Abstract

We consider same model of planning the defense of edges of a supply network. The vertices of the network represent the consumers and the providers of a resource, while the edges allow us to transmit the resource without delays and capacity constraints. The Defender commits a bounded budget to protect some of the edges, aiming to minimize the damage that is caused by the destruction of the unprotected edges. To measure the damage, we apply the value of the total resource deficit caused by the worst-case scenario of partial network destruction. The Defender’s problem falls into the family of “Defender–Attacker” problems that are formalized as the minimax mixed-integer programming problems. To find an optimal Defender’s solution, we suggest some two cut generation schemes based on a reformulation of the problem as a mixed-integer problem with exponentially many constraints.

中文翻译：

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在供应网络破坏最坏的情况下，计划能够最大限度地减少资源赤字的防御措施

摘要

我们考虑规划供应网络边缘防御的相同模型。网络的顶点代表资源的使用者和提供者，而边缘则使我们能够传输资源而没有延迟和容量限制。防御者投入有限的预算来保护某些边缘，旨在最大程度地减少因破坏未受保护的边缘而造成的损坏。为了衡量损害，我们应用了由部分网络破坏的最坏情况导致的总资源赤字的值。防御者的问题属于“防御者-攻击者”（Defender-Attacker）问题系列，这些问题形式化为minimax混合整数编程问题。为了找到最佳的后卫解决方案，