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

   file e6vanrent.mos
   ``````````````````
   Fleet planning for van rental
   
   A chain of stores uses a fleet of vans rented from
   multiple rental agencies. There is a choice between rental
   contracts of varying lengths. Which contracts should be 
   signed each month so that the number of vans meet the 
   requirements and there are no vans rented beyond the last month
   while minimizing rental costs?
   
   The implementation uses the Mosel functions 'maxlist' and 'minlist'
   to calculate the range of available months for each contract
   length. Note that these are different from the operators 'max'
   and 'min' which are used with set expressions.
   
   (c) 2008-2022 Fair Isaac Corporation
       author: S. Heipcke, Mar. 2002, rev. Mar. 2022
*******************************************************!)

model "E-6 Van rental"
 uses "mmxprs"

 declarations
  NM = 6
  MONTHS = 1..NM                      ! Months
  CONTR = 3..5                        ! Contract types

  REQ: array(MONTHS) of integer       ! Monthly requirements
  COST: array(CONTR) of integer       ! Cost of contract types
  NINIT: integer                      ! Vans rented at beginning of plan

  rent: array(CONTR,MONTHS) of mpvar  ! New rentals every month
 end-declarations

 initializations from 'e6vanrent.dat'
  REQ COST NINIT
 end-initializations

! Objective: total cost
 Cost:= sum(c in CONTR, m in MONTHS) COST(c)*rent(c,m)

! Fulfill the monthly requirements
 forall(m in MONTHS) 
  if(m<=2, NINIT, 0) + 
   sum(c in CONTR, n in maxlist(1,m-c+1)..minlist(m,NM-c+1)) rent(c,n) >= 
    REQ(m)

! Solve the problem
 minimize(Cost)
 
! Solution printing
 declarations
  NAMES: array(MONTHS) of string
 end-declarations

 initializations from 'e6vanrent.dat'
  NAMES
 end-initializations
 
 writeln("Total cost: ", getobjval)
 setparam("realfmt","%5g")   ! Reserve 5 char.s for display of real numbers
 write("new rents  ")
 forall(m in MONTHS) write(NAMES(m), "  ")
 writeln
 forall(c in CONTR) do
  write(c, " months ")
  forall(m in MONTHS) write(getsol(rent(c,m)))
  writeln
 end-do
 write("Total    ")
 forall(m in MONTHS) write(getsol(if(m<=2, NINIT, 0) + 
  sum(c in CONTR, n in maxlist(1,m-c+1)..minlist(m,NM-c+1)) rent(c,n)))
 writeln   

end-model