Appropriate gate reassignment is crucially important in efficiency improvement on airport sources and service quality of travelers. The paper divides delay flight into certain delay time flight and uncertain delay time flight based on flight delay feature. The main objective functions of model are to minimize the disturbance led by gate reassignment in the case of certain delay time flight and uncertain delay time flight, respectively. Another objective function of model is to build penalty function when the gate reassignment of certain delay time flight influences uncertain delay time flight. Ant colony algorithm (ACO) is presented to simulate and verify the effectiveness of the model. The comparison between simulation result and artificial assignment shows that the result coming from ACO is obvious prior to the result coming from artificial assignment. The maximum disturbance of gate assignment is decreased by 13.64%, and the operation time of ACO is 118 s. The results show that the strategy of gate reassignment is feasible and effective.
Gate reassignment is a necessary procedure when its planned gate assignment is influenced by real-time operation situation and cannot be normally implemented. With the significant improvement of air transportation, gates become the key resources in airport, which are to be the bottleneck in maximizing operational efficiency. An appropriate gate assignment will make a difference in improving airport capacity and passenger satisfaction. However, in practice, disturbed by factors such as weather condition, flow control, flight schedule, and passengers, the advanced gate assignment plan cannot achieve original goal, so gate manager (or airport manager) must conduct gate reassignment timely to improve the operation effectiveness on airport surface. Rapid and effective gate reassignment plays an important role in improving operation efficiency and airport volume, decreasing operation cost of airlines, and improving service quality of passengers.
The characteristics of gate assignment based on flight delays should be described in following aspects. The difficulty in predicting the accurate flight delay, which is caused by the complicate delight delay, increases the complexity of gate assignment. Therefore, it is necessary to gate assignment on time. Almost all the flights should be assigned proper gate under the condition of large-scale flight delay newly. The workload is very heavy, so that the traditional method of gate assignment is difficult to work effectively in gate assignment. Large-scale flight delay can reduce the operation of airport. Constraint condition and multiobjective should be taken into account in the gate reassignment under the condition of large-scale delay in hub airport.
Considering the above characteristics of gate assignment, the intricate gate assignment under the condition of large-scale delay is a multiobject assign problem based on uncertain information.
Thus, gate reassignment is widely discussed in the world-wide research. In the way of gate preassigned, Yan and Chang [
There are increasing researches on gate reassignment. For example, Maharjan and Matis [
In the paper, the characteristics of gate reassignment based on flight delay in hub airport have been analyzed. The deposition of gate assignment and conformation of objective function are applied to reduce the complexity of research problems.
The paper divides delay flights into certain delay time flight and uncertain delay time flight base on flight delay feature. The main objective functions of model are to minimize the disturbance led by gate reassignment in the case of certain delay time flight and uncertain delay time flight, respectively. Ant colony optimization method, which is the representative method in discrete optimization, has been used to model real-time gate assignment and multiobjective optimization based on flight delay in hub airport. The remainder of paper is organized as follows. In Section
The purpose of gate reassignment is to obtain a new flight-to-gate scheme according to scheduled assignment to reassign the delay flights in order to avoid flight conflicts in view of operation safety. Therefore, in the course of gate reassignment, certainty information, stochastic issues, and reassignment disturbance should be taken into account.
In practice, gate managers will constantly receive estimated time information of each delay flight. From the time point of gate reassignment operation, if the estimated time of the delay flight is more close to the actual operation time, the managers will get more certain information of delay flights. That is to say the managers can schedule the delay flights actually. Otherwise, the arrival-departure information of delay flights needed by managers is not easy to be gotten correctly, so the delay feature is difficult to be holed. In the paper, the authors classified the follow-up arrival-departure flights into certain delay time flight and uncertain delay time flight. Some scheduled time node after gate reassignment is a demarcation point to reassign the follow-up arrival-departure flights into the appropriate gate. The gate reassignment is based on the gate reassignment scheduled time. The time node is decided by the acquired information and operation condition the same day. If the delay time of delay flight is confirmed, the arrival-departure time is conformed, so the reassignment demand is urgent.
