An efficient solution methodology for the airport slot allocation problem with preprocessing and column-and-row generation

Airport coordination is a demand control mechanism that maximizes the use of existing infrastructure at congested airports. Aircraft operators submit a list of regular flights that they wish to operate over a five to seven-month period and a designated coordinator is responsible for allocating the available airport slots, which represent the permission to operate a flight at a specific date and time. From an optimization perspective, this problem is a special class of the Resource Constrained Project Scheduling Problem where the objective is to minimize the difference between the allocated and requested slots subject to airport capacity constraints and other operational restrictions. Most studies on the topic focus on developing complex models and fast heuristics. Little attention has been paid to exact methods despite their potential to obtain higher quality solutions with better airline acceptability and fewer slot rejections. In this paper, we present Caracal, an efficient column-and-row generation algorithm to solve the single airport slot allocation problem. We also present a problem-specific preprocessing scheme that can identify more redundant constraints and variables than a commercial solver in a fraction of the time. We propose a novel formulation to model historic overages in Level 3 airports, and we find optimal or near optimal solutions to instances originating from practical slot allocation models and real data from UK airports coordinated by Airport Coordination Limited significantly faster than the best exact method in the literature to date. We also conduct experiments on a set of synthetic, realistic instances that we include in this paper, along with the code to generate them, to facilitate benchmarking of slot allocation software.