Aircraft Landing Planning is challenging because the inherently limited capacity of airport runways causes bottlenecks. This type of planning involves different stakeholders (e.g., airlines, air traffic services providers, airport authorities, and passengers) and faces various uncertainties (e.g., take-off time variability, or wind speeds). This study, conducted in collaboration with the European Organization for the Safety of Air Navigation (EUROCONTROL), proposes a mathematical formulation of the problem and a simulation framework that accounts for uncertainties. We also propose different solution methods: a descent and a tabu search, as well as a mechanism for guiding restarts, to diversify the search process. These methods provide, in our simulated environment, more effective and stable solutions than the popular first-come-first-served practice regarding three objective functions (namely, delay, fuel, and landing sequence stability), which are considered lexicographically. Indeed, the average delays and fuel costs are reduced by 50% and 10%, respectively, at the cost of a small number of landing-sequence modifications, as each flight is repositioned an average of 0.5 times. Moreover, the computations can be performed quickly, which is crucial because re-optimization needs to be done online when flight information is updated.

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At the scale of Switzerland, the national railway company SBB Cargo AG has to schedule its locomotives and drivers in order to be able to pull all trains. Two objective functions are considered in a two-stage lexicographic fashion: (1) the locomotive and driver costs and (2) the driver time that is spent without driving. As the problem instances tend to reach really big sizes (up to 1900 trains), we propose to schedule locomotives and drivers in a sequential way, thus having a sequence of smaller problems to solve. Moreover, for smaller instances, we also propose to schedule jointly locomotives and drivers in an integrated way, therefore increasing the search space but possibly leading to better solutions. In this paper, we present a mathematical formulation and model for the problem. We also consider the contract-related constraints of the drivers, and we propose a way to integrate some time flexibility in the schedules. Next, we propose an innovative matheuristic to solve the problem, relying on a descent local search and a rolling horizon decomposition. An important goal of this method is to explore thoroughly at which extent a general-purpose solver can be used on this problem. Finally, the benefits of each aspect of the model and of the method are analyzed in detail on the results obtained for 20 real SBB Cargo AG instances.

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