A Time-Dependent Subgraph-Capacity Model for Multiple Shortest Paths and Application to $$\text {CO}_{\text {2}}$$ CO 2 /Contrail-Safe Aircraft Trajectories

This paper proposes a study motivated by the problem of minimizing the environmental impact of air transport considering the complete air network, thereby several aircraft. Both CO $$_2$$ 2 and non-CO $$_2$$ 2 effects are taken into account to calculate this impact. The proposed methodology takes a network point of view in which airspace capacities evolve as well as the traffic itself over time. Finding the shortest path with numerous constraints and various cost functions is a common problem in operations research. This study deals with the special case of multiple shortest paths with capacity constraints on a time-dependent subgraph. Multiple shortest paths are understood as one shortest path per vehicle considered. The static special case is modeled as a mixed integer linear program so that it can be efficiently solved by standard off-the-shelf optimization solvers. The time-dependent nature of the problem is then modeled via a sliding-window approach. Encouraging numerical results on the contrail-avoidance application show that the environmental impact can be significantly reduced while maintaining safety by satisfying the airspace capacity constraints.