An Analytical Optimisation Framework for Airport Terminal Capacity Expansion

This article considers how to allocate additional physical resources within airport terminals. An optimization model was developed to determine where additional resources should be placed to minimise passenger waiting times. The objective function is stochastic and can only be evaluated using discrete event simulation. As this model is stochastic and nonlinear, a Simulated Annealing (SA) metaheuristic was implemented and tested. The SA algorithm repeatedly perturbs a resource allocation solution using one of two methods. The ﬁrst method is creating new solution randomly in each iteration, and the second method is local search that is mimicked by any move of the current solution of x solution chosen randomly in its neighborhood. Numerical testing shows that the random approach is best, and solutions that are 12.11% better can be obtained.


Introduction
e high growth in passenger numbers in recent years has created considerable strains on airports. Airport terminals are expected to process the increasing passenger numbers efficiently and with minimum delay. At the same time, the required expansion of the airport capacity might be limited by the available resources (e.g., limited available land), environmental impacts, and lengthy approval processes [1]. In addition, extension of the major airport infrastructure is typically time-consuming and costly, which raises the need for the development of smart systems and methods to improve airport performance within the available infrastructure.
Airport terminals are complex systems and are inherently stochastic in nature. Passenger numbers continually change throughout the day, depending on the status of incoming or outgoing flights. It is an integrated system, and operational problems within any of its internal processes can jeopardise the performance of other elements, creating significant bottlenecks, long passenger queues, congestion, and overall delays [2][3][4]. For example, disruption, congestion, and uneven passenger inflow into the terminal processing points, caused by the operation of the landside element (including the infrastructure and facilities associated with the arrival of passengers to the airport), could have a significant impact on the performance of the terminal (such as passenger boarding and take-off procedures). It involves multiple stakeholders, and each is responsible for performing particular terminal process such as check-in, security, and immigration [5].
It is conventional to subdivide airport operations into those relevant to the arrival procedures of incoming passengers and departure procedures for outgoing passengers. e arrival processes and facilities include disembarking, immigration, baggage claim, and quarantine procedures [6]. e departure processes and facilities include check-in, security screening, immigration and customs, boarding, and take-off procedures. It is these departure flow processes that have the greatest impact on the entire operation of passenger terminals and other elements of the airport. According to Neufville and Odoni [7], the departure process requires significantly more time than the arrival process because it sometimes involves services provided to transit passengers. Due to the complex structure of airport terminals, the development of an analytical optimization framework for studying passengers flow in airports under uncertainty of future demand is a difficult task. ese difficulties and challenges have led to studies of overall terminal capacity planning problems. Previous studies have generally focused on one element of the terminal or have not accounted for expandability [8]. e general aim of this paper is to propose a mathematical approach for capacity expansion planning.
is model will determine where additional resources should be placed within airport terminal processes. Hence, the objective function of the proposed model is to minimise the cost of used resources and the total waiting time. A number of technical constraints exist. e main contribution of this work is to provide a Capacity Expansion Planning Model (CEPM) for airports. erefore, this paper has contributed to the body of knowledge by enabling two levels of planning, operational and strategic. In comparison with existing approaches, the new approach is more accurate because real waiting time can be identified and effects of uncertainty can be included. For example, Sun and Schonfeld [9] used mathematical functions, which are more approximate.

