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## [Help-glpk] Problem representing c = min (a, b)

**From**: |
dhiguero |

**Subject**: |
[Help-glpk] Problem representing c = min (a, b) |

**Date**: |
Thu, 18 Nov 2010 13:09:21 +0100 |

**User-agent**: |
RoundCube Webmail/0.4 |

Hi everybody,

` I am trying to represent a problem using linear programming and I
``got stuck in how to model the minimum function. My problem is being
``c,a,b variables of the problem (not params), I would like to declare c
``as c = min(a,b). I have tried the approach of introducing a new binary
``variable B, such as:
`
# c = min (a, b)
(a-b)B >= 0
(a-b)(1-B) <= 0
c = aB+b(1-B)

` But the problem is that I receive a "multiplication of linear forms
``not allowed". Does anybody have any suggestion or solution on how to
``model this type of requirement? In order to clarify the context of the
``problem, imagine that a set of machines can be assigned different
``network cards (type A with speed 10, type B with speed 100). The
``assignation of type A and type B depends on the cost function, let's
``say A cost 100€ and B cost 200€. In this scenario I now want to add the
``cost of transfering data between 2 machines which is limited by the
``minimum speed.
`
Thanks for your time, any comment is appreciated.
Best Regards,
Daniel

**[Help-glpk] Problem representing c = min (a, b)**,
*dhiguero* **<=**