*******************************************************
*   Mosel Example Problems
*   ======================
*
*  Origin file foliodata.mos
*   ``````````````````
*   Modeling a small LP problem
*   to perform portfolio optimization.
*   -- Parameters, data input from file,
*      result output to file --
*
*   (c) 2003 Dash Associates
*       author: S. Heipcke
********************************************************

* model "Portfolio optimization with LP"
* uses "mmxprs"                       ! Use Xpress-Optimizer

* Set of shares
Set SHARES / treasury , hardware , theater  , telecom  ,    brewery  ,
             highways , cars     , bank     , software , electronics / ;

* Set of shares issued in N.-America
Set NA_1(SHARES) / treasury , hardware , theater , telecom / ;

* Max. investment into high-risk values
Scalar MAXRISK / 1 / ; MAXRISK = MAXRISK/3 ;
* Max. investment per share
Scalar MAXVAL  / 0.3 / ;
* Min. investment into N.-American values
Scalar MINAM   / 0.5 / ;

* Set of high-risk values among shares
Set RISK(SHARES) / hardware
                   theater
                   telecom
                   software
                   electronics / ;

* Estimated return in investment
Parameter RET[SHARES] / treasury      5 ,
                        hardware     17 ,
                        theater      26 ,
                        telecom      12 ,
                        brewery       8 ,
                        highways      9 ,
                        cars          7 ,
                        bank          6 ,
                        software     31 ,
                        electronics  21 / ;

* Fraction of capital used per share
Variable frac[SHARES] ,
         Return       ;

Equation Eq_1    ,
         Eq_2    ,
         Eq_3    ,
         Def_Obj ;

* Limit the percentage of high-risk values
Eq_1..
   Sum{SHARES$RISK(SHARES), frac[SHARES]} =l= MAXRISK ;

* Minimum amount of North-American values
Eq_2..
   Sum{SHARES$NA_1(SHARES), frac[SHARES]} =g= MINAM ;

* Spend all the capital
Eq_3..
   Sum{SHARES, frac[SHARES]} =e= 1 ;

* Objective: total return
Def_Obj..
    Return =e= Sum{SHARES, RET[SHARES]*frac[SHARES] } ;

* Upper bounds on the investment per share
frac.up[SHARES] = MAXVAL ;

* Lower bounds on the investment per share
frac.lo[SHARES] = 0 ;

* Solve the problem
Model Portfolio_optimization / all / ;

* Solve the problem
Solve Portfolio_optimization using LP maximazing Return ;

Display Return.l ;