When solving the linear programming (LP) relaxation of a mixed-integer program (MIP) with column generation, columns might be generated that are not needed to express any integer optimal solution. Such columns are called strongly redundant and the dual bound obtained by solving the LP relaxation is potentially stronger if these columns are not generated. We introduce a sufficient condition for strong redundancy that can be checked by solving a compact LP. Using a dual solution of this compact LP we generate classical Benders cuts for the subproblem so that the generation of strongly redundant columns can be avoided. The potential of these cuts to improve the dual bound of the column generation master problem is evaluated computationally using an implementation in the branch-price-and-cut solver GCG. While their efficacy is limited on classical problems, the benefit of applying the cuts is demonstrated on structured models to which a temporal decomposition can be applied.

解决带有列生成的混合整数程序（MIP）的线性规划（LP）松弛时，可能会生成不需要表达任何整数最优解的列。这样的列称为强冗余，如果不生成这些列，则通过解决LP弛豫获得的对偶边界可能会更强。我们介绍了一个强冗余的充分条件，可以通过解决紧凑的LP来检查。使用此紧凑型LP的双重解决方案，我们为子问题生成了经典的Benders切口，从而可以避免生成强冗余的色谱柱。使用分支价格和割价解算器GCG中的实现，通过计算评估了这些割伤改善列生成主问题的双重界限的潜力。