Facets of the Stochastic Network Flow Problem

40 Pages Posted: 16 Sep 2019

See all articles by Alexander Estes

Alexander Estes

University of Minnesota - Institute for Mathematics and its Applications

Michael O. Ball

University of Maryland - Decision and Information Technologies Department

Date Written: September 6, 2019

Abstract

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

Estes, Alexander and Ball, Michael O., Facets of the Stochastic Network Flow Problem (September 6, 2019). Available at SSRN: https://ssrn.com/abstract=3449409 or http://dx.doi.org/10.2139/ssrn.3449409

Alexander Estes (Contact Author)

University of Minnesota - Institute for Mathematics and its Applications ( email )

425 Lind Hall
207 Church St SE
Minneapolis, MN 55455
United States

HOME PAGE: http://asestes1.github.io

Michael O. Ball

University of Maryland - Decision and Information Technologies Department ( email )

Robert H. Smith School of Business
4313 Van Munching Hall
College Park, MD 20815
United States
301-405-2227 (Phone)
301-405-8655 (Fax)

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