Distributionally Robust Airport Ground Holding Problem under Wasserstein Ambiguity Sets

Abstract: The airport ground holding problem seeks to minimize flight delay costs due to reductions in the capacity of airports. However, the critical input of future airport capacities is often difficult to predict, presenting a challenging yet realistic setting. Even when capacity predictions provide a distribution of possible capacity scenarios, such distributions may themselves be uncertain (e.g., distribution shifts). To address the problem of designing airport ground holding policies under distributional uncertainty, we formulate and solve the airport ground holding problem using distributionally robust optimization (DRO). We address the uncertainty in the airport capacity distribution by defining ambiguity sets based on the Wasserstein distance metric. We propose reformulations which integrate the ambiguity sets into the airport ground holding problem structure, and discuss dicretization properties of the proposed model. We discuss comparisons (via numerical experiments) between ground holding policies and optimized costs derived through the deterministic, stochastic, and distributionally robust airport ground holding problems. Our experiments show that the DRO model outperforms the stochastic models when there is a significant difference between the empirical airport capacity distribution and the realized airport capacity distribution. We note that DRO can be a valuable tool for decision-makers seeking to design airport ground holding policies, particularly when the available data regarding future airport capacities are highly uncertain.