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A Comparison of Formulations for the Single-Airport Ground-Holding Problem with Banking Constraints

Metron Scientific Consulting, 11911 Freedom Dr. Suite 800, Reston, Virginia 20190
R.H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, Maryland 20742
hoffman{at}metsci.com
mball{at}rhsmith.umd.edu

Both the single-airport ground-holding problem (GH) and the multi-airport ground-holding problem can be extended by the addition of banking constraints to accommodate the hubbing operations of major airlines. These constraints enforce the desire of airlines to land certain groups of flights, called banks, within fixed time windows, thus preventing the propagation of delays throughout their entire operation. GH can be formulated as a transportation problem and readily solved. But in the presence of banking constraints, GH becomes a difficult integer programming problem. In this paper, we construct five different models of the single-airport ground-holding problem with banking constraints (GHB). The models are evaluated both computationally and analytically. For two of the models, we show that the banking constraints induce facets of the convex hull of the set of integer solutions. In addition, we explore a linear transformation of variables and a branching technique.

Subject classifications: Programming: integer, algorithms; Transportation: models, air traffic management.
History: Received March 1997; revision received October 1997; accepted September 1998.

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