 
  change: array(MODES,MODES,1..NL-1) of mpvar  ! 1 if change from mode m to n
                                               ! at end of leg, 0 otherwise
 end-declarations

! Objective: total cost
 Cost:= sum(m in MODES, l in LEGS) CTRANS(m,l)*use(m,l) +
         sum(m,n in MODES,l in 1..NL-1) CCHG(m,n)*change(m,n,l)

! One mode of transport per leg        
 forall(l in LEGS) sum(m in MODES) use(m,l) = 1
 
! Change or maintain mode of transport between every pair of legs 
 forall(l in 1..NL-1) sum(m,n in MODES) change(m,n,l) = 1

! Relation between modes used and changes
 forall(m,n in MODES,l in 1..NL-1) use(m,l) + use(n,l+1) >= 2*change(m,n,l)

 forall(m in MODES, l in LEGS) use(m,l) is_binary
 forall(m,n in MODES,l in 1..NL-1) change(m,n,l) is_binary
 
! Solve the problem
 minimize(Cost)
 
! Solution printing
 writeln("Total cost: ", getobjval)
 forall(l in LEGS) do
  write("  ",l, "-", l+1,": ")
  forall(m in MODES | getsol(use(m,l))>0) do
   write(m)
   break
  end-do
 end-do 
 writeln

end-model