We study stochastic integer programming models for assigning delays to flights that are destined for an airport whose capacity has been impacted by poor weather or some other exogenous factor. In the existing literature, empirical evidence seemed to suggest that a proposed integer programming model had a strong formulation, but no existing theoretical results explained the observation. We apply recent results concerning the polyhedra of stochastic network flow problems to explain the strength of the existing model, and we propose a model whose size scales better with the number of flights in the problem and that preserves the strength of the existing model. Computational results are provided that demonstrate the benefits of the proposed model. Finally, we define a type of equity property that is satisfied by both models.
- Air traffic flow management
- Equity properties
- Facet-defining inequalities
- Single airport ground holding problem
- Stochastic integer programming