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A Stochastic Integer Program with Dual Network Structure and Its Application to the Ground-Holding Problem

R. H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, Maryland 20742
Metron Aviation, Inc., 131 Elden St., Herndon, Virginia 20170
Massachusetts Institute of Technology, Room 33-219, Cambridge, Massachusetts 02139
Center for Biological and Computational Learning, 45 Carleton Street, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
mball{at}rhsmith.umd.edu
hoff{at}metsci.com
arodoni{at}mit.edu
rif{at}alum.mit.edu

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.

Subject classifications: Transportation: air-traffic management; Programming integer: embedded networks.
History: Received February 1999; revision received July 2000; accepted August 2001.

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