Facets of the Stochastic Network Flow Problem
40 Pages Posted: 16 Sep 2019
Date Written: September 6, 2019
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.
Keywords: network flows, stochastic integer programming, F-graphs, facet-defining inequalities, directed hypergraphs
JEL Classification: C61
Suggested Citation: Suggested Citation