A dynamic Stochastic model for the single airport ground holding problem

In this paper, we present a dynamic stochastic integer programming (IP) model for the single airport ground holding problem, in which ground delays assigned to flights can be revised during different decision stages, based on weather forecasts. The performance gain from our model is particularly significant in the following cases: (1) under stringent ground holding policy, (2) when an early ground delay program (GDP) cancellation is likely, and (3) for airports where the ratio between adverse and fair weather capacities is lower. The choice of ground delay cost component in the objective function strongly affects the allocation policy. When it is linear, the optimal solution involves releasing the long-haul flights at or near their scheduled departure times and using the short-haul flights to absorb delays if low-capacity scenarios eventuate. This policy resembles the current practice of exempting long-distance flights during ground delay programs. For certain convex ground delay cost functions, the spread of ground delay is more or less uniform across all categories of flights, which makes the overall delay assignment more equitable. Finally, we also present a methodology that could enable intra-airline flight substitutions by airlines after our model has been executed and scenario-specific slots have been assigned to all flights, and hence to the airlines that operate them. This makes our model applicable under the collaborative decision making (CDM) paradigm by allowing airlines to perform cancellations and substitutions and hence reoptimize their internal delay cost functions.