I learned cutting plane based methods for solving integer programming problems. A good example is the cover inequalities for Knapsack problems. Strong cutting planes can improve the computational results a lot.
For set covering problems, I noticed there are several papers on valid inequalities (another name for cutting planes) by Sassano (Facets and lifting procedures for the set covering polytope), Balas (On the set covering polytope: I. All the facets with coefficients in (0, 1, 2)) around 1990.
However, it seems that there isn't any efficient cutting plane based methods for it; all efficient integer programming methods I know are based on primal and dual methods. Why are these strong valid inequalities developed by Balas and Sassano not helpful in the computational studies? Is it because they are difficult to separate? Are there any efficient heuristics for the separation problem? Or is it because they are actually weak in computational studies?