Exact and heuristic approaches to the airport stand allocation problem

• We prove that the stand allocation feasibility problem is NP-complete.
• We propose a strong mixed integer programming (MIP) for the stand allocation problem.
• We introduce two heuristic algorithms based on spatial and temporal decompositions.
• Performances of MIP approaches are significantly better than the state of the art.

The Stand Allocation Problem (SAP) consists in assigning aircraft activities (arrival, departure and intermediate parking) to aircraft stands (parking positions) with the objective of maximizing the number of passengers/aircraft at contact stands and minimizing the number of towing movements, while respecting a set of operational and commercial requirements. We first prove that the problem of assigning each operation to a compatible stand is NP-complete by a reduction from the circular arc graph coloring problem. As a corollary, this implies that the SAP is NP-hard. We then formulate the SAP as a Mixed Integer Program (MIP) and strengthen the formulation in several ways. Additionally, we introduce two heuristic algorithms based on a spatial and time decomposition leading to smaller MIPs. The methods are tested on realistic scenarios based on actual data from two major European airports. We compare the performance and the quality of the solutions with state-of-the-art algorithms. The results show that our MIP-based methods provide significant improvements to the solutions outlined in previously published approaches. Moreover, their low computation makes them very practical.