airport delay problems

In the US and Europe, the passenger demand and flight traffic at airports have been rapidly increasing, while airport capacity has been limited due to a huge cost involved in capacity expansion. It results in severe congestion and delay problems for airports and airlines. Ground-holding policy is a short-term approach to solve the congestion and delay problems, in which optimally controlling the flow of aircraft by adjusting their release times into the airspace is a cost effective method to reduce the impact of congestion on the air traffic system (Bertsimas and Stock Patterson, 1998).

The literature of ground-holding problem can mainly be divided into four categories, static, dynamic, deterministic and stochastic versions. The static version of ground-holding problem makes the hold decisions once at the beginning of daily operations. For example, Vranas et al. (1994) formulated and studied several integer-programming models to assign ground-holding delays optimally in a general network of airports with the assumption that these ground holds were decided once at the beginning of the day. For each case, they further compared the optimal objective function values for three mathematical optimization problems: the integer problem, the corresponding linear programming relaxation, and the decomposed program defined as the integer program without the connections between flights. The results showed that when cost functions differed and/or when capacities were not uniform, the difference between the optimal objective function values of the integer and the decomposed problems could be large. It also showed that finite departure capacities had negligible impact if they were assumed not to influence arrival capacities, and as far as the model with flight cancellations was concerned, high cancellation costs were impractical because they resulted in no flights ever being cancelled.

In contrast to the static version of ground-holding problem, the dynamic version makes the holding decisions of aircraft during time of the day as better capacity estimates become available. Richetta and Odoni (1994) extended the ground-holding problems from a static version to a dynamic version. They proposed a dynamic model that optimally solved the problem by allowing decisions to be made with the most up-to-date forecast information, and by simplifying the structure of the control mechanism, in which they exercised ground holding on groups of aircraft instead of individual flights. Rather than assigning holds to all flights at once, they assigned holds as the scheduled departure time approached. They also demonstrated that using the linear-programming model they could solve the problem for one of the largest airports in the US, and then illustrated the advantage of the dynamic solution over the static solution and the passive strategy of no ground-holding.

The deterministic version of ground-holding problem considers airport capacities as fixed. For example, Janić (2005) developed an analytical model for quantification of the economic consequence of the large-scale disruptions of an airline single hub-and-spoke network with deterministic practical capacity of the hub airport. The economic consequences had been measured by the total airline costs of the delayed and cancelled complexes of flights. The disruptive event was assumed to affect the airport capacity with different intensity, and was characterized in terms of duration, intensity of impact and the time of occurrence. The results showed that the disruption costs had generally increased with increasing duration and intensity of impact of the disruptive event on the airport capacity. The larger and more expensive affected complexes and flights with the higher proportion of the passengers given up had the higher disruption costs.

In contrast with the deterministic version, the stochastic version takes into account the uncertainty in airport capacities. For example, Mukherjee and Hansen (2007) proposed a

stochastic dynamic optimization model that assigned ground delays to individual flights under time-varying arrival capacity to optimize some objective related to quantities of airborne and ground delay, and that allowed for the revision of ground delays for flights that had not yet departed in response to updated information. In the stochastic aspect, they represented the evolution of airport arrival capacity by a scenario tree, in which each branch of the tree represented a capacity scenario or a group of scenarios realized as the day progressed. A capacity scenario corresponded to a possible time-varying arrival capacity profile. The results showed the proposed model produced lower expected total delay cost than a previous model, and this performance gap increased under a stringent ground-holding policy as well as when an early ground delay program cancellation. In cases where airborne delays were permitted, the proposed model would sometimes hold a flight in anticipation of better information about weather clearance times. It also showed that the choice of ground delay cost component in the objective function strongly affected the allocation policy.

When it was linear, the optimal solution involved releasing the long-haul flights at or near their scheduled departure times and using the short-haul flights to absorb delays When it was convex, the spread of ground delay was more uniform across all categories of flights, obtaining an equitable solution. Table 2.7 summarizes the main issues and features as well as important results in the existing literature on airport delay problems.

Table 2.7 Main issues, features and results on airport delay problems related literature Authors Main issues and features Important results

Vranas et al. (1994) Formulate several integer- programming models of ground-holding delays using a static approach

When cost functions differ and/or when capacities are not uniform, the difference between the optimal objective function values of the integer and the decomposed problems could be large to flights as the scheduled departure time approaches

The linear-programming model can solve the problem for one of the largest airports in the US, and the advantage of the dynamic solution is over the static solution

Janić (2005) Develop an analytical model for quantification of the economic consequence of the large-scale disruptions with deterministic practical capacity of the hub airport

The disruption costs have generally increased with increasing duration and intensity of impact of the disruptive event on the airport capacity, and larger and more expensive affected complexes and flights with the higher proportion of the passengers given up have the higher disruption costs

Mukherjee and Hansen (2007)

Propose a stochastic dynamic optimization model that assigns ground holds to individual flights under time-varying arrival capacity

The proposed model produces lower expected total delay cost than a previous model, in which this performance gap increases when an early ground delay program cancellation, and the choice of ground delay cost component in the objective function strongly affects the allocation policy

Source: this dissertation

Summary:

There is an amount of literature on airport delay problems. These proposed models in the literature conventionally minimized the total (ground plus airborne) delay cost to optimally decide the number of time periods that each flight is held on the ground before take-off. These models were usually accompanied with various heuristic algorithms for yielding integer solutions from the linear programming relaxation. When solving ground-holding problems, the use of linear cost functions tends to assign the arrival slots to those flights with high delay cost. A recent study (Mukherjee and Hansen, 2007) allows for applying nonlinear cost functions, showing it tends to obtain more equitable slot allocation across flights than linear cost functions. There is scant research on investigating multiairport ground-holding problems, which were generally restricted to the case when aircraft is delayed, the next flight performed by the same aircraft will also be delayed. Few studies, however, have explored the influences of small-world properties of air transportation network on the duration and propagation of flight delay, so as to investigate how the network connectivity facilitates the delay propagation across flights and airports in response to different allocation strategies.