A probabilistic comparison of the strength of split, triangle, and quadrilateral cuts

We consider mixed integer linear sets defined by two equations involving two integer variables and any number of non‐negative continuous variables. We analyze the benefit from adding a non‐split inequality on top of the split closure. Applying a probabilistic model, we show that the importance of a type 2 triangle inequality decreases with decreasing lattice width, on average. Our results suggest that this is also true for type 3 triangle and quadrilateral inequalities.