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[Help-glpk] Help using auxiliar variables

From: dhiguero
Subject: [Help-glpk] Help using auxiliar variables
Date: Mon, 22 Nov 2010 16:21:34 +0100
User-agent: RoundCube Webmail/0.4

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.



Attachment: min_problem_reduced_v2.mod
Description: Text document

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