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 algorithm for the optimal solution of variable knockout problems

In this paper we consider a class of problems related to variable knockout. Given an optimisation problem formulated as an integer program the question we face in problems of this type is what might be an appropriate set of variables to delete, i.e. knockout of the problem, in order that the optimal solution to the problem that remains after variable knockout has a desired property. We present an algorithm for the optimal solution of the problem. We indicate how our algorithm can be adapted when the number of variables knocked out is specified (i.e. when we have a cardinality constraint). Computational results are given for the problem of finding the minimal number of arcs to knockout from a directed network such that, after knockout, the shortest path from an origin node to a destination node is of length at least a specified value. We also present results for shortest path cardinality constrained knockout

Sub-Milliarcsecond Precision of Pulsar Motions: Using In-Beam Calibrators with the VLBA

We present Very Long Baseline Array phase-referenced measurements of the parallax and proper motion of two pulsars, B0919+06 and B1857-26. Sub-milliarcsecond positional accuracy was obtained by simultaneously observing a weak calibrator source within the 40' field of view of the VLBA at 1.5 GHz. We discuss the merits of using weak close calibrator sources for VLBI observations at low frequencies, and outline a method of observation and data reduction for these type of measurements. For the pulsar B1919+06 we measure a parallax of 0.31 +/- 0.14 mas. The accuracy of the proper motions is approximately 0.5 mas, an order of magnitude improvement over most previous determinations.Comment: 11 pages plus 4 figures. In press, Astronomical Journa