Air traffic flow management problem with stochastic capacities
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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.
KeywordsAir traﬃc ﬂow management
Two-stage stochastic programming
In-teger L-shaped algorithm
Partial Benders’ decomposition
Conditional value at risk