The airport gate assignment problem (AGAP) is one of the most important problems operations managers face daily. Many researches have been done to solve this problem and tackle its complexity. The objective of the task is assigning each flight (aircraft) to an available gate while maximizing both conveniences to passengers and the operational efficiency of airport. This objective requires a solution that provides the ability to change and update the gate assignment data on a real time basis. In this paper, we survey the state of the art of these problems and the various methods to obtain the solution. Our survey covers both theoretical and real AGAP with the description of mathematical formulations and resolution methods such as exact algorithms, heuristic algorithms, and metaheuristic algorithms. We also provide a research trend that can inspire researchers about new problems in this area.
The complexity of airport management has increased significantly. Flight delays or accidents might happen if operations were not handled well, and domino effect might happen to influence the whole operations of airport. In airports, the tasks related to gate assignment problem (AGAP) are one of the most important daily operations many researches have been published on with the aim of solving the problem in spite of its complexity. The objective of the task is assigning each flight (aircraft) to an available gate while maximizing both conveniences to passengers and the operational efficiency of airport. Large airlines typically need to manage different gates across an airport in the most efficient way in a dynamic operational environment. This requires a solution that provides the ability to change and update the gate assignment data on a real time basis. It should also provide robust and efficient disruption management, while maintaining safety, security, and cost efficiency.
Numerous methods have been developed to solve this problem since 1974. Steuart [
Dorndorf et al. [
The solution approaches and the solving techniques are varied with no methods, until nowadays, that provide a robust technique for such problem. This study focuses on assessing the trend of solving gate assignment problem in light of the preceding four points. Specifically, this study will address the following research questions.
From a mathematical view, AGAP has been formulated as integer, binary, or mixed integer, general linear or nonlinear models. Specific formulation as binary or mixed binary quadratic models has also been suggested. Other well-known related problems in combinatorial optimization such as quadratic assignment problem (QAP), clique partitioning problem (CPP), and scheduling problem have been used to formulate AGAP. However, few publications on AGAP tackled stochastic or robust optimization.
While the goal of combinatorial optimization research is to find an algorithm that guarantees an optimal solution in polynomial time with respect to the problem size, the main interest in practice is to find a nearly optimal or at least good-quality solution in a reasonable amount of time. Many approaches to solve the GAP have been proposed, varying from Brand and Bound (B&B) to highly esoteric optimization methods. The majority of these methods can be broadly classified as either “exact” algorithms or “heuristic” algorithms. Exact algorithms are those that yield an optimal solution. As discussed in Section
Basically the GAP is a QAP and it is an NP-hard problem as shown in Obata [
This paper surveys a large number of models and techniques developed to deal with GAP. In Section
Many researchers formulated the AGAP as an integer, binary, or mixed integer linear or nonlinear model and some of them formulated it as binary or mixed binary quadratic models, whereas some of the researchers have formulated the AGAP as well-known related problems in combinatorial optimization such as quadratic assignment problem (QAP), clique partitioning problem (CPP), and scheduling problem or even as a network representation. However, some of the researchers formulated the AGAP as a robust optimization model. In this section, according to the way of how the researchers deal with the gate assignment problem, a classification for the AGAP has been made as follows.
Lim et al. [
Constraint (
In the first model and according to the linearity of the objective function and constraints, they used a standard IP solver (CPLEX) to find the optimal solution, whereas in the second model authors used several heuristic algorithms, namely, the “Insert Move Algorithm,” the “Interval Exchange Move Algorithm,” and a “Greedy Algorithm” to generate solutions. The generated solutions then have been improved using a tabu search (TS) and memetic algorithm. The results showed that the used heuristics performed better than the IP solver (CPLEX) in both CPU time and solutions quality.
Diepen et al. [
This constraint defined the flight preferences; for example, a flight should be assigned to the same gate due to the ownership or security. The coefficient 0.5 refers to the extra flight defined in constraint (
They checked the solution’s optimality using pricing problem (minimum reduced cost) since they had dual multipliers Sort the gates based upon the quality. Sort the gate plans from the highest on the total number of departing passengers that are on the flights in that gate plan. Assign the gate plan to the best gate considering the highest number of departing passengers, assign the next gate plan to the next-best gate, and so on.
