Multiobjective Gate Assignment Based on Passenger Walking Distance and Fairness

Abstract

Passenger walking distance is an important index of the airport service quality. How to shorten the walking distance and balance the airlines' service quality is the focus of much research on airport gate assignment problems. According to the problems of airport passenger service quality, an optimization gate assignment model is established. The gate assignment model is based on minimizing the total walking distance of all passengers and balancing the average walking distance of passengers among different airlines. Lingo is used in the simulation of a large airport gate assignment. Test results show that the optimization model can reduce the average walking distance of passenger effectively, improve the number of flights assigned to gate, balance airline service quality, and enhance the overall service level of airports and airlines. The model provides reference for the airport gate preassignment.

1. Introduction

Airport gate is a main component of airport resource. Rational and efficient gate assignment is an important way to improve airport operation efficiency and passenger service level. Airport gate is divided into contact gate (a gate with an aerobridge) and remote stand (on the apron). The type and layout lead to different distance from gate to security check, baggage hall, and transit counters. The distance between different areas has a direct impact on passenger activities in the terminal. How to optimize the gate assignment from the perspective of passengers becomes a hot research area at home and abroad.

At present, the main research findings of gate assignment from the perspective of passengers took the shortest passenger walking distance and the minimum embarking and transit time as objective function to optimize gate assignment; for example, Braaksma, [1], Babic et al. [2], Mangoubi and Mathaisel [3], Yan and Huo [4], Bolat [5], Yan et al. [6], and Cheng’s [7] research findings showed that reasonable gate assignment could reduce passenger walking distance appropriately. In 1998, Haghani and Chen [8] took the number of transfer passengers of different flights and the distance between different gates into account comprehensively while minimizing passenger walking distance in a terminal. Assuming that all passengers were converted into transit passengers and had taken the shortest transit time as the objective function, Xu and Bailey [9] established quadratic mixed 0-1 integer programming model of gate assignment through virtual assumption. In further research, some scholars began to consider minimizing the number of flights, which are assigned to remote stands, and the passenger walking distance/time, such as Pintea et al. [10], Ding et al. [11, 12], and so on; some scholars considered minimizing walking distance together with delay costs, like Zhu et al. [13], balancing usage of airport gates, like Wei and Liu [14, 15], passenger waiting time, like Hu and Paolo [16], and fuel consumption of aircraft taxiing, like Maharjan and Matis [17], respectively.

Optimization gate assignment from the perspective of passengers can reduce passenger walking distance and improve passenger service levels to a certain extent. However, there are some deficiencies in research findings. Firstly, in some large hub airporsts, the proportion of transit passengers is large and the actual walking distance of transit passengers is not equal to the actual distance between two gates. The walking distance is related with the layout of transit counters and transit halls. In the research, ignoring transit passengers can cause the model to be inaccurate. Secondly, civil airport service quality issued by the Civil Aviation Administration in 2006 requires that the number of passengers embarking/disembarking through aerobridges should be above 80%. But in most current research, the proportion of passengers is not taken into account. Thirdly, most current researches do not consider the balance of passenger walking distance between different airlines, which can lead to reducing the passenger service level and can be unfair for some airlines, especially for small airlines.

Optimizing gate assignment can improve passengers’ satisfaction and balance the service quality of each airline. In this research, we propose a new model which is different from previous researches; the gates are categorized into contact gate and remote stand in the mode, the proportion of passenger embarking/disembarking through aerobridges is taken into account, and the model considers the fairness between airlines besides reducing the overall passengers’ walking distance.

The paper is organized as follows. The gate assignment model is detailed in Section 2. Section 3 briefs the simulation software and analyzes the results under different conditions in detail. Some conclusions are drawn in the last section.

2. Gate Assignment Model

2.1. Description of Gate Assignment

Gate assignment is to arrange a reasonable gate for each arrival-departure flight timely according to the flight plan, which is submitted by every airline. Safety operation of aircraft and gate is the premise of gate assignment.

Passenger walking distance in a large airport is composed of three parts: arrival passenger walking distance, departure passenger walking distance, and transit passenger walking distance. The arrival passenger walking distance refers to the distance from gate to baggage hall; the departure passenger walking distance refers to the distance from security check to gate; the transit passenger walking distance refers to the distance from gate to transit counter and then to the next flight gate. The arrival-departure transit passengers are known collectively as transit passengers in the paper. The walking distance of transit counter passengers includes the arrival passengers’ distance from gate to transit counter and the departure passengers’ distance from transit counter to gate.

