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Folio - Modelling examples from 'Getting started'

Description
  • Chapter 3 Inputting and Solving a Linear Programming problem
    • foliolp.mos: modeling and solving a small LP problem
    • foliolperr.mos: LP model with syntax errors
    • foliolps.mos: LP model using string indices
  • Chapter 4 Working with data
    • foliodata.mos (data file: folio.dat): data input from file, result output to a file, model parameters
    • folioodbc.mos (data files: folio.xls, folio.mdb, folio.sqlite): data input from a spreadsheet or database, result output to a spreadsheet or database, model parameters
    • folioexcel.mos (data file: folio.xls): same as folioodbc.mos but with Excel-specific data input and output (Windows only)
    • foliosheet.mos (data file: folio.xls): same as folioodbc.mos but with data input and output through generic spreadsheet access
    • foliocsv.mos (data file: folio.csv): same as folioodbc.mos but with data input and output through generic spreadsheet access in CSV format
  • Chapter 5 Drawing user graphs
    • folioloop.mos (data files: folio.dat, foliodev.dat): re-solving with varied parameter settings
    • folioloop_graph.mos (data files: folio.dat, foliodev.dat): re-solving with varied parameter settings, graphical solution display
    • foliolps_graph.mos: same as foliolps, adding graphical solution display
  • Chapter 6 Mixed Integer Programming
    • foliomip1.mos (data file: folio.dat): modeling and solving a small MIP problem (binary variables)
    • foliomip2.mos (data file: folio.dat): modeling and solving a small MIP problem (semi-continuous variables)
  • Chapter 7 Quadratic Programming
    • folioqp.mos (data file: folioqp.dat): modeling and solving a QP and a MIQP problem
    • folioqp_graph.mos (data files: folioqp.dat, folioqpgraph.dat): re-solving a QP problem with varied parameter settings, graphical solution display
    • folioqc.mos (data file: folioqp.dat): modeling and solving a QCQP and
    • foliomiqc.mos (data file: folioqp.dat): modeling and solving a MIQCQP
  • Chapter 8 Heuristics
    • folioheur.mos (data file: folio.dat): heuristic solution of a MIP problem


Source Files

Data Files





folioqp.mos

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

   file folioqp.mos
   ````````````````
   Modeling a small QP problem 
   to perform portfolio optimization.
   -- 1. QP: minimize variance
      2. MIQP: limited number of assets ---
   
  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, Aug. 2003, rev. Sep. 2017
*******************************************************!)

model "Portfolio optimization with QP/MIQP"
 uses "mmxprs", "mmnl"

 parameters
  MAXVAL = 0.3                      ! Max. investment per share
  MINAM = 0.5                       ! Min. investment into N.-American values
  MAXNUM = 4                        ! Max. number of different assets
  TARGET = 9.0                      ! Minimum target yield
 end-parameters

 declarations
  SHARES = 1..10                    ! Set of shares
  RISK: set of integer              ! Set of high-risk values among shares
  NA: set of integer                ! Set of shares issued in N.-America
  RET: array(SHARES) of real        ! Estimated return in investment
  VAR: array(SHARES,SHARES) of real ! Variance/covariance matrix of
                                    ! estimated returns
 end-declarations

 initializations from "folioqp.dat"
  RISK RET NA VAR
 end-initializations

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

! **** First problem: unlimited number of assets ****

! Objective: mean variance
 Variance:= sum(s,t in SHARES) VAR(s,t)*frac(s)*frac(t) 

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

! Spend all the capital
 sum(s in SHARES) frac(s) = 1
 
! Target yield
 sum(s in SHARES) RET(s)*frac(s) >=  TARGET

! Upper bounds on the investment per share
 forall(s in SHARES) frac(s) <= MAXVAL

! Solve the problem
 minimize(Variance)

! Solution printing
 writeln("With a target of ", TARGET, " minimum variance is ", getobjval)
 forall(s in SHARES) writeln(s, ": ", getsol(frac(s))*100, "%")  

! **** Second problem: limit total number of assets ****

 declarations
  buy: array(SHARES) of mpvar       ! 1 if asset is in portfolio, 0 otherwise
 end-declarations

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

 forall(s in SHARES) do
  buy(s) is_binary
  frac(s) <= buy(s)
 end-do

! Solve the problem
 minimize(Variance)

 writeln("With a target of ", TARGET," and at most ", MAXNUM,
          " assets,\n minimum variance is ", getobjval)
 forall(s in SHARES) writeln(s, ": ", getsol(frac(s))*100, "%") 
 
end-model 

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