Cross-Border Capacity Planning in Air Traffic Management Under Uncertainty

In European air traffic management (ATM), it is an important decision how much capacity to provide for each airspace, and it has to be made weeks or even months in advance of the day of operation. Given the uncertainty in demand that may materialize until then along with variability in capacity provision (e.g., due to weather), Airspace Users could face high costs of displacements (i.e., delays and reroutings) if capacity is not provided where and when needed. We propose a new capacity sharing scheme in which some proportion of overall capacities can be flexibly deployed in any of the airspaces of the same alliance (at an increased unit cost). This allows us to hedge against the risk of capacity underprovision. Given this scheme, we seek to determine the optimum budget for capacities provided both locally and in cross-border sharing that results in the lowest expected network costs (i.e., capacity and displacement costs). To determine optimum capacity levels, we need to solve a two-stage newsvendor problem: We first decide on capacities to be provided for each airspace, and after uncertain demand and capacity provision disruptions have materialized, we need to decide on the routings of flights (including delays) as well as the sector opening scheme of each airspace to minimize costs. We propose a simulation optimization approach for searching the most cost-efficient capacity levels (in the first stage), and a heuristic to solve the routing and sector opening problem (in the second stage), which is NP-hard. We test our approach in a large-sized simulation study based on real data covering around 3,000 flights across Western European airspace. We find that our stochastic approach significantly reduces network costs against a deterministic benchmark while using less computational resources. Experiments on different setups for capacity sharing show that total variable costs can be reduced by more than 8% if capacity is shared across borders: even though we require that no airspace can operate lower capacities under capacity sharing than without (this is to avoid substitution of expensive air traffic controllers with those in countries with a lower wage level). We also find that the use of different technology providers is a major obstacle to reap the benefits from capacity sharing and that sharing capacities across airspaces of the same country may instead be preferred.