Minimizing and balancing the walking distance of all passengers from different airlines are goals to model gate assignment in the paper. Then Lingo software is adopted to verify the effectiveness of a model in order to improve the service level of airport and airline.

2.2. Model Assumptions

(1)Gate assignment is a continuous operation course. In order to reduce the scale of the problem, the paper selects some time intervals for gate assignment.(2)The capacity of gates can meet the demand of all flights in the research time; it means that every flight can be assigned to a gate.(3)The arrival-departure flight performed by the same aircraft is assigned to the same gate and it used the same flight number.(4)All information, such as flight plan, aircraft basic information, the usage status of gates, and so on, is known in research time.(5)Only the gate assignment of domestic flights is considered in the paper.

2.3. Symbol Definition

𝐹:flight set,𝐹={𝑓₁,𝑓₂,…,𝑓_𝑚},𝑚is the total number of flights in research period.𝑓_𝑖(1≤𝑖≤𝑚)is flight number which is ordered by the arrival time of flights; the bigger𝑖means the later flight𝑓_𝑖arrives at the airport. 𝑐_𝑓𝑖:size of the aircraft which executes flight𝑓_𝑖. The bigger𝑐_𝑓𝑖is, the larger aircraft is. The smaller𝑐_𝑓𝑖is, the smaller aircraft is. 𝐿:airline set,𝐿={𝑙₁,𝑙₂,…,𝑙_𝑞},𝑞is the total number of airlines in research period.𝑙_𝑎(1≤𝑎≤𝑞)is airline code. 𝐹_𝑙𝑎:the flights set of airline𝑙_𝑎. 𝐺:gate set,𝐺={𝑔₁,𝑔₂,…,𝑔_𝑛},𝑛is the total number of gates.𝑔_𝑘(1≤𝑘≤𝑛)is gate code.

Assuming that the number of gates is𝑥, if𝑘≤𝑥, it means that𝑔_𝑘gate is a contact gate; otherwise, it is a remote stand. 𝑐_𝑔𝑘: size of gate𝑔_𝑘; the bigger𝑐_𝑔𝑘means the larger aircraft can be parked on the gate; the smaller𝑐_𝑔𝑘means the smaller aircraft can be parked. 𝑎_𝑓𝑖: arrival time of flight𝑓_𝑖; the unit is minute. 𝑑_𝑓𝑖: departure time of flight𝑓_𝑖; the unit is minute. 𝑇: minimum time interval of two flights which are assigned to the same gate; the unit is minute. 𝑆^𝑎_𝑔𝑘: distance of arrival passenger walking from gate𝑔_𝑘to baggage hall. 𝑆^𝑑_𝑔𝑘: distance of departure passenger walking from security checking to gate𝑔_𝑘. 𝑆^𝑚_𝑔𝑘: distance between gate𝑔_𝑘and transit counter. 𝑁^𝑎_𝑓𝑖: number of arrival passengers of flight𝑓_𝑖. 𝑁^𝑑_𝑓𝑖: number of departure passengers of flight𝑓_𝑖. 𝑁^𝑚_𝑓𝑖: number of transit passengers of flight𝑓_𝑖.

Consider 𝑦_{𝑓𝑖,𝑔𝑘}=1,ifflight𝑓_𝑖isassignedtogate𝑔_𝑘,𝑧0,otherwise,_{𝑓𝑖,𝑓𝑗}=1,ifflight𝑓_𝑖and𝑓_𝑗areassignedtothesamegate,0,otherwise. (1)

2.4. Modeling

Minimizing the total walking distance of all passengers in research period is one of the goals in the paper.

Consider min𝑍₁=_{𝑓𝑖∈𝐹𝑔𝑘∈𝐺}𝑦_{𝑓𝑖,𝑔𝑘}𝑁^𝑎_𝑓𝑖𝑆^𝑎_𝑔𝑘+𝑁^𝑑_𝑓𝑖𝑆^𝑑_𝑔𝑘+𝑁^𝑚_𝑓𝑖𝑆^𝑚_𝑔𝑘, (2) where𝑁^𝑎_𝑓𝑖𝑆^𝑎_𝑔𝑘represents the total walking distance of arrival passengers of flight𝑓_𝑖walking from gate𝑔_𝑘to baggage hall;𝑁^𝑑_𝑓𝑖𝑆^𝑑_𝑔𝑘represents the total walking distance of departure passengers of flight𝑓_𝑖walking from security checking point to gate𝑔_𝑘;𝑁^𝑚_𝑓𝑖𝑆^𝑚_𝑔𝑘represents the total walking distance of transit passengers of flight𝑓_𝑖.

