Air traffic flow management problem with stochastic capacities

Air traffic systems have substantial effects on transportation, logistics, and economics in a global scope. Due to both practical significance and intellectual challenges, air traffic flow management problems have been extensively studied for many decades. The aim of air traffic flow management problems is to plan the flow throughout the air traffic network while satisfying capacity constraints. In this study, we consider the case of stochastic capacities in the air traffic network. We propose both stochastic multistage integer and stochastic two-stage integer modeling approaches for the problem. In multistage and two-stage models, we aim to resolve the demand-capacity imbalances at each element of the air traffic network. To achieve this, we decide on the take-off times and routes of each flight for a given time horizon. We propose integer L-shaped and partial Benders’ decomposition approaches to solve the two-stage model. Additionally, we analyze the effect of conditional value-at-risk constraints on delay time distributions. To incorporate conditional value-at-risk to solution methodologies, we propose a novel approximation technique. We present a detailed analysis of delay distributions, demonstrate the effect of the approximation technique on solution quality and computational performance. For computational experiments, we explicitly describe data generation procedures to obtain realistic instances. We demonstrate that the Partial Benders’ modification outperforms the commercial solver (CPLEX) in almost every instance.