An exact algorithm for Aircraft Landing Problem

This paper addresses the problem of scheduling aircraft landings at an airport. Given a set of planes and runways, the objective is to minimize the total (weighted) deviation from the target landing time for each plane. There are costs associated with landing either earlier or later than a target landing time for each plane. Each plane has to land on one of the runways within its predetermined time windows such that separation criteria between all pairs of planes are satisfied. This type of problem is a large-scale optimization problem, which occurs at busy airports where making optimal use of the bottleneck resource (the runways) is crucial to keep the airport operating smoothly. This paper is the first attempt to develop a column generation-based exact decomposition algorithm for the Aircraft Landing Problem (ALP). We formulate the problem as an mixed integer program, then reformulate it, using Dantzig-Wolfe decomposition, as a set partitioning problem with side constraints. We also present a mixed integer formulation for the subproblem to generate the columns with negative reduce cost. Based on the set partitioning formulation, a branch-and-bound algorithm is developed to obtain the exact solution for the problem. Computational results are presented for publicly available test problems involving up to 50 aircrafts and 4 runways. The initial implementation shows that optimal solutions can be produced with less than 500 columns generated in acceptable CPU time.