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

   file foliocbio.mos
   ``````````````````
   Modeling a MIP problem 
   to perform portfolio optimization.

   Same model as in foliomip3.mos.
   -- Defining an integer solution callback 
      to write out solution information to external program --

  *** This model cannot be run with a Community Licence 
      for the provided data instance ***

  (c) 2011 Fair Isaac Corporation
      author: S.Heipcke, July 2011, rev. Mar. 2022
*******************************************************!)

model "Portfolio optimization with MIP"
 uses "mmxprs"
 uses "mmjobs"

 parameters
  MAXRISK = 1/3                     ! Max. investment into high-risk values
  MINREG = 0.2                      ! Min. investment per geogr. region
  MAXREG = 0.5                      ! Max. investment per geogr. region
  MAXSEC = 0.25                     ! Max. investment per ind. sector
  MAXVAL = 0.2                      ! Max. investment per share
  MINVAL = 0.1                      ! Min. investment per share
  MAXNUM = 15                       ! Max. number of different assets
  DATAFILE = "folio250.dat"         ! File with problem data
  OUTPUTFILE = "sol10out.dat"       ! File for solution output
  FRACSOL = "FRAC"                  ! Locations for solution output
  BUYSOL = "BUY"
  NUMSHARES = "NUMSHARES"
  RETSOL = "RETSOL"
  SOLCOUNT = "SOLCOUNT"
 end-parameters

 forward procedure printsol

 declarations
  SHARES,S: set of string            ! Set of shares
  RISK: set of string                ! Set of high-risk values among shares
  REGIONS: set of string             ! Geographical regions
  TYPES: set of string               ! Share types (ind. sectors)
  LOC: array(REGIONS) of set of string ! Sets of shares per geogr. region
  RET: array(SHARES) of real         ! Estimated return in investment
  SEC: array(TYPES) of set of string ! Sets of shares per industry sector
 end-declarations

 initializations from DATAFILE
  RISK RET LOC SEC
 end-initializations

 declarations
  frac: array(SHARES) of mpvar      ! Fraction of capital used per share
  buy: array(SHARES) of mpvar       ! 1 if asset is in portfolio, 0 otherwise
 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

! Limits on geographical distribution
 forall(r in REGIONS) do
  sum(s in LOC(r)) frac(s) >= MINREG
  sum(s in LOC(r)) frac(s) <= MAXREG
 end-do 

! Diversification across industry sectors
 forall(t in TYPES) sum(s in SEC(t)) frac(s) <= MAXSEC

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

! Limit the total number of assets
 sum(s in SHARES) buy(s) <= MAXNUM

 forall(s in SHARES) do
  buy(s) is_binary                  ! Turn variables into binaries
  frac(s) <= MAXVAL*buy(s)                 ! Linking the variables
  frac(s) >= MINVAL*buy(s)                 ! Linking the variables
 end-do


! Display Optimizer log
 setparam("XPRS_verbose", true)

! Adapt Mosel comparison tolerance to Optimizer feasibility tolerance
 setparam("zerotol", getparam("XPRS_feastol")/10)

! Set a MIP solution callback
 setcallback(XPRS_CB_INTSOL, ->printsol)

! Solve the problem
 maximize(Return)

 if getprobstat <> XPRS_OPT then exit(1); end-if 


!******** Solution output********

!**** Auxiliary function creating an array of solution values ****
 function getvalues(v: array(SHARES) of mpvar): dynamic array(S) of real
  forall(s in SHARES | v(s).sol<>0) returned(s):= v(s).sol  
 end-function


!**** Definition of the MIP solution callback function ****
 procedure printsol
  initializations to OUTPUTFILE
   evaluation of getparam("XPRS_MIPSOLS") as SOLCOUNT
   evaluation of sum(s in SHARES | buy(s).sol<>0) 1 as NUMSHARES
   evaluation of getsol(Return) as RETSOL
   evaluation of getvalues(frac) as FRACSOL
   evaluation of getvalues(buy) as BUYSOL
  end-initializations
 end-procedure

end-model