Scheduling of take-offs and landings at airports can be regarded as a complex, multi-objective optimisation problem due to the diverse sets of constraints and objectives that may be considered. The Worldwide Airport Slot Guidelines (WASG), published by the International Air Transport Association (IATA), explain how this should be done in a fair and transparent manner. The procedure relies upon the “declared capacities” of individual airports, which tend to be determined more by empirical judgement than by advanced mathematical modelling.

In the aviation research literature, it is well-understood that a trade-off exists between “schedule displacement” and “operational delays”. Schedule displacement is a measure of the lack of conformity of a set of allocated slots to the requests originally made by airlines, and can be minimised efficiently via integer programming methods. On the other hand, “operational delays” are experienced by passengers as flight delays due to air traffic congestion, and should be modelled using stochastic methods due to the various uncertain factors (e.g. weather, mechanical issues, etc.) which affect on-time performance. It is desirable to achieve an effective balance between these two measures.

In this talk we propose a new optimisation model to slot allocation which directly incorporates stochastic queueing dynamics into the slot allocation decision. The model takes the form of a two-stage stochastic programming model where the first stage consists of allocates slots and setting queuing service rates, and the second stage the evaluation of queue lengths given random aircraft delays and service times. In particular, our model uses a conditional value-at-risk metric to measure queue lengths in order to mitigate more effectively against peak time queuing. Finally, we present solution approaches to this model and initial numerical results.