We deal with the hassle of increasing column technology (CG) for set-masking formulations through twin most reliable inequalities (DOIs). We examine novel training of DOIs, that are known as Flexible DOIs (F-DOIs) and Smooth-DOIs (S-DOIs), respectively (and at the same time as SF-DOIs). F-DOIs offer rebates for masking objects extra than necessary. S-DOIs describe the fee of a penalty to allow the undercoverage of objects in trade for the overinclusion of different objects. Unlike different training of DOIs from the literature, the S-DOIs and F-DOIs depend upon little or no hassle–precise expertise and, as such, have the ability to be implemented to a great wide variety of hassle domains. In particular, we talk the utility of the brand new DOIs to 3 applicable issues: the single-supply capacitated facility region hassle, the capacitated p-median hassle, and the capacitated vehicle-routing hassle. We offer computational proof of the energy of the brand new inequalities via way of means of embedding them inside a column-technology solver for those issues. Substantial speedups may be determined as while as compared with a nonstabilized variation of the equal CG system to attain the linear-rest decrease sure on issues with dense columns and dependent challenge costs.