Influenced by delay features, different flights have different uncertain degrees. Stochastic factors have a significant effect on unidentified flights, which will lead to varieties of uncertain situation. Assume that there are only 2 gates (Gate 1 and Gate 2) and 3 flights (Flight 1, Flight 2, and Flight 3), Figure
Influence on gate reassignment by stochastic factors.
From Figure
From the point of minimizing the reassignment influence, it is just necessary to consider scenarios that delay time are
The influence coming from stochastic factors for uncertain delay information should be taken into consideration. Some constraints of unidentified delay flights are tolerable to be conflicted, which means that time overlap (or time violation) is allowable in one gate. Relax constraints can lead to infeasible solution in some scenarios, which needs penalty coefficients and functions to deal with. Details about penalty coefficients and functions will be described in Section
There are three main processes for gate reassignment, allocating flights to aprons (apron disturbance), allocating flights to gates different from scheduled (gate disturbance), and making flights wait until gates are available (time disturbance). All of these processes will disturb the normal operation of airport and will have serious impact on passenger service level and stall scheduling. Thus, to maximize airport operation efficiency, benefits, and passenger service level, aforementioned constrains are necessary to be considered. The objective of research is to minimize the reassignment disturbance value and penalty value of certain and uncertain delay flight compared to planned gate assignment. Real-time gate reassignment is a continuous operation process. In order to obtain perfect reassignment scheme, the real-time operation process need a fixed time circle to complete all gate reassignment tasks in one day.
In order to avoid extra delay or propagation delay caused by airport operation for certain flight, only apron disturbance and gate disturbance are considered. On the contrary, for uncertain flight, because they lack reassignment urgency, it is better to delay their gate reassignment starting time rather than assign them to aprons when no gates are available. Thus, gate disturbance, time disturbance, and the penalty caused by relax constraints are considered. In actual airport operation, only the reassignment results of certain flights are released to gate managers, while the calculation results data of uncertain flights are key influence factors to improve the flexibility of certain flight gate reassignment results.
The assumptions used for the real-time gate assignment model are listed as follows. The result of planned gate assignment is known in advance. The arrival-departure time distribution of each flight is known. For simplicity, the research divides the minimum safety interval time and necessary buffer time between two consecutive flights into two parts and pluses them into gate occupation time of the two flights, respectively, according to aircraft type request. Thus, the minimum interval constrains need not to be considered. For simplicity and maximum reassignment efficiency, constrains, such as airlines preference, are not considered. The aprons in airport, which includes three types, are sufficient. When a flight is assigned to the apron, it does not need to consider time overlap and aircraft type matching.
Consider
The basic ideology of the objective function in the paper deems that the original gate assignment is the optimal scheme under no flight delay. The objective function is consisting of three parts. The first part is the gate reassignment aimed at the certain information; the second part is the gate reassignment aimed at the uncertain information; the third part is to analyze the influence of gate assignment under certain information on the gate assignment under uncertain information. The objective function selected in the paper is to minimize the cost of gate assignment, which is caused by flight delay, rather than act the arrival-departure time as the input to gate reassignment. Therefore, the gate assignment schedule is not the optimal schedule aiming at some gates but the schedule ensuring the minimum number of flight delay accord with the basic principle of airport operation and management. The optimal schedule of gate assignment has not an effect on the normal order of airport operation and cannot lead to safety risk.
Consider the following:
The paper selects Ant colony algorithm to solve the gate assignment problem. Ant colony optimization algorithm is a metaheuristic optimization method proposed by Dorigo et al. [
There are some reasons to explain the selection of ant colony algorithm. First, ant colony algorithm is applied to solve combinatorial optimization problem, which accords with the characteristics of gate assignment. Second, the characteristics of ant colony algorithm are to add the solution to the solution system step by step until it acquires a complete solution. Therefore, it is superior to solve gate assignment relative to adjusting the part solution of algorithm.
Our research designs an ant colony algorithm to solve the gate reassignment problem. The set of the number of ants is
Integrated searching of ants.
Setting heuristic information as
When ants
When ants complete an iteration, pheromone on each node should be updated. New pheromone will be added to nodes, while residual pheromone on each node should be volatilized. Therefore, the rule of pheromone modulation is shown as follows:
Figure
Algorithm flow.
