[Help-glpk] Help using auxiliar variables

[dhiguero]

Hi everybody,

  After solving the min(a,b) problem, I have found another issue with 
the formalization. I attach the code so you can test it. The current 
scenario is:

  - A set of elements and a set of possible types.
  - Each type has an associated bandwidth so the bandwidth of each 
element must be the bandwidth of its type.
  - Minimum and maximum thresholds for the number of elements in the 
system per type. Some elements may not be used.
  - The objective is to minimize the number of elements used in the 
system. Right now, it is only the number of elements but in a future it 
will contain the cost associated with the work performed per element.

  The problem is associated with assigning bandwidth to elements. It 
seems that the solver has problems when I include equations such as:

s.t. available_bandwidth_on_elements {e in Elements}: bandwidth[e] == 
sum{t in Type} (elementType[e, t] * bandwidth_per_type[t]);

  If I use the equal, the solver introduces more elements than 
expected from the minimum threshold. If I change to greater or equal, 
the solver puts non-zero values in the bandwidth of unused elements.

  Any idea on how to model this type of assignations? The bandwidth 
variable is not part of the objective function, but I need these type 
of auxiliar variables to create future constraints in the model. Let's 
say I want to calculate the minimum number of elements such as a 
multicast message arrives on time to every element in the system and 
the total work is performed using the mimimum number of elements.

  Regards,

  Daniel

min_problem_reduced_v2.mod
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