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Congestion is a problem at airports where capacity does not meet demand. At many such airports, airlines must request time slots for the purpose of landing or take off. Given the imbalance between demand and capacity, slot requests cannot always be scheduled as requested. The difference between the requested and allocated time slots is called displacement. Minimization of the total displacement is a key slot-scheduling objective and expresses the efficiency of the slot-scheduling process. Additionally, fairness has been proposed as a slot-scheduling criterion. Fairness relates to the allocation of the total schedule displacement among the various airlines. Single- and multiobjective models have been proposed for slot scheduling. However, currently the literature lacks models that incorporate the preferences of airlines regarding the allocation of displacement to their flights. This paper proposes a two-stage mechanism for the scheduling of slots at congested airports. The proposed mechanism considers efficiency and fairness objectives and incorporates the preferences of airlines in allocating the total displacement associated with the flights of each airline. The first stage of the mechanism constructs a reference schedule that is fair to the participating airlines. In the second stage, the airlines specify how the displacement allocated to them in the reference schedule should be distributed among their requests. The mechanism then adjusts the fair reference schedule to meet as many of these preferences as possible. The development and implementation of the proposed slot-scheduling mechanism is demonstrated using real data from a coordinated airport and simulated displacement preference data. The proposed slot-scheduling mechanism provides useful information to decision makers regarding the equity–efficiency trade-off and enhances the transparency and acceptability of the slot-scheduling outcome.

We propose a general Markovian model for the optimal control of admissions and subsequent routing of customers for service provided by a collection of heterogeneous stations. Queue-length information is available to inform all decisions. Admitted customers will abandon the system if required to wait too long for service. The optimisation goal is the maximisation of reward rate earned from service completions, net of the penalties paid whenever admission is denied, and the costs incurred upon every customer loss through impatience. We show that the system is indexable under mild conditions on model parameters and give an explicit construction of an index policy for admission control and routing founded on a proposal of Whittle for restless bandits. We are able to gain insights regarding the strength of performance of the index policy from the nature of solutions to the Lagrangian relaxation used to develop the indices. These insights are strengthened by the development of performance bounds. Although we are able to assert the optimality of the index heuristic in a range of asymptotic regimes, the performance bounds are also able to identify instances where its performance is relatively weak. Numerical studies are used to illustrate and support the theoretical analyses.