Efficient approaches for the robust network loading problem

We consider the Robust Network Loading problem with splittable flows and demands that belong to the budgeted uncertainty set. Four routing schemes are investigated: static, volume, affine and dynamic. First, following what done for static and dynamic routing, we derive capacity formulation for affine and volume routing. This is done using a Benders reformulation approach. Then, we introduce the robust 3-partition inequalities and discuss their facet-defining status and the one of the well-known robust cutset inequalities. Finally, we test the effectiveness, from a computational viewpoint, of robust cutset, 3-partition and Benders-like inequalities. We compare the results obtained considering all routing schemes, using both the flow formulation and the Benders-like formulation on the capacity variables. We report computational experiments realized on several realistic instances from SNDlib, including instances based on historical traffic data.