Given a bipartite graph $G=(U\cup V,E)$, $\left|U\right|⩽\left|V\right|$, the surplus of $G$ is defined by the maximum number $k$ such that a matching covering all vertices of $U$ still exists upon removal of any $k$ vertices from $V$. Given a partition $\mathcal{U}=\{U_1,\dots ,U_m\}$ of $U$, the Multiple Bipartite Complete Matching Vertex Blocker Problem (MBCMVBP) consists in finding a partition $\mathcal{V}=\{V_1,\dots ,V_m\}$ of $V$ such that the smallest surplus among those of the induced subgraphs $G[U_i\cup V_i]$ is maximized. The removed vertices are related to the blocker notion. We show the strong NP-hardness of the MBCMVBP by using a reduction from the stable set problem. We also propose two integer linear programs for solving this problem. After comparing these two models, we introduce some valid inequalities for the model that outperforms the other one, and we analyze its facial structure. We then derive a Branch-and-Cut algorithm based on these results and conclude by an analysis of the experimental results.

给定二部图 $G=（ü\cup V，Ë）$， $\left|ü\right|⩽\left|V\right|$，盈余 $G$ 由最大数量定义 $ķ$ 这样一个匹配覆盖了所有顶点 $ü$ 移除后仍然存在 $ķ$ 来自的顶点 $V$。给定一个分区$\mathcal{ü}=\{{ü}_{\mathrm{1个}}，\dots ，{ü}_{米}\}$ 的 $ü$，多重二部完全匹配顶点阻止程序问题（MBCMVBP）在于查找一个分区 $\mathcal{V}=\{V_{\mathrm{1个}}，\dots ，V_{米}\}$ 的 $V$ 这样，在归纳的子图中，最小的盈余 $G[{ü}_{\mathrm{一世}}\cup V_{\mathrm{一世}}]$被最大化。删除的顶点与阻塞概念有关。通过使用稳定集问题的减少，我们展示了MBCMVBP的强NP硬度。我们还提出了两个整数线性程序来解决此问题。比较这两个模型后，我们引入了一些优于另一个模型的有效不等式，并分析了其面部结构。然后，我们根据这些结果得出“分支并剪切”算法，并通过对实验结果的分析得出结论。