Planning, particularly scheduling of limited resources is one of the main challenges of air traffic management (ATM). Uncertainty almost always leads to a deviation from the original plan or schedule. A recently completed SESAR exploratory research project, RobustATM, has developed a new mathematical model to help stabilise and optimise schedule planning.

The scheduling problem studied by the project was that of setting take-off times for aircraft flying from different airports into a common single-runway destination airport. The goal was to optimise departure times in order to ensure optimum delivery into the arrival runway. First, the project took real data from a large German airport to find a mathematical model to describe how aircraft take-off times may differ from the plan. Next, they ran Montecarlo simulations to see how operations based on two well-established and radically different schedule planning strategies would result. In one strategy, the “Robust” approach, scheduling was done assuming a worst-case scenario – everything that can go wrong will go wrong, and buffers are included to account for it. In the other strategy, the “stochastic” optimisation technique, only the most likely disturbances are considered, resulting in better use of resources in most cases, but sometimes ending in run-time situations that are unrecoverable in the sense that the timetable can no longer be followed and a full re-scheduling process becomes necessary.

Then, the RobustATM team used state-of-the-art mathematical optimization to develop a new “mixed” technique, which they called “recoverable robustness”. With the new scheduling scheme, recovery from stochastically-generated schedules is embedded in the design of the system. They found that running times were very low, allowing to solve realistic instances with about 200 aircraft to global optimality. The increase in delay was very moderate even in the case of important deviations from the original plan, and the level of re-scheduling was drastically reduced compared to the stochastic approach.

RobustATM shows that it is indeed possible to stabilise pre-tactical planning using mathematical optimisation approaches that include information about uncertainties and the impact of potential rescheduling needs already in the planning phase. These methods could be used in other ATM applications, for example tactical planning to one or several runways, gate assignment or taxiing, and they may also be useful beyond the ATM domain.