Air traffic flow management under uncertainty: application of chance constraints

This paper is part of the ONBOARD1 project, whose goal is to investigate the incorporation of probabilistic information about the levels of uncertainty in ATFM. The efficiency of ATFM optimizations in preventing local demand-capacity imbalances is reliant on accurate predictions of future capacity states. However these predictions are inherently uncertain due to factors such as weather effects and unscheduled demand. This paper presents a novel application of chance constrained optimization techniques for uncertainty management in Air Traffic Flow Management (ATFM) problems. A deterministic discrete-decision Mixed-Integer Linear Programming (MILP) optimization model of ATFM is augmented to include constraints on the chance of sector capacity violations occurring given probabilistic information about the future capacity states. Two initial formulations of chance constraints are considered: those formulated on probabilities within individual sectors; and those formulated on the joint probabilities between sectors. Results are presented demonstrating the effects of incorporating both forms of the chance constraints on the problem solutions. However, it is considered that these initial formulations may prove over conservative for larger problem instances. The directions of the ongoing research are discussed.