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

   file foliolp.mos
   ````````````````
   Modeling a small LP problem 
   to perform portfolio optimization.
   
  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, Aug. 2003
*******************************************************!)

model "Portfolio optimization with LP"
 uses "mmxprs"

 declarations
  SHARES = 1..10                     ! Set of shares
  RISK = {2,3,4,9,10}                ! Set of high-risk values among shares
  NA = {1,2,3,4}                     ! Set of shares issued in N.-America
  RET: array(SHARES) of real         ! Estimated return in investment

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

 RET:: [5,17,26,12,8,9,7,6,31,21]
 
! 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) <= 1/3

! Minimum amount of North-American values
 sum(s in NA) frac(s) >= 0.5

! Spend all the capital
 sum(s in SHARES) frac(s) = 1
 
! Upper bounds on the investment per share
 forall(s in SHARES) frac(s) <= 0.3

! Solve the problem
 maximize(Return)

(!
 declarations
  Status:array({XPRS_OPT,XPRS_UNF,XPRS_INF,XPRS_UNB,XPRS_OTH}) of string
 end-declarations

 Status::([XPRS_OPT,XPRS_UNF,XPRS_INF,XPRS_UNB,XPRS_OTH])[
          "Optimum found","Unfinished","Infeasible","Unbounded","Failed"]
 
 writeln("Problem status: ", Status(getprobstat))
!)
 
! Solution printing
 writeln("Total return: ", getobjval)
 forall(s in SHARES) writeln(s, ": ", getsol(frac(s))*100, "%")  

end-model