The model can select PSO method to complete the relative parameters learning in ant colony algorithm in order to avoid the defects of ant colony algorithm itself under large-scale flight delay.
In the numerical test, the starting and ending time of certain flights gate assignment are determined by two parts: one is the latest estimated time of departure (ETD) and arrival (ETA) delivered by airlines; the other is the minimum safety interval time and necessary buffer time according to aircraft types. The time of uncertain flights is also determined by the two parts as Table
Values of gate stating and ending time.
Flight type | Flight number | STA | ETA | STD | ETD |
---|---|---|---|---|---|
Identified flight | f1 | 1035 |
|
1140 |
|
f2 | 1125 |
|
1225 |
|
|
| |||||
Unidentified flight | f3 |
|
— |
|
— |
f4 |
|
— |
|
— |
The bold font represents the actual time of departure and arrival for the flight.
The simulation and verification in the paper is based on operation of a hub airport in China. The airport has a passenger throughput of more than 19 million and aircraft movements of 166 thousand, which is an important regional hub airport of East China. The Terminal B in the airport is domestic terminal, which has 41 gates and consists of 6 gates of type E, 7 gates of type D, and 28 gates of type C. In the simulation and verification, we assume that the gates and aprons have enough capacity such as sufficient runway and taxiway systems. Data is based on the timetable of May 20, 2013, of Terminal B, when there are 418 aircraft movements or 281 flight pairs, including departure, transferring, and arrival flights. The evaluation is based on the planned gate assignment of flights and the real-time tracked data between 6:00 and 15:00 which is used to be input information to gate reassignment. Affected by storm at that day, extensive flights delayed at about 12:00, and there was considerable deviation between flights schedule and real-time operation at airport.
This research selects time points 7:00, 9:00, 11:00, 13:00, and 15:00 to perform the test and has a comparison with manual reassignment methods. The manual method which based on experience operates can be used as follows: if there is a free gate when conflict occurs, assign the flight to the free gate, otherwise, assign to apron. The test is performed on an AMD TurionX2 2.2 GHz with 2 GB RAM in the environment of Microsoft Windows Vista and uses the C computer language to write the program.
Based on the case of gate reassignment of time point 9:00, the number of considered flights which needs to be allocated is 246, which includes 32 identified flights. Table
Gate reassignment results of identified flight at time point 9:00.
Flight number | ETA | ETD | Planned assign- |
Manual |
Optimized |
---|---|---|---|---|---|
1 | 900 | 1044 | 6 | 6 | 6 |
2 | 906 | 1025 | 29 | 29 | 29 |
3 | 911 | 1025 | 3 | 3 | 3 |
4 | 915 | 1106 | 19 | 19 | 19 |
5 | 924 | 1048 | 8 | 14 | 8 |
6 | 925 | 1113 | 10 | 10 | 14 |
7 | 929 | 1103 | 4 | 20 | 33 |
8 | 942 | 1109 | 11 | 11 | 11 |
9 | 945 | 1127 | 15 | 30 | 32 |
10 | 948 | 1154 | 14 | Apron | 41 |
11 | 954 | 1127 | 7 | 7 | 7 |
12 | 955 | 1105 | 13 | 13 | 13 |
13 | 956 | 1133 | 39 | 39 | 39 |
14 | 956 | 1130 | 23 | Apron | 40 |
15 | 1000 | 1100 | 16 | 16 | 16 |
16 | 1006 | 1136 | 20 | Apron | 20 |
17 | 1010 | 1050 | 36 | 36 | 36 |
18 | 1012 | 1310 | 34 | 34 | 34 |
19 | 1015 | 1136 | 12 | 12 | 12 |
20 | 1030 | 1200 | 2 | 2 | 2 |
21 | 1030 | 1155 | 27 | 27 | 27 |
22 | 1031 | 1208 | 24 | 24 | 24 |
23 | 1034 | 1200 | 37 | 37 | 37 |
24 | 1037 | 1318 | 26 | 26 | 26 |
25 | 1039 | 1148 | 33 | 33 | 33 |
26 | 1042 | 1227 | 31 | 31 | 31 |
27 | 1045 | 1220 | 5 | 5 | 5 |
28 | 1045 | 1213 | 38 | 38 | 38 |
29 | 1048 | 1217 | 30 | 25 | 30 |
30 | 1050 | 1210 | 17 | 17 | 17 |
31 | 1051 | 1213 | 35 | 35 | 35 |
32 | 1059 | 1156 | 18 | 18 | 18 |
Gate optimization and manual reassignment results are shown in Figures
Gate optimization reassignment result at time point 9:00.
