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 hy- pergraph 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.