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

   file foliomip2.mos
   ``````````````````
   Modeling a small MIP problem 
   to perform portfolio optimization.
   -- Imposing a minimum investment per share --
   
  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, Aug. 2003
*******************************************************!)

model "Portfolio optimization with MIP"
 uses "mmxprs"

 parameters
  MAXRISK = 1/3                     ! Max. investment into high-risk values
  MINAM = 0.5                       ! Min. investment into N.-American values
  MAXVAL = 0.3                      ! Max. investment per share
  MINVAL = 0.1                      ! Min. investment per share
 end-parameters

 declarations
  SHARES: set of string             ! Set of shares
  RISK: set of string               ! Set of high-risk values among shares
  NA: set of string                 ! Set of shares issued in N.-America
  RET: array(SHARES) of real        ! Estimated return in investment
 end-declarations

 initializations from "folio.dat"
  RISK RET NA
 end-initializations

 declarations
  frac: array(SHARES) of mpvar      ! Fraction of capital used per share
 end-declarations

! Objective: total return
 Return:= sum(s in SHARES) RET(s)*frac(s) 

! Limit the percentage of high-risk values
 sum(s in RISK) frac(s) <= MAXRISK

! Minimum amount of North-American values
 sum(s in NA) frac(s) >= MINAM

! Spend all the capital
 sum(s in SHARES) frac(s) = 1
 
! Upper and lower bounds on the investment per share
 forall(s in SHARES) do
  frac(s) <= MAXVAL
  frac(s) is_semcont MINVAL
 end-do

! Solve the problem
 maximize(Return)

! Solution printing
 writeln("Total return: ", getobjval)
 forall(s in SHARES) writeln(s, ": ", getsol(frac(s))*100, "%")  
 
end-model