Related Work
is section analyses existing research conducted to address the issues of passenger flows within airports. e irregular flows occurring in airport terminal areas represent a significant management challenge, for instance, determining the number of service counters to open, and personnel allocation and reallocation issues [5-8, 10, 11]. A significant problem when studying passenger flow is capturing stochastic elements. is is because, as Guizzi et al. [12] argued, passengers behave differently inside airports according to their previous experiences. us, in order to assist decisionmakers at the airport terminal to address sudden and unforeseen congestion conditions, extensive research has been conducted on uncertainty. Yamada et al. [13] examined links between passenger behavior and facilities and identified several sources of congestion.
Additionally, Alodhaibi et al. [14] conducted their research using a simulation framework developed in [15] to investigate how the arrival pattern of passengers affects international terminal operations. e simulation outcomes provided a better understanding of the behavior of passenger airport access, which could lead to reduced waiting time and possible congestion by increasing the number of working stations (i.e., number of check-in counters) at peak times.
Safety concerns in recent times have caused many changes to security screening procedures and this impacts passenger throughput times. Previous research can be categorized according to related topic areas, including the significance of the security screening system in airport operations, the capacity of security screening areas, and dynamic system management [16][17][18][19][20][21]. For instance, Dorton and Liu [21] proposed the application of a DES for the security screening system coupled with a queuing. e aim is to analyze external factors influencing security screening operation efficiency and to identify the effect on throughput and cycle time.
In airport apron areas, a common optimization problem is gate assignment, which considers the minimization of passenger walking distance, from check-in to baggage claim area. Genç et al. [22] applied a heuristic to solve stochastic approaches to minimise the total duration of ungated flight. Similarly, Ding et al. [23] applied a Tabu Search metaheuristic to identify the problem when the number of aircraft exceeds the number of available gates. e two objective functions optimized were number of ungated aircraft and total walking distance. Finally, the research by Mota [24] is noteworthy as a mix of two models was applied to satisfy the different mandatory restricted policies related to airport terminal processing units, such as opening or closing check-in counters for each flight, check-in starting time, and load balance.
Capacity planning problems feature prominently in airport terminal research. For instance, Solak et al. [8] considered terminal operations to be a network system and used a multistage stochastic-integer linear programing model to determine the optimal capacity, taking into account optimal future expansion and desired LOS. e main objective was to minimise the maximum delay of each passageway and processing station by considering the variation in demand as a significant constraint. Also, Sun and Schonfeld [9] investigated uncertainties within the terminal. ey found that facility performances are nonlinear functions. ese functions are represented by delay level as a function of utilisation rates of capacity and demand fluctuations as indicated by uncertainties in traffic predictions. It is known that passenger departure flow is an important process for any airport facility because of the fixed departure time of flights. e same researchers [25,26] go further by considering strategic airport facility planning under demand uncertainty and proposed a mixed-integer nonlinear program to determine when and where to adjust process capacity over a number of planning periods. Airport congestion and delay cost are approximated using some appropriate mathematical functions. e novelty of our work lies in integrating a discrete event simulation to an optimization model for airport terminal capacity planning. Hence, undertaking such research is significant to identify a real waiting time and to know the effect of decision. Other models like Sun and Schonfeld's [9,27], for instance, use mathematical functions, which are exact. Furthermore, in [26], the same authors used a discrete approximation technique when the model is solved where the mathematical relations in the formulation are accurate. Hence, a simulated annealing metaheuristic was applied to perform airport terminal capacity expansion and this may be the first application of such an approach to this domain.

Problem Description and Formulation
is section defines the variables and parameters used in our capacity expansion model. e purpose of the model is to determine where additional resources should be placed in order to reduce the waiting costs. Each resource type has different costs, and a budget for total spending has been provided.

Model Notation
(i) Indices p, r, k, t, f: process, resource, passenger types, period, and shift.

(iii) Parameters
N r,p , N r : maximum number of resources of type r in process p and across all processes C r,p : cost of providing a resource of type r in process p V k,p : cost incurred per unit of waiting time for passengers of type k in process p B: total budget available for capacity expansion n r,p : current number of resources of type r in process p τ k,p : expected time taken to serve passenger k in process p.
(iv) Decision variables N r,p : number of resources to open of type r in process p W k,p : total waiting time incurred in process p for passengers of type k. e model is as follows: e objective function (1) has two components: (i) the cost of purchasing/acquiring additional resources of type r in process p and (ii) the total passenger waiting time converted to a dollar value. Constraints (2) and (3) ensure that the additional resources of type r do not exceed the maximum number of resources. Constraint (4) restricts spending to a particular budget. Constraint (5) restricts the decision variable N r,p to be positive. e waiting time of passengers at different processes is a stochastic auxiliary variable and depends on the number of resources assigned and the processing time, which is a random variable. It is computed using simulation in equation (7) using the simulation model from [11,15].

