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A key feature of trajectory based operations (TBO)-a new concept developed to modernize the air traffic system-is the inclusion of preferences and priorities of the air traffic management (ATM) stakeholders. In this paper, we present a new mathematical model to optimize flights' 4D-trajectories. This is a multi-objective binary integer programming (IP) model, which assigns a 4D-trajectory to each flight, while explicitly modeling priorities and highlighting the trade off involved with the Airspace Users (AUs) preferences. The scope of the model (to be used at pre-tactical level) is the computation of optimal 4D pre-departure trajectory for each flight to be shared or negotiated with other stakeholders and subsequently managed throughout the flight. These trajectories are obtained by minimising the deviation (delay and rerouting) from the original preferred 4D-trajectories as well as minimizing the air navigation service (ANS) charges subject to the constraints of the system. Computational results for the model are presented, which show that the proposed model has the ability to identify trade-offs between the objectives of the stakeholders of the ATM system under the TBO concept. This can therefore provide the ATM stakeholders with useful decision tools to choose a trajectory for each flight.

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The delay management problem arises in public transportation networks, often characterized by the necessity of connections between different vehicles. The attractiveness of public transportation networks is strongly related to the reliability of connections, which can be missed when delays or other unpredictable events occur. Given a single initial delay at one node of the network, the delay management problem is to determine which vehicles have to wait for the delayed ones, with the aim of minimizing the dissatisfaction of the passengers. In this paper, we present strengthened mixed integer linear programming formulations and new families of valid inequalities. The implementation of branch-and-cut methods and tests on a benchmark of instances taken from real networks show the potential of the proposed formulations and cuts.

In a railway network, a deadlock occurs when two or more trains are preventing each other from moving forward by each occupying the tracks required by the other. Deadlocks are rare but pernicious events in railroad operations, and, in most cases, they are caused by human errors and involve only two extra-long trains missing their last potential meet location. In “Easy Cases of Deadlock Detection in Train Scheduling,” V. Dal Sasso, L. Lamorgese C. Mannino, A. Tancredi, and P. Ventura prove that the identification of two-train deadlocks can be performed in polynomial time. Moreover, they also present a pseudo-polynomial but efficient oracle that allows real-time early detection and prevention of any (potential) two-train deadlock in the Union Pacific (a U.S. class 1 rail company) railroad network. A deadlock prevention module based on the work in this paper will be put in place at Union Pacific to prevent all deadlocks of this kind.