Fairness in the Aircraft Landing Problem M.J. Soomer *,a,b , G.M. Koole a a VU University, De Boelelaan 1081a, 1081 HV Amsterdam, the Netherlands b National Aerospace Laboratory NLR, Anthony Fokkerweg 2, 1059 CM Amsterdam, the Netherlands * email: MJ.Soomer@few.vu.nl June 9, 2008 Abstract The last few decades a lot of attention has been paid to Collaborative Decision Making (CDM) in Air Traffic Management. A lot of models are proposed in which information of stakeholders (mainly airlines) is used in some way to improve the decision process. When doing this, fairness becomes an important issue. However, it is not always clear what will be considered fair by the airlines involved. In this paper we will use the aircraft landing problem to illustrate various definitions of fairness, that stem from the use of airline preferences. In this problem, a landing order and feasible landing times have to be determined for a set of flights at a runway. The airlines cost and the various definitions of fairness are used as objective for the problem. Local search heuristics are introduced to solve these formulations. Numerical experiments using schedule data from a large European airport are used to evaluate how the fairness definitions and heuristics behave for real life problems. The results show that it is possible to achieve more fairness, while still obtaining considerable cost savings compared to the First Come First Served schedule. The heuristics obtain reductions of up to 26% in the root mean square deviation of the average cost per airline. The different heuristics show that schedules with different trade-offs between efficiency, cost, delay and fairness can be obtained. Hopefully, these results can be a starting point for discussing the fairness issues related to the introduction of CDM processes among air traffic stakeholders. 1 Introduction The last few decades Collaborative Decision Making (CDM, [11], [12]) has become an impor- tant concept in Air Traffic Management. Several models are proposed in which information of stakeholders (mainly airlines) is used to improve the decision process. Air Traffic Management authorities need to make sure that this done in a manner such that the outcome is fair to all airlines. In this paper we will discuss fairness considering the aircraft landing problem. Airport runway capacity is unpredictable and subject to large changes during operations, mainly because of weather and visibility conditions. The demand for runway capacity at large hub airports is subject to large peaks, because of the hub and spoke network that most airlines use. This often leads to imbalance between capacity and demand on the day of operations. Decisions how to assign scarce landing capacity among competing airlines should me made in a manner that is considered fair by all airlines involved. Runway landing capacity depends on the weight categories of the aircraft and their landing sequence. This is because the separation that is required between consecutive aircraft depends on the weight categories of the aircraft. A light aircraft flying behind a heavy aircraft requires more separation than the reverse order. However, in practice not much is done actively sequencing flights. Flights approaching the airport are under the guidance of the so-called approach controller from less than 30 minutes before the actual landing. From this moment on, the controller must create a correctly separated flow of aircraft toward the runway. Because of the limited time 1