In [
In 2009, Tang et al. [
time inconsistency value indicating that the space inconsistency value indicating that the
The following sets have been defined: considered flights; available gates; gates that the time points in which the flights that can be assigned to the all time points (i.e., the time points from the planning time at each stage to the end of daily operations); time points (starting times) assigned to the conflicting flight pairs for the flights included in the adjacent gate pairs.
Equation (
Kumar et al. [
Mangoubi and Mathaisel [
Vanderstraeten and Bergeron [
Bihr [
subject to
Bolat [
In 2001, Bolat [
Şeker and Noyan [
Li [
As mentioned in Section
Solutions were obtained using tabu search based on some initial (starting) solutions; the results were compared with those of a random algorithm developed in the literature. Using data from Beijing International Airport (10 gates and 100 of flights between 6:00 and 16:00), the initial solutions using metaheuristic and random algorithm were 9821 and 15775, respectively.
Bolat [
Xu and Bailey [
The B&B and tabu search algorithm were used to solve the generated instances (seven instances, up to 400 flights and 50 gates for 5 consecutive working days). The results of the analyzed instances showed an average saving of the connection time of 24.7%.
In 2005, Ding et al. [
Using the same case study by Ding et al. [
Hu and Di Paolo [
In 2001, Yan and Huo [
Column generation approach, simplex method, and B&B algorithm were used to solve the proposed problem, which was a case study in Chiang Kai-Shek Airport, Taiwan. The problem consisted of 24 gates (of which two were temporary; eight out of 24 gates were only available for the wide type of aircrafts, whereas the rest were available for the other types) and 145 flights. The results showed that the obtained solution (7,300,660 s the best feasible solution found so far) was away from the optimal one by 0.077% (5595s).
Wipro Technologies [
Kaliszewski and Miroforidis [
Yan and Tang [
The formulation of the stochastic gate assignment model (the objective was to minimize the total waiting time of the passengers) was addressed as follows:
The value of the performance measure (the objective, minimizing the total waiting time of the passengers) for each scenario in the real time stage was calculated as follows:
Genç et al. [
In some of the publications on the GAP the researchers have formulated the AGAP as well-known related problems such as quadratic assignment problem (QAP), clique partitioning problem (CPP), and scheduling problem or even as a network representation. However, some of the researchers formulated the AGAP as a robust optimization model. In this section, we will present the work that has been done on the GAP as a well-known related problem.
Drexl and Nikulin [
Haghani and Chen [
In 2010, Li [
Dorndorf et al. [
Maharjan and Matis [
: binary variable representing initial assignment of gate : binary variable representing assignment of gate : binary variable representing last assignment of gate : binary variable representing no assignment of gate
The above model was with a quadratic objective function and a linearization for that objective was made as follows:
According to the passengers comfort, a cost function
The constraints of (
Diepen et al. [ according to preference
where
Formulations of AGAP and related problems.
