A Stochastic Integer Program with Dual Network Structure and its Application to the

Ground Holding Problem

Michael O. Ball, Robert Hoffman^{∗} Amedeo Odoni, Ryan Rifkin^{†}

March 26, 2000

Abstract

In this paper, we analyze a generalization of a classic network flow model. The generalization involves the replacement of deterministic demand with stochastic demand. While this generalization destroys the original network structure, we show that the matrix underlying the stochastic model is dual network. Thus, the integer program associated with the stochastic model can be solved efficiently using network flow or linear programming techniques. We also develop an application of this model to the ground holding problem in air traffic management. The use of this model for the ground holding problem improves upon prior models by allowing for easy integration into the newly developed ground delay program procedures based on the Collaborative Decision Making paradigm.

∗University of Maryland at College Park †Massachusetts Institute of Technology