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## Re: [Help-glpk] Piecewise linear objective functions

**From**: |
Andrew Makhorin |

**Subject**: |
Re: [Help-glpk] Piecewise linear objective functions |

**Date**: |
Thu, 9 Aug 2007 13:37:16 +0400 |

>* I would like to know if it is possible with GLPK to solve problems*
>* with a piecewise linear objective function.*
It is possible. However, you need to reformulate your problem,
because glpk does not support non-linear objective and constraints.
A standard way to model a piecewise objective is using SOS2
constraints, which, in turn, can be modeled as follows:
http://lists.gnu.org/archive/html/help-glpk/2007-06/msg00005.html
>* I currently work on a model for supply chain planning which uses a*
>* term in the objective funktion with is equal to zero as long as the*
>* value of a decision variable is greater than a given constant value,*
>* and wich is equal to the product of a cost constant and the*
>* difference of the constant and the decision variable.*
>* I use ILOG OPL Studio for developing the model and CPLEX for solving*
>* it.*
Please note that glpk is much weaker than cplex in the sense of
ability to solve large or hard MIPs.
>* Recently I got the hint to look for GLPK, so I made it running on my*
>* PC and ported the model. Everything is fine except the piecewise*
>* objective term.*
>* (In ILOG OPL I modeled it with a function within the objective*
>* function:*
>* maximize sum(...) ... + cost * maxl(0, constant - Variable); )*
>* BTW: is there any GUI for GLPK which has similar functionality like*
>* OPL Studio for CPLEX?*
Unfortunately, not.