Simulated Annealing.
To solve the proposed model, a metaheuristic approach is advocated as constraint (7) cannot be handled using mixed-integer programing, without the application of a simulation model. Of the different metaheuristics, simulated annealing was chosen. It is an effective and computationally fast search algorithm for solving hard optimization problems by Burdett and Kozan [27][28][29] and is well suited to probabilistic and nonlinear optimization problems.
e algorithm is iterative and comprises two nested "for" loops. e outer loop controls and alters the "temperature" parameter T. In the inner loop, a specified number of solution refinements (a.k.a. perturbations) are entertained and evaluated. Refinements are accepted when they are explicitly better; otherwise, they are accepted/ rejected probabilistically according to the following function: where Δf � f ′ − f is the difference between the new solution f ′ and the current solution f. At every temperature, a selected number of perturbations are evaluated. SA requires several parameters (i.e., primary temperature, the cooling rate, the number of function evaluations at every temperature, and the final temperature). At early stages of the search, the temperature is high and many nonimproving moves are accepted. As the search progresses, the temperature is reduced and solutions are only accepted if a strict improvement occurs. With the slow reduction in temperature, worse solutions are accepted with less probability. e SA metaheuristic was implemented in C++ and the simulation model was integrated to evaluate the waiting times. Preliminary numerical testing was performed to identify an appropriate starting temperature (see Figure 1). It is evident from the graph below that the best parameter values of this problem are as follows: temperature (T) � 15000, cooling rate (α) � 0.015, and total number of iterations � 600.

Simulated Annealing Algorithm Description
(1) Phase 1: Create Initial Solution. SA may be initialized with a randomly created solution or via some heuristic/constructive algorithm. However, because of the resource limitation constraints, some of the generated solutions will Complexity 3 not be feasible. e solution chromosome should simultaneously reflect two main characteristics: (i) Number of resources for each process, such as checkin resources (i.e., economy and business counters), security screening resources, and immigration resources (i.e., common counters and SmartGates). (ii) e number of assignment resources for each shift. ese solutions should be corrected via a corrective algorithm. Algorithm 1 is used to initialize a set of solutions.
(2) Phase 2: Perturbing a Solution. To create a new solution, it is necessary to perturb the current solution. ere are many perturbation techniques that can be applied. In this article, a new solution is created by randomly changing the number of resources assigned to a randomly selected airport process. e creation of a new solution is performed by Algorithm 2.
(3) Phase 3: Assess New Solution. In this step, the goodness of the new solution is evaluated. Algorithm 3 demonstrates the assessment procedures. e generated solution will be simulated to measure a performance matrix, such as the average waiting time at each processing point. Also, the best cost will be selected by comparing it with the current cost.

