مقاله سال ۲۰۱۶

ATM systems are driven by economic interests of the participating stakeholders and, therefore, are performance oriented. As possibilities of enlarging airport capacities are limited, one has to enhance the utilization of existing capacities to meet the continuous growth of traffic demand. The runway system is the main element that combines airside and groundside of the ATM System. Therefore, it is crucial for the performance of the whole ATM System that the traffic on a runway is planned efficiently. Such planning is one of the main challenges in ATM. Uncertainty, inaccuracy and non-determinism almost always lead to deviations from the actual plan or schedule. A typical strategy to deal with these changes is a regular re-computation or update of the schedule. These adjustments are performed in hindsight, i.e. after the actual change in the data occurred. The challenge is to incorporate uncertainty into the initial computation of the plans so that these plans are robust with respect to changes in the data, leading to a better utilization of resources, more stable plans and a more effi- cient support for ATM controllers and stakeholders. Incorporating uncertainty into the ATM planning procedures further makes the total ATM System more resilient, because the impact of disturbances and the propagation of this impact through the system is reduced.

In the present paper, we investigate the problem of optimizing runway utilization under uncertainty. The goal is to incorporate uncertainties into the initial plan in order to retain its feasibility despite changes in the data. We focus on the pre-tactical planning phase, i.e. we assume the actual planning time to be several hours, or at least 30 min, prior to actual arrival/departure times. We develop an appropriate mathematical optimization model for this particular planning phase. The basic idea is that in pre-tactical planning we can reduce the complexity of the problem by not determining an exact arrival/departure sequence in terms of exact landing/take-off times for each aircraft, as we do later in tactical planning. Instead, we answer the question of how many aircraft can be scheduled to one time window of a given size without violating distance requirements. (For example, it is definitely possible toassign more than one aircraft to a time window from 12:00 pm to 12:10 pm.) Then, we consider a discretized time horizon consisting of such time windows and assign each aircraft to one of them.

This paper is an extension of Fürstenau et al. (2014), where the authors set up a mixed integer program (MIP) for the pre-tactical optimization of runway utilization. Afterwards, the impact of disturbances on the deterministic solutions was investigated. The results showed that it is crucial to enrich the optimization approach by protection against uncertainties, in order to produce less necessary replanning. In the current paper, we thus incorporate uncertainties directly into the model by using techniques from robust and stochastic optimization. The remainder of this paper is organized as follows: In Section 2, we give an overview over the literature related to runway optimization and explain why our approach is different. We develop the pre-tactical runway optimization model in Section 3. In Sections 4 and 5 we describe our approaches to incorporate uncertainties into this model, and present some computational results in Section 4. In order to be able to test our approaches in a more realistic setting, we analyze realworld delay data from a large German airport in Section 7 (extending the descriptions in Fürstenau et al. (2014)), where we also describe our simulation environment to test current and future solution methods. Finally, we conclude in Section 8.