SIAM Journal on Optimization, Volume 30, Issue 3, Page 2355-2378, January 2020.
We study a type of network flow problem that we call the minimum-cost F-graph flow problem. This problem generalizes the typical minimum-cost network flow problem by allowing the underlying network to be a directed hypergraph rather than a directed graph. This new problem is pertinent because it can be used to model network flow problems that occur in a dynamic, stochastic environment. We formulate this problem as an integer program, and we study specifically the case where every node has at least one outgoing edge with no capacity constraint. We show that even with this restriction, the problem of finding an integral solution is NP-hard. However, we can show that all of the inequality constraints of our formulation are either facet-defining or redundant.

中文翻译：

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随机网络流量问题的各个方面

SIAM优化杂志，第30卷，第3期，第2355-2378页，2020年1月。
我们研究了一种网络流量问题，我们称其为最小成本F图流量问题。通过允许基础网络成为有向超图而不是有向图，此问题概括了典型的最小成本网络流问题。此新问题是相关的，因为它可以用于对动态，随机环境中发生的网络流问题进行建模。我们将这个问题表述为一个整数程序，并且我们专门研究每个节点至少有一个输出边且没有容量约束的情况。我们证明，即使有此限制，找到积分解的问题也是NP-hard。但是，我们可以证明，我们公式的所有不平等约束都是刻面定义的或多余的。