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The Robust Maximum Flow Problem

We consider the robust maximum ow problem (RMFP) using the robust linear optimization methodology. We discuss two types of uncertainty on the arc capacities: box uncertainty and ellipsoidal uncertainty. In both cases, the RMFP is the usual maximum ow problem with modifed arc capacities.

In the case of box uncertainty the flow of each arc is bounded by the lower bounds of the box. In the case of ellipsoidal uncertainty, the capacity of each arc a is replaced by c n a – Qak where c n a is the nominal arc capacity and Qa is the corresponding column of the ellipsoidal scaling matrix Q. We present some examples.