Formulation | References | Criterion (comments) | Problem type |
---|---|---|---|
Integer linear programming (IP) | Lim et al. [ |
(i) Minimizing the sum of the delay penalties |
Theoretical |
Diepen et al. [ |
(i) Minimizing the deviation of arrival and departure time |
Real case (Amsterdam Airport Schiphol) | |
Diepen et al. [ |
Minimizing the deviations from the expected arrival and departure times | Real case (Amsterdam Airport Schiphol) | |
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Binary integer programming | Mangoubi and Mathaisel [ |
Minimizing passenger walking distances | Real case (Toronto International Airport); Real case (Chiang Kai-Shek Airport) |
Vanderstraeten and Bergeron [ |
Minimizing the number off-gate event | Theoretical | |
Bihr [ |
Minimizing of the total passenger distance | Theoretical | |
Tang et al. [ |
Developing a gate reassignment framework and a systematic computerized tool | Real case (Taiwan International Airport) | |
Prem Kumar and Bierlaire [ |
(i) Maximizing the gate rest time between two turns |
Theoretical | |
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Mixed integer linear programming (MILP) | Bolat [ |
Minimizing the range of slack times | Real case (King Khaled International Airport) |
Bolat [ |
Minimizing the variance or the range of gate idle time | Real case (King Khaled International Airport) | |
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Mixed integer nonlinear programming | Li [ |
Minimizing the number of gate conflicts of any two adjacent aircrafts assigned to the same gate | Real case (Continental Airlines, Houston Gorge Bush Intercontinental Airport) |
Bolat [ |
Minimizing the variance or the range of gate idle time | Real case (King Khaled International Airport) | |
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Multiple objective GAP formulations |
Hu and Di Paolo [ |
Minimize passenger walking distance, baggage transport distance, and aircraft waiting time on the apron | Theoretical |
Wei and Liu [ |
(i) Minimizing the total walking distance for passengers |
Theoretical | |
B.A.C.o.E.B. Team and A.I.C.o.E. Team [ |
(i) Minimizing walking distance |
Theoretical | |
Yan and Huo [ |
(i) Minimizing passenger walking distances |
Real case (Chiang Kai-Shek Airport) | |
Kaliszewski and Miroforidis [ |
Finding gate assignment efficiency which represents rational compromises between waiting time for gate and apron operations | Theoretical | |
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Stochastic model | Yan and Tang [ |
Minimizing the total passenger waiting time | Real case (Taiwan International Airport) |
Genç et al. [ |
Maximizing gate duration, which is total time of the gates allocated | Theoretical and real case (Ataturk Airport of Istanbul, Turkey) | |
Şeker and Noyan [ |
Minimizing the expected variance of the idle time | Theoretical | |
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Quadratic assignment problem (QAP) | Drexl and Nikulin [ |
(i) Minimizing the number of ungated flights |
Theoretical |
Haghani and Chen [ |
Minimizing the total passenger walking distances | Theoretical | |
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Scheduling problems |
Li [ |
(i) Maximizing the sum of the all products of the flight eigenvalue |
Theoretical |
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Quadratic mixed binary programming | Bolat [ |
Minimizing the variance of idle times | Real case (King Khaled International Airport) |
Zheng et al. [ |
Minimizing the overall variance of slack time | Real case (Beijing International Airport, China) | |
Xu and Bailey [ |
Minimizing the passenger connection time | Theoretical | |
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Binary quadratic programming | Ding et al. [ |
Minimize the number of ungated flights and the total walking distances or connection times | Theoretical |
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Clique partitioning problem (CPP) | Dorndorf et al. [ |
(i) Maximizing the total assignment preference score |
Theoretical |
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Network representation |
Maharjan and Matis [ |
Minimizing both fuel burn of aircraft and the comfort of connecting passengers | Real case (Continental Airlines at George W. Bush Intercontinental Airport in Houston (IAH)) |
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Robust optimization |
Diepen et al. [ |
Maximizing the robustness of a solution to the gate assignment problem | Real case (Amsterdam Airport Schiphol) |
As mentioned before in Section
Exact algorithms are those that yield an optimal solution. According to the literature, different exact solution techniques have been used to solve the GAP. As an example branch and bound was used as well as column generation and other methods, and in some research, the authors used some optimization programming languages like CPLEX and AMPL. In this section, only the research work that has been done on the exact solution techniques for solving the AGAP is presented.
Li [
Basically the GAP is a QAP and it is an NP-hard problem as shown in Obata [
Yan and Tang [
Thengvall et al. [
As mentioned before in Section
Gu and Chung [
Cheng et al. [
Zheng et al. [
Resolution methods.