Gate manual reassignment result at time point 9:00.
Figure
As shown in Figure
Table
Comparisons of optimization and manual gate reassignment.
Time point | Reassignment method | Gate disturbance proportion | Apron disturbance proportion | Total disturbance proportion | Identified flight number | Total considered flight number | Disturbance value | Time costs (s) |
---|---|---|---|---|---|---|---|---|
6:00 | Optimization | 8% | 0 | 8% | 50 | 281 | 2051.073 | 184.746 |
Manual | 4% | 4% | 8% | 50 | 281 | 2173.52 | ||
| ||||||||
9:00 | Optimization | 15.60% | 0 | 15.60% | 32 | 246 | 1314.537 | 117.996 |
Manual | 12.50% | 9.40% | 21.90% | 32 | 246 | 1686.63 | ||
| ||||||||
11:00 | Optimization | 36.11% | 0 | 36.11% | 36 | 207 | 1480.92 | 78.622 |
Manual | 36.11% | 2.78% | 38.89% | 36 | 207 | 1604.34 | ||
| ||||||||
13:00 | Optimization | 44.80% | 0 | 44.80% | 29 | 173 | 1028.72 | 77.729 |
Manual | 44.80% | 6.90% | 51.70% | 29 | 173 | 1317.35 | ||
| ||||||||
15:00 | Optimization | 36.36% | 0 | 36.36% | 44 | 151 | 1698.24 | 105.112 |
Manual | 47.73% | 2.27% | 50.00% | 44 | 151 | 1931.66 |
Comparisons of optimization and manual gate reassignment on disturbance proportion.
Comparisons of optimization and manual reassignment on disturbance proportion.
As shown in Figures
In the aforementioned tests of 5 time point, none of the flights are allocated to the aprons. Proportion and disturbance value of disturbed identified flights in optimization results are less than those of manual reassignment results. The maximum decrement of disturbed flights proportion reaches 13.64% at 15:00, while the maximum decrement of disturbance value is 327.093 at 9:00. As a consequence, the optimization gate reassignment strategy is better than the manuals, no matter in one operation or one day’s operation. The resolving time for performing tests by ant-based algorithm has a tendency to decrease with the decrease of considered flight. The longest resolving time is 184.746 s, which can reach the strict request of real-time operation.
Gate manual reassignment only considers recent flight information and actual gate utilization situation, while optimization reassignment can consider the long time in some degrees. Optimization reassignment will follow the airport delay trending order to look for more satisfied reassignment schemes. Therefore, it will largely decline the disturbance of gate reassignment.
Thus it can be seen that, in actual situation, test results of optimization reassignment in our research are much better than those in manual reassignment. The similarity between optimization gate reassignment and planned gate assignment is high.
In the paper, airport gate reassignment problem under flight delay situation is studied. Flights are divided into different types considering delay feature. Real-time gate reassignment model has been presented, whose objective is to minimize the disturbance compared to planned gate assignment scheme. An ant-based heuristic algorithm is designed to solve the problem. With the numerical test, the method is proved to be effective and efficient, which can meet the request of real-time operation of hub airport.
Some conclusions can be drawn in the paper. First, the real-time gate assignment is very important in increasing the effectiveness and volume of airport. Second, the real-time gate assignment is difficult because that the flight delay is uncertain. Last, the gate reassignment schedule is decided by the selection of objective function directly. Airport operation and some kinds of influence factors should be taken into account in the actual gate assignment schedule. Therefore, the gate assignment is a typical a multiobjective optimization problem. It should be noted that the research only considers the general situation of gate reassignment. How to operate gate reassignment considering the tradition of gate assignment and importance of flight priority and the reassignment after situation as airport closures is worthy future research topics.
This work was supported by National Natural Science Foundation and Aviation Fund of China U1233115, Civil Aviation Science Fund of China (MHRD201127), and Qinglan Project.