According to the objective function (2), gate assignment may result in longer walking distance of some airlines’ passengers while some others are shorter. The objective function (2) can lead to unbalanced passenger walking distance among airlines and reduce the airlines’ service quality. Therefore, in order to improve the service quality of the entire airport, it is necessary to balance passenger walking distance of each airline from the viewpoint of airline fairness.

Consider min𝑍₂=max_{𝑙𝑎∈𝐿}𝑍_𝑆𝑙𝑎,𝑆_𝑙𝑎=∑_{𝑓𝑖∈𝐹𝑙𝑎}∑_{𝑔𝑘∈𝐺}𝑦_{𝑓𝑖,𝑔𝑘}𝑁^𝑎_𝑓𝑖𝑆^𝑎_𝑔𝑘+𝑁^𝑑_𝑓𝑖𝑆^𝑑_𝑔𝑘+𝑁^𝑚_𝑓𝑖𝑆^𝑚_𝑔𝑘∑_{𝑓𝑖∈𝐹𝑙𝑎}𝑁^𝑎_𝑓𝑖+𝑁^𝑑_𝑓𝑖+𝑁^𝑚_𝑓𝑖,∑𝑆=^{𝑓𝑖∈𝐹}∑_{𝑔𝑘∈𝐺}𝑦_{𝑓𝑖,𝑔𝑘}𝑁^𝑎_𝑓𝑖𝑆^𝑎_𝑔𝑘+𝑁^𝑑_𝑓𝑖𝑆^𝑑_𝑔𝑘+𝑁^𝑚_𝑓𝑖𝑆^𝑚_𝑔𝑘∑_{𝑓𝑖∈𝐹}𝑁^𝑎_𝑓𝑖+𝑁^𝑑_𝑓𝑖+𝑁^𝑚_𝑓𝑖,𝑍_𝑆𝑙𝑎=𝑆_𝑙𝑎−𝑆𝑆,𝑙_𝑎∈𝐿. (3)(4)(5)(6) The objective function (3) is to minimize the ratio between the difference and the average walking distance of all passengers, where𝑆_𝑙𝑎represents the average passenger walking distance of airline𝑙_𝑎in research period;𝑆represents the average walking distance of all passengers in research period;𝑍_𝑆𝑙𝑎represents the ratio of the difference and walking distance of all passengers, where the difference is the average passenger walking distance of airline𝑙_𝑎and all passengers.

Subject to ∑_{𝑓𝑖∈𝐹}∑_{𝑘≤𝑥,𝑔𝑘∈𝐺}𝑦_{𝑓𝑖,𝑔𝑘}𝑁^𝑎_𝑓𝑖+𝑁^𝑑_𝑓𝑖+𝑁^𝑚_𝑓𝑖∑_{𝑓𝑖∈𝐹}𝑁^𝑎_𝑓𝑖+𝑁^𝑑_𝑓𝑖+𝑁^𝑚_𝑓𝑖≥0.8,_{𝑔𝑘∈𝐺}𝑦_{𝑓𝑖,𝑔𝑘}=1,∀𝑓_𝑖𝑦∈𝐹,_{𝑓𝑖,𝑔𝑘}∈{},𝑧0,1_{𝑓𝑖,𝑓𝑗}=_{𝑓𝑖∈𝐹𝑗>𝑖,𝑓𝑗∈𝐹𝑔𝑘∈𝐺}𝑦_{𝑓𝑖,𝑔𝑘}×𝑦_{𝑓𝑗,𝑔𝑘},𝑎_𝑓𝑗−𝑑_𝑓𝑖+1−𝑧_{𝑓𝑖,𝑓𝑗}𝑐𝑀≥𝑇,𝑖<𝑗,_𝑓𝑖≤𝑐_𝑔𝑘+1−𝑦_{𝑓𝑖,𝑔𝑘}𝑀,𝑖,𝑗,𝑎,𝑞,𝑘,𝑥∈𝑍⁺. (7)(8)(9)(10)(11)(12)(13) Equation (7) is to restrain the proportion of passengers who are required to embark/disembark aircraft through aerobridges. Civil airport service quality, which was issued by the Civil Aviation Administration in 2006, requires that the number of passengers that embark/disembark through aerobridges should be above 80%.

Equations (8) and (9) indicate that each flight has one and only one gate to be assigned. That is, for flight𝑓_𝑖, in the gate set𝐺, there is only one gate𝑔_𝑘to make𝑦_{𝑓𝑖,𝑔𝑘}=1.