Method | References | Approach/results | Problem type |
---|---|---|---|
Exact algorithms | Mangoubi and Mathaisel [ |
Linear programming relaxation | Real case (Toronto International Airport) |
Bihr [ |
Primal-dual simplex | Theoretical | |
Yan and Huo [ |
Simplex; |
Real case (Chiang Kai-Shek Airport) | |
Bolat [ |
Branch and bound | Real case (King Khaled International Airport, KSA); theoretical | |
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Heuristic algorithms | Thengvall et al. [ |
Bundle algorithm approach | Theoretical |
Yan and Tang [ |
Heuristic approach embedded in a framework designed | Real case (Taiwan International Airport) | |
Ding et al. [ |
Greedy algorithm | Theoretical | |
Lim et al. [ |
The Insert Move Algorithm, the Interval Exchange Move Algorithm, and a Greedy Algorithm | Theoretical | |
Diepen et al. [ |
Column generation | Real case (Amsterdam Airport Schiphol) | |
Dorndorf et al. [ |
Heuristic based on the ejection chain algorithm | Theoretical | |
Mangoubi and Mathaisel [ |
Heuristic approach | Real case (Toronto International Airport) | |
Vanderstraeten and Bergeron [ |
ADAP | Theoretical | |
Yan et al. [ |
Greedy heuristics | Real case (Chiang Kai-Shek Airport) | |
Bolat [ |
Heuristic branch and trim | Real case (King Khaled International Airport, KSA) | |
Bolat [ |
Heuristic branch and bound, SPH heuristic | Real case (King Khaled International Airport, KSA) | |
Haghani and Chen [ |
Heuristic approach | Theoretical | |
Genç [ |
Ground time maximization heuristic, and idle time minimization heuristic | Theoretical and real case (Ataturk Airport of Istanbul, Turkey) | |
B.A.C.o.E.B. Team and A.I.C.o.E. Team [ |
A hybrid heuristics algorithm guided by simulated annealing and greedy heuristic | Theoretical | |
Bouras et al. [ |
Heuristic approach | Theoretical | |
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Metaheuristic algorithms | Ding et al. [ |
Tabu search | Theoretical |
Ding et al. [ |
Simulated annealing, hybrid of simulated annealing and tabu search | Theoretical | |
Lim et al. [ |
TS algorithm and a memetic algorithm | Theoretical | |
Hu and Di Paolo [ |
New genetic algorithm with uniform crossover | Theoretical | |
Drexl and Nikulin [ |
Pareto simulated annealing | Theoretical | |
Xu and Bailey [ |
Tabu search | Theoretical | |
Bolat [ |
Genetic algorithm | Real case (King Khaled International Airport, KSA) | |
Şeker and Noyan [ |
Tabu search algorithms | Theoretical | |
Zheng et al. [ |
A tabu search algorithm and metaheuristic method | Real case (Beijing International Airport, China) | |
Wei and Liu [ |
A hybrid genetic algorithm | Theoretical | |
Gu and Chung [ |
Genetic algorithms approach | Theoretical | |
Cheng et al. [ |
Genetic algorithm (GA), tabu search (TS), simulated annealing (SA), and a hybrid approach based on SA and TS | Real case (Incheon International Airport, South Korea) | |
Bouras et al. [ |
Genetic algorithm (GA), tabu search (TS), and simulated annealing (SA) | Theoretical | |
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OPL | Li [ |
Optimization programming language (CPLEX) | Real case (Continental Airlines, Houston Gorge Bush Intercontinental Airport) |
Tang et al. [ |
Using CPLEX 10.0 solver concert with C language | Real case (Taiwan International Airport) | |
Prem Kumar and Bierlaire [ |
Optimization |
Theoretical | |
Maharjan and Matis [ |
AMPL/CPLEX 11.2 | Real case (Continental Airlines at George W. Bush Intercontinental Airport in Houston (IAH)) |
Recently, Bouras et al. [
In this survey, we have presented the very recent publications about the airport gate assignment problem. The collected literature has the aim of identifying the contributions and the trends in the research using exact or approximate methods.
An abundant literature is listed to describe mathematical formulation on AGAP or other related problems. They have been grouped in such a way that the user is guided to identify each problem specification. For single objective, integer/binary models are described along with mixed integer ones. Nonlinear formulations are also described for mixed/integer models. Rare are the authors who really came out with exact solutions using existing commercial optimization software or their own exact methods (branch and bound…). Heuristics were suggested to build feasible solutions and improve the latter solutions using metaheuristics.
