A dynamic programming approach for the airport capacity allocation problem

In most of the optimization models developed to manage airportsoperations, arrivals and departures capacities are treated asindependent variables: that is the number of flights allowedto take off does not affect the number of landings in any unitof time, and vice versa. This assumption is seldom verifiedin most of the congested airports, where many interactions betweenarrivals and departures take place. In this paper, we face the problem of finding the optimal trade-offbetween the number of arrivals and departures in order to reducea delay function of all the flights, using a more realisticrepresentation of the airport capacity, i.e. the capacity envelope. Under the assumption of piecewise linear convex capacity envelopesand of the exact interpolation of all the Pareto-optimal operationalpoints, we show that the problem can be formulated as a linearprogramming model. For general airport capacity envelopes, wepropose a dynamic programming formulation with a correspondingbackward solution algorithm, which is robust, easy to implementand has a linear computational complexity. The algorithm performancesare evaluated on different realistic scenarios, and the optimalsolutions are compared with those computed by a greedy algorithm,which can be seen as an approximation of the current decisionprocedures. The percentage deviation of the cost of these twosolutions ranges from 3.98 to 35.64%.