Finding a shortest path with various constraints and cost functions is a common problem in operations research. This paper deals with the special case of the problem of computing multiple shortest paths with capacity constraints on a subgraph that evolves over time. Multiple shortest paths is understood as paths for each vehicle considered. The static special case is modeled as a Mixed Integer Linear Programming (MILP) problem, so that it can be solved directly by a standard commercial solver. The time-dependent nature of the problem is then modeled thanks to a sliding-window approach. This study is motivated by the problem of minimizing the environmental impact of air transport at the level of a complete air network, considering thereby several aircraft. Both CO2 and non-CO2 effects are taken into account to calculate the impact. The proposed methodology takes into account a network point of view where airspace (subgraph) capacities evolve as well as the traffic itself over time. Encouraging numerical results on the CO2 /contrail-safe aircraft trajectories application are obtained and show that the environmental impact can be reduced while maintaining safety by guaranteeing the respect of airspace capacities.