For multiobjective optimization, several models have been formulated as nonlinear objectives with little success in solving such problems with exact methods in a reasonable time.
Related problems to AGAP have also been introduced in the survey. Some cases of AGAP have been formulated as some well-known combinatorial optimization problems such as QAP.
Since 2005 (Table
Number of publications per year.
Year | Number of publications | References |
---|---|---|
1974 | 1 | Steuart [ |
1985 | 1 | Mangoubi and Mathaisel [ |
1988 | 1 | Vanderstraeten and Bergeron [ |
1990 | 1 | Bihr [ |
1998 | 1 | Haghani and Chen [ |
1999 | 2 | Bolat [ |
2000 | 1 | Bolat [ |
2001 | 3 | Bolat [ |
2002 | 2 | Lam et al. [ |
2003 | 1 | Thengvall et al. [ |
2004 | 2 | Ding et al. [ |
2005 | 3 | Ding et al. [ |
2007 | 4 | Diepen et al. [ |
2008 | 4 | Diepen et al. [ |
2009 | 4 | Wei and Liu [ |
2010 | 4 | Dorndorf et al. [ |
2011 | 2 | Prem Kumar and Bierlaire [ |
2012 | 5 | Li [ |
2014 | 1 | Bouras et al. [ |
Number of publications per year.
Number of publications per 5 years.
In practice, major airlines may have more than 1000 daily flights to handle at more than 50 gates, which results in billions of binary variables in formulation. B&B based MIP solvers (i.e., CPLEX) will not be able to handle such huge size problems within a reasonable time bound.
A growing interest in metaheuristics (Table
Number of publications per research area.
Area | Number of publications | References |
---|---|---|
Integer linear programming (IP) | 3 | Lim et al. [ |
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Binary integer programming | 6 | Mangoubi and Mathaisel [ |
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Mixed integer linear programming (MILP) | 3 | Bolat [ |
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Mixed integer nonlinear programming | 3 | Li [ |
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Quadratic programming (QP) | 6 | Bolat [ |
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Multiple objective GAP formulations | 5 | Hu and Di Paolo [ |
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Stochastic models | 3 | Yan and Tang [ |
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Quadratic assignment problem (QAP) | 2 | Drexl and Nikulin [ |
|
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Scheduling problems | 1 | Li [ |
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Clique partitioning problem (CPP) | 1 | Dorndorf et al. [ |
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Network representation | 1 | Diepen et al. [ |
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Robust optimization | 1 | Maharjan and Matis [ |
|
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Exact algorithms | 7 | Mangoubi and Mathaisel [ |
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Heuristic algorithms | 16 | Thengvall et al. [ |
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Metaheuristic algorithms | 14 | Ding et al. [ |
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OPL | 4 | Li [ |
Number of publications per research area.
It is quite understandable that researches move towards the use of such methods. Airport managers usually face changes on their plans and need to change their plans due to uncertainties.
With a lack of studies on robust methods or stochastic methods, where only few papers appeared on these subjects, researchers have at their disposal a battery of methods such as evolutionary methods, parallel metaheuristics, and self-tuning metaheuristics to apply on this interesting problem.
With the actual trend of heuristics use, it would be interesting to work on a combination of these algorithms
In the framework of a hyperheuristic approach, many hard combinatorial optimization problems have already been tackled using heuristics (Burke et al. [
There is an alternative to these approximate methods, which could be explored: the use of efficient exact methods (branch and bound…) with the introduction of tight lower bounds. In our review, we found that only Tang et al. [
We have also noticed the absence of a data set for AGAP. It could be interesting to have a set of instances of different sizes that can be shared by researchers, with benchmarks (optimal and best-known values) and CPU times to help comparing methods as it is the case for known problems: quadratic assignment problem and travelling salesman problem.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors extend their appreciation to the Deanship of Scientific Research Center of the College of Engineering at King Saud University for supporting this work.