Scheduling aircraft landings - the static case

This is the publisher version of the article, obtained from the link below.In this paper, we consider the problem of scheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time for each plane such that each plane lands within a predetermined time window and that separation criteria between the landing of a plane and the landing of all successive planes are respected. We present a mixed-integer zero–one formulation of the problem for the single runway case and extend it to the multiple runway case. We strengthen the linear programming relaxations of these formulations by introducing additional constraints. Throughout, we discuss how our formulations can be used to model a number of issues (choice of objective function, precedence restrictions, restricting the number of landings in a given time period, runway workload balancing) commonly encountered in practice. The problem is solved optimally using linear programming-based tree search. We also present an effective heuristic algorithm for the problem. Computational results for both the heuristic and the optimal algorithm are presented for a number of test problems involving up to 50 planes and four runways.J.E.Beasley. would like to acknowledge the financial support of the Commonwealth Scientific and Industrial Research Organization, Australia

An ant colony algorithm for the sequential testing problem under precedence constraints.

We consider the problem of minimum cost sequential testing of a series (parallel) system under precedence constraints that can be modeled as a nonlinear integer program. We develop and implement an ant colony algorithm for the problem. We demonstrate the performance of this algorithm for special type of instances for which the optimal solutions can be found in polynomial time. In addition, we compare the performance of the algorithm with a special branch and bound algorithm for general instances. The ant colony algorithm is shown to be particularly effective for larger instances of the problem