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One of the key issues in air travel is assigning gates in an airport to individual aircraft. Finding an optimal solution to this problem is becoming ever more critical as air travel increases and airports become more congested, increasing the pressure to use space efficiently to increase the number of flights that can be handled at an airport while also preserving a reasonable experience for passengers on those flights. The goal of the Airport Gate Assignment Problem (AGAP) is to optimize gate assignment, taking into account many factors. It is an extremely complex problem, classified in mathematical terms as an NP-hard problem (nondeterministic polynomial-time hard) problem, meaning that there is no known algorithm for optimizing it within a practical amount of time.

The Airport Gate Assignment Problem

The Airport Gate Assignment Problem is concerned with optimizing gate assignment, with particular regard to passengers who must connect from one flight to another in a limited period of time. The basic concept behind AGAP is simple—each plane must be assigned to one gate, and no two planes can be assigned to the same gate at the same time—but in reality the problem is quite complex because of the number of factors involved.

Because most airlines today operate on a hub-and-spoke system, where most flights are to and from one or more hubs, and flying between two nonhub points usually requires flying to a hub, transferring to another plane, and then flying to one's destination, gate assignment is a particularly important aspect of airline management. The problem is complicated by the fact that normally different gates, and perhaps even different terminals, may be used for the arriving and departing flights. While passengers tend to prefer tight connections, in order to spend less total time on their flight (and less time waiting in the airport), booking systems require a specific amount of time between two connecting flights in order to raise the probability that the passenger can actually make the connection; however, if the time allowed is near the minimum, it raises the probability that any delay or disruption will cause the passenger to miss the connection, thus introducing further disruption to the system.

A gate lounge area at Edinburgh Airport in Scotland in 2009. Because one delayed flight can disrupt many other flights, “gate rest,” or idle time between the departure of one flight and the arrival of the next, must be considered when assigning gates.

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The “turn” is the period of time an airplane is on the ground between arriving and departing flights, and an airplane must be assigned to a gate for every turn. Gate assignment is based on several factors, including the geography of the specific airport (including walking time between gates, and the distance baggage must be transferred between flights), the size of the aircraft, the number of passengers on a flight that must connect with another flight, and the amount of time they have to make that connection. Gate assignments also play a key role in maintaining flight schedules—one delayed flight can disrupt many other flights due to constraints in the facilities and equipment available—and for this reason “gate rest,” meaning a period of time when a gate is idle between the departure of one flight and the arrival of the next, is included in AGAP models.

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