Equation (10) is used to judge whether the two flights are assigned to the same gate. When𝑦_{𝑓𝑖,𝑔𝑘}×𝑦_{𝑓𝑗,𝑔𝑘}=1,𝑧_{𝑓𝑖,𝑓𝑗}=1, it indicates that the later arrival flight𝑓_𝑗and the front flight𝑓_𝑖are arranged in the same gate; otherwise,𝑧_{𝑓𝑖,𝑓𝑗}=0.

Equation (11) requires that the two flights which were assigned to the same gate should meet certain safety interval. According to (10) when𝑧_{𝑓𝑖,𝑓𝑗}=1, it needs to meet𝑎_𝑓𝑗−𝑑_𝑓𝑖≥𝑇; the front and later flights should meet the minimum safety interval. When𝑧_{𝑓𝑖,𝑓𝑗}=0, the two flights are not assigned in the same gate; it need not meet safety interval. Therefore, value𝑀, which is big enough, is introduced to ensure the inequality holds.

Equation (12) means that the gate type should match the aircraft type. When𝑦_{𝑓𝑖,𝑔𝑘}=1, flight𝑓_𝑖is assigned to gate𝑔_𝑘; it should meet𝑐_𝑓𝑖≤𝑐_𝑔𝑘. When𝑦_{𝑓𝑖,𝑔𝑘}=0, there is no relationship between flight𝑓_𝑖and gate𝑔_𝑘.

Equation (13) is a positive integer constraint.

3. Simulations

The decision variables in the gate assignment model are 0 and 1, belonging to 0-1 planning of integer programming problem. Due to nonlinear constraints involved in the model, the model is called integer nonlinear programming (INLP). The paper uses Lingo software to simulate and verify the model. The Global (global optimization algorithm) and Multistart (more initial point algorithm) built-in Lingo are specifically used to solve nonlinear programming (Scharge [18]). In addition, Lingo can be connected with EXCEL, database, and other software conveniently; it also can easily input and output the simulation results. Another important superiority of Lingo is convenient to describe large-scale optimization problems concisely and intuitionisticly. Therefore, the paper uses Lingo software to simulate and verify the effectiveness of the model.

The simulation data of domestic flights to be assigned in a typical time interval (8:00–11:00) in a large airport is shown in Tables 1 and 2. The minimum time interval𝑇=15minutes; this is the time when the two flights are to be assigned to the same gate continuously. The constant value𝑀=300.The paper uses Lingo 11.0 and selects Global Solver (Global optimization solve) and Global set strategy (Branching: Rel Violation; Box Selection: Worst Bound; Reformulation: High) to verify the effectiveness of models.

Table 1 

Domestic flight to be assigned from 8:00 to 11:00.

Table 2 

Data of available gates.

The paper uses Lingo to simulate the results of the random assignment, the objective function (2) (𝑍₁optimal) and the objective function (3) (𝑍₂optimal), respectively. The simulation result is shown in Table 3, where𝑍₁and𝑍₂represent the value of the objective function (2) and the objective function (3), respectively. The smaller𝑍₁is, the shorter passenger walking distance is. The smaller𝑍₂is, the fairer between airlines is.𝑄represents the proportion of passengers embarking/disembarking through aerobridge (referring to passing rate); the larger𝑄is, the more passengers embarking/disembarking through aerobridge are.𝑆represents the overall average passenger walking distance.𝑆_𝐴1--𝑆_𝐴4represents the average passenger walking distance of four airlines, respectively.𝑆_maxrepresents the maximum difference of average passenger walking distance between airlines. (the unit of𝑍₁,  𝑆,  𝑆_𝐴1--𝑆_𝐴4,  and  𝑆_max  is meters.)

Table 3 

Comparison of simulation results between random assignment, optimization 𝑍₁, and optimization 𝑍₂.

