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

[dhiguero]

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