Originally posted by: SusanneFeder

Hi,

I want to solve a robust model of a network flow problem.

In the model I have the following set: 

S:={z \in [0,1]^|E|| \sum z_e <= K}

z is a vector that gives every arc e a value z_e that defines how much the capacity of this edge ist reduced.

K is a fixed integer.

The following constraint should be fulfilled for all possible z \in the set S:

For all vertices in the graph: \sum (over all incoming edges)(1-z_e)*(Flow on Edge e)-\sum(over all outgoing edges)(Flow on edge e) >=0;

How can I integrate that in the model as z is no decision variable?

I hope someone can help me with this question.

Hi,

let me give you a small example for the syntax about how to add a robust constraint.

Let's start with the example netflow that is in

http://www-01.ibm.com/support/knowledgecenter/SSSA5P_12.6.2/ilog.odms.ide.help/examples/html/opl/models/Netflow/netflow.mod.html?lang=en

and

CPLEXStudio1263\opl\examples\opl\models\Netflow

This model is not robust and gives TotalFlow 150

Now let's add your robust constraint

// Robust constraint

   forall(reduce in maxKarc) forall(a in arcReduce[reduce]) ctRobust:Flow[a]<=a.ub-1;

Then the TotalFlow gets 153 (Minimization model)

Let me attach the robust model.

Regards

NB:

You may also have a look at the uncertainty toolkit : http://www.research.ibm.com/labs/ireland/research_areas/uncertainty.html