Towards balancing efficiency and customer satisfaction in airplane boarding: An agent-based approach

Fabrin, Bruna H. P.; Ferrari, Denise B.; Arraut, Eduardo M.; Neumann, Simone Article Towards balancing efficiency and customer satisfaction in airplane boarding: An agent-based approach Operations Research Perspectives Provided in Cooperation with: Elsevier Suggested Citation: Fabrin, Bruna H. P.; Ferrari, Denise B.; Arraut, Eduardo M.; Neumann, Simone (2024) : Towards balancing efficiency and customer satisfaction in airplane boarding: An agentbased approach, Operations Research Perspectives, ISSN 2214-7160, Elsevier, Amsterdam, Vol. 12, pp. 1-19, https://doi.org/10.1016/j.orp.2024.100301 This Version is available at: https://hdl.handle.net/10419/325783 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Contents lists available at ScienceDirect Operations Research Perspectives journal homepage: www.elsevier.com/locate/orp Towards balancing efficiency and customer satisfaction in airplane boarding: An agent-based approach Bruna H.P. Fabrin a, Denise B. Ferraria, Eduardo M. Arrauta, Simone Neumann b,∗ aAeronautics Institute of Technology, Praça Marechal Eduardo Gomes 50, São José dos Campos, 12228-900, São Paulo, Brazil bUniversität Hamburg, Moorweidenstrasse 18, Hamburg, 20148, Germany ARTICLE INFO Keywords: Airplane boarding Agent-based modeling Simulation ABSTRACT The airplane boarding process, which can have a significant impact on a flight’s turnaround time, is often viewed by researchers and airlines primarily in terms of minimizing total boarding time (TBT). Airplane capacity, number of passengers on board, amount of luggage, and boarding strategy are common factors that affect TBT. However, besides operational efficiency, airlines are also concerned with customer satisfaction, which affects customer loyalty and financial return. One factor that influences passenger experience is the individual boarding time (IBT), here defined by the time passengers stand inside the cabin. Considering these two aspects, an agent-based model is presented that compares the performance of three alternative mainstream boarding strategies in a 132-seat and a 160-seat single-aisle commercial airplane. An important characteristic of the model that differentiates it from previous work is that overhead bins have a physical limitation, which could lead to an increase in aisle interferences on full flights as passengers take longer to find a place for their carry-on luggage. Another important contribution is the analysis of how passenger seat location affects IBT. Our results show that outside-in (OI) produces shorter TBT than random and back-to-front boarding, and also shorter IBT and much shorter maximum IBT than BTF, particularly for passengers seated in the middle of the airplane. This suggests that among the three most popular boarding strategies used by airlines across the world, OI is the best when it comes to balancing airplane boarding efficiency with individual customer satisfaction. 1. Introduction In 2022, airlines revenue reached US$ 727 billion, representing 87% of pre-pandemic levels [1]. As the industry continues its recovery, the aviation market is expected to grow annually by 3.3% and reach nearly 8 billion passenger trips per year by 2040 [2]. With this anticipated market growth, airport operations are expected to encounter more infrastructure challenges, such as traffic control or airport capacity constraints. Many airports around the world already face regular delays and crowding, primarily caused by air carrier delays, airplane late arrivals, and reactionary delays [3–5]. These delays not only contribute to airport congestion but also increase the workload of air traffic controllers [6]. As a result, airlines are under increasing pressure not only to improve operational efficiency, but also to maintain or enhance current levels of customer satisfaction. From the passenger’s perspective, overcrowding and delays are perceived as signs of poor service quality, which may lead to negative feedback and influence the airline choice [7]. ∗Corresponding author. E-mail address: [email protected] (S. Neumann). A key performance indicator used by airlines that is closely tied to revenue and customer satisfaction is the turnaround time. Turnaround time is defined as the time interval between the arrival of an airplane and its departure from the gate. During this time, several operations are performed, such as fueling, catering, boarding and deboarding of passengers and crew, as well as the airplane maintenance [8]. Since airline companies generate revenue only while flying, the shorter the turnaround time, the more revenue the airlines should be able to generate. Moreover, airlines must adhere to schedules set by air traffic control and the airport. It is estimated that each minute on the ground costs the airline between US$ 30 and US$ 250, depending on the type of airplane [9,10]. Boarding is a crucial activity that takes place during the turnaround time because it is one of the lengthiest procedures [11] and falls on the critical path of the turnaround [12], which means that a delay in boarding usually leads to a delay in the whole process. Additionally, boarding is highly variable, since it is very much influenced by https://doi.org/10.1016/j.orp.2024.100301 Received 9 November 2023; Received in revised form 5 April 2024; Accepted 6 April 2024 Operations Research Perspectives 12 (2024) 100301 2 B.H.P. Fabrin et al. the human factors involved. It significantly affects passengers’ experiences [13], which in turn influences their perception of the airline’s service quality [14]. Consequently, it is a key determinant of customer satisfaction or dissatisfaction [15]. The boarding process consists of passengers entering the airplane one at a time. They may or may not have luggage. Upon entering, the passenger proceeds to their assigned row, stores their luggage (if applicable) in the overhead bin, and then takes their assigned seat. In the process, the passenger may need to wait while others stand in the aisle to store luggage or resolve a seat interference. Seat interference occurs when a passenger cannot take their window or middle seat immediately because another passenger already seated in the same row (in the middle or aisle seat) must get up first [16]. Due to limited storage capacity, nearby overhead bins may be full by the time a passenger arrives at their assigned seat. As a result, they may have to move around to find an available space to stow their carry-on bag. Key factors that affect the airplane boarding process include the number of passengers on board, the airplane model (cabin layout), the type of flight (business or leisure), the presence of groups or families traveling together, the number of carry-on items on board, as well as passenger’s characteristics