Numerical Testing and Analysis
In this section, the SA metaheuristic approach coupled with discrete event simulation is analyzed. In this numerical investigation, there are three types of process and five types of resources that were considered. Process type 1, the checkin process, has five separate lines, each with eight counters, two for business and six for economy. Process type 2 is security screening with five lanes. Process type 3 is immigration, which has eight common counters and 10 Smart-Gates. It is assumed that there are three periods during the day to which these processes are assigned to be operated. Figure 2 is a snapshot of the simulation outputs, for instance, the appropriate number of resources that need to be opened, the average waiting time that passengers spent at each process, and the cost of resources ending with the total cost. e cost of waiting time is considered based on the given policy of acceptable queue time in a particular process. is is named the cost of inconvenience, as it exceeds given acceptable average waiting time. For example, passengers at the check-in process can be classified as business and economy, each with different queue time limits. Kazda and Caves [30] argued that the average waiting time should not be higher than 12 minutes for economy class and 3 minutes for business. e summary of input data used in this study is listed in Table 1.
Two different methods of creating new solutions were used to generate a starting solution. e first is creating a new solution randomly and the second is local search. e  Tables 2 and 3. e general parameters used for both methods are as follows: temperature (T) � 15000, cooling rate (α) � 0.015, and the maximum number of runs � 1500. e first column refers to the number of better solutions, where the average number of better solutions obtained by random search approach is 7.9 and the local search approach is able to find 7.8 better solutions on average. e second column presents the total average waiting time spent in the airport terminal process. It is evident that local search provides lower waiting times compared with the random approach. It also has shorter run-time, with an average of 15.27 minutes compared to 21.05 minutes for the random approach. However, from the results presented in both tables, it can be clearly seen that the random search method reduces the objective function value by 12.11%. e mean μ value of the objective function obtained from the random approach is $1998.3, whereas μ of objective function value of the local search is $2256.
Complexity 5 provide the minimum total average waiting time in the airport. Figure 3 demonstrates the best solution given by the random search for the solution run number 4. e optimal solution for this simulation run with regard to opening additional resources for check-in is summarized in Table 4. e average waiting time is 1.91 minutes for business-class passengers and 34.5 minutes for economy-class passengers.

Complexity
For the security screening checkpoints, the opening resources are 5, 2, and 3 control checkpoints for shift 1, shift 2, and shift 3, respectively, having an average waiting time of 3.04 minutes. e opening common immigration process is 4, 3, and 5 counters, while for SmartGates there are 8, 9, and 7 kiosks for the three shifts, having average waiting times of 0.11 and 0.02 minutes for the common immigration desks and SmartGate kiosk, respectively. e total cost of opening all resources is $2038 given that the total average time spent in the queues is 39.57 minutes. Figure 4 illustrates the optimal solution provided by the SA algorithm using local search for creating a new solution. In this simulation run, the solution is characterised from the total cost of $2250 given that the total average waiting time Result of simulation run 6 of local search approach  8 Complexity spent in the system is 28.89 minutes. e optimal solution for this simulation run is opening a check-in resource based on the detailed information listed in Table 5. By adding this resource, the average waiting time at the check-in process will be 1.56 minutes for business-class passengers and 7.03 minutes for economy-class passengers, reductions of 20.17% for business-class passengers and 132.29% for economyclass passengers compared with the random search method. For the process of security screening checkpoints, the best solution can be found when opening 4, 4, and 5 security control checkpoints for shift 1, shift 2, and shift 3, respectively. By opening these numbers of resources at the security screening process, the average waiting time is 7.92 minutes. Finally, the immigration process should open 5, 4, and 3 common immigration counters and 10, 10, and 9 Smart-Gates for the three shifts, in order to get the optimal solution, having the average waiting of 0.10 minutes and 0.012 minutes for the common counters and SmartGates, respectively.

Conclusion
is paper has discussed the development of a mathematical approach to perform capacity planning in airport terminals.
e objective of the model is determining where additional resources should be opened to decrease the cost of time spent in the queues of the airport terminal. Since the proposed problem is probabilistic and nonlinear, a metaheuristic approach is advocated. e waiting times are computed using discrete event simulation and those times are used in the objective function. Two different approaches for creating new solutions were used in this study. e first one is creating a new solution using the random technique and the other is creating a new solution by using the local search technique. e random technique decreased the objective function value by 12.11%. It also has shorter runtimes, with average of 15.27 minutes compared to 21.05 minutes for the random approach. e developed model can be more accurate because the effect of decision can be known and real time can be identified. It also can provide strategic planning, while the proposed simulation model can be used for the operational planning level. is work has contributed to the body of knowledge by enabling two levels of planning, operational and strategic.
On the other hand, the lack of access to the detailed data related to operational facilities due to the recent strict regulations with respect to security issues resulted in some difficulties in developing the modelled passengers' flows within international terminal. Because of these difficulties, this model has been simplified by, firstly, utilizing available data collected by previous research, and, secondly, making an assumption where needed.

Data Availability
No data were used to support this study.