We address the solution of Mixed Integer Linear Programming (MILP) models with strong relaxations that are derived from Dantzig-Wolfe decompositions and allow a pseudo-polynomial pricing algorithm. We exploit their network-flow characterization and provide a framework based on column generation, reduced-cost variable-fixing, and a highly asymmetric branching scheme that allows us to take advantage of the potential of the current MILP solvers. We apply our framework to a variety of cutting and packing problems from the literature. The efficiency of the framework is proved by extensive computational experiments, in which a significant number of open instances could be solved to proven optimality for the first time.

翻译：我们处理混合整形线性规划模型(MILP)的解决方案,这些模型来自丹兹格-沃尔菲分解法,具有很强的放松作用,并允许假球定价算法。 我们利用这些模型的网络流量特征,并提供一个基于柱子生成、降低成本的可变固定和高度不对称的分支计划的框架,使我们能够利用目前的MILP解答器的潜力。 我们将我们的框架应用于文献中的各种切割和包装问题。 框架的效率通过广泛的计算实验得到了证明,其中大量公开的事例可以首次被证明是最佳的。