With Table 3 and Figures 1 and 2, we can draw the conclusions.(1)When𝑍₁is optimal, the value of𝑍₁is a minimum. It means that the total passenger walking distance is the shortest. The maximum value of𝑄is 1, which means the passing rate is 100%. But the difference of average passenger walking distance between four airlines is comparatively large and the value of𝑍₂(0.299) is also the largest; it means that the ration between the average and total passenger walking distance of airlines is large; the largest ration is approaching 30%.(2)When𝑍₂is optimal, the value of𝑍₂is approximately zero and the average passenger walking distance of four airlines (Figure 2) is basically flat. That is, the gate assignment is the fairest. But the average passenger distance is 180.8 meters higher than the value of optimal𝑍₁. and the passing rate is only 80% (𝑄=0.800), which is the lowest in the three simulation groups.(3)The three values of𝑍₁,𝑍₂, and𝑄in random gate assignment are relatively concentrated. But compared with the value of optimal𝑍₁, the value of𝑍₁in random gate assignment is high and the value of𝑄is low. Compared with the value of optimal𝑍₂, the value of𝑍₂in random gate assignment is high. And the difference of average passenger walking distance between airlines is the largest, which is 156.5 meters. The gate assignment schedule is much unfair to airline𝐴₄because the average walking distance is larger than other airlines distinctly.

Figure 1 

Comparison of𝑍1,𝑍2, and𝑄.

Figure 2 

Comparison of𝑆and𝑆𝐴1--𝑆𝐴4.

From the above simulation results, the three groups all have shortcomings. To find a set of ideal solution, the paper takes the objective function (2) as primary objective and transfers the objective function (3) into constraint. Assuming𝑍₂≤0.10and𝑍₂≤0.20, the simulation results can be acquired (Table 4).

Table 4 

Comparison of simulation results under five different conditions.

According to Table 4 and Figures 3 and 4, when the objective function (2) is the objective and𝑍₂≤0.10, all the indexes of simulation are in the state of ideal according to the five group simulation results. Compared with the random gate assignment, the simulation result of𝑍₂≤0.10is as follows.(1)The total walking distance of passengers is 1,368,320 meters and decreases by 34.5%;(2)the passing rate is 96.4% and improves by 13.3%;(3)the total average passenger walking distance is 268.5 meters and decreases by 141.6 meters;(4)the simulation results show that it is relatively fair among airlines. The largest difference of average walking distance among airlines is only 20.3 meters; it is more inferior to the random gate assignment.

Figure 3 

Comparison value of𝑍1,𝑍2, and𝑄in five groups.

Figure 4 

Comparison value of𝑆,𝑆𝐴1--𝑆𝐴4, and𝑆maxin five groups.

Flight Gantt chart of the random gate assignment and the situation of𝑍₂≤0.10are shown in Figures 5 and 6. Distribution of passengers and the average distance of gate are shown in Figure 7.

Figure 5 

The flight Gantt chart of random gate assignment.

Figure 6 

The flight Gantt chart of𝑍2≤0.10.

Figure 7 

Distribution of passengers and the average distance of gate.

It is convenient for passengers to embark/disembark the aircraft through aerobridge because the distance is close and passengers will not be influenced by weather. The average distance from gate to baggage hall, security check, and transit counter is shorter; the total walking distance of passengers assigned to the gate is shorter. Thus the passenger will feel comfortable. We can draw the conclusions from Figure 5 to Figure 7:(1)the number of flights assigned to the remote stands (G009, G010) is only one, and this gate assignment schedule can improve the passing rate;(2)two flights are reduced to be assigned to gate which is near the remote stand; one flight is added to be assigned to G001, G003, G004, and G008 gate, respectively;(3)the gate, where the average walking distance is short, is assigned efficiently. Making effective use of a gate can reduce the walking distance and improve the service level of passengers.

In summary, the simulation optimization results can not only reduce the average passenger walking distance effectively and improve passing rate, but also reduce the difference of average walking distance of passengers among airlines and enhance the overall passenger service quality of airports and airlines.

4. Conclusions

The paper presents a new idea for the airport gate assignment problem. Unlike the previous researches, it takes the restraint of passenger passing rate and airlines’ fairness into account under the premise of airport safety operation. Combining with the objective of minimizing the whole passengers’ walking distances, the paper builds a multiobjective optimization model of gate assignment. Lingo software is used to verify the effectiveness of model by simulating a large airport gate assignment. According to the test results, we can draw some conclusions.(1)The assignment can ensure the passengers passing rate by setting (7).(2)The two objectives are interactional between each other. And decision makers can get a set of suitable results by adjusting the value range of the second objective.(3)Compared to the random assignment, this model can reduce the whole passengers’ walking distances and improve the fairness between airlines at the same time.(4)The research scope of the paper is only part of the domestic flights. How to combine with international flights and effective resource schedule should be further researched.

Acknowledgments

This work was supported by the National Natural Science Foundation of China and Civil Aviation Administration of China (no. U1333117), China Postdoctoral Science Foundation (no. 2012M511275), and the Fundamental Research Fund for the Central Universities (nos. NS2013067, NN2012019, and NS2012115).