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

   file h4retire.mos
   `````````````````
   Financing an early retirement scheme
  
   To finance a pre-retirement scheme, a bank can invest 
   in three different types of bonds during a given period
   of years. Bonds can be acquired only at the beginning of
   the first year. Some technical conditions are defined on
   the money not invested, the quantity of bonds to be bought 
   and the available money to be distributed. How many bonds 
   of each type should the bank acquire to minimize the money
   spent to cover the retirement scheme?

   A MIP model is implemented to determine the best way to 
   finance the retirement plan. To model the constraints 
   based on the maturity (duration) of the bond, conditionals
   over sums and the inline 'if' are used to generalize
   the set of constraints.

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

model "H-4 Retirement"
 uses "mmxprs"

 declarations
  BONDS = {"SNCF","Fujitsu","Treasury"}  ! Set of bonds
  NT = 7                              ! Length of planning period
  YEARS = 1..NT
  
  DEM: array(YEARS) of integer        ! Annual payments for retirement
  VALUE: array(BONDS) of real         ! Unit price of bonds
  RATE: array(BONDS) of real          ! Remuneration rates paid by bonds
  RET: array(BONDS) of real           ! Unit annual interest of bonds
  DUR: array(BONDS) of real           ! Duration of loans
  INTEREST: real                      ! Interest for other secure investment
  
  buy: array(BONDS) of mpvar          ! Number of bonds acquired
  invest: array(YEARS) of mpvar       ! Other annual investment
  capital: mpvar                      ! Total capital required
 end-declarations

 initializations from 'h4retire.dat'
  DEM VALUE RATE DUR INTEREST
 end-initializations

 forall(b in BONDS) RET(b):= VALUE(b)*RATE(b)/100

! Annual balances
 capital - sum(b in BONDS) VALUE(b)*buy(b) - invest(1) = DEM(1)

 forall(t in 2..NT)
  sum(b in BONDS | DUR(b)+1>=t) (RET(b)*buy(b) + 
                                 if(DUR(b)+1=t, VALUE(b)*buy(b), 0)) +
   (1+INTEREST/100)*invest(t-1) - if(t<NT, invest(t), 0) = DEM(t)

 forall(b in BONDS) buy(b) is_integer

! Solve the problem: minimize invested capital
 minimize(capital)
 
! Solution printing
 writeln("Total capital: ", getobjval)
 writeln("Number of bonds to buy:")
 forall(b in BONDS) write(b, ": ", getsol(buy(b)), 
                          " (price: ", VALUE(b)*getsol(buy(b)), ") ")
 writeln("\nOther investment:") 
 forall(t in 1..NT-1) write("   year ", t)
 writeln
 forall(t in 1..NT-1) write(strfmt(getsol(invest(t)),9,3))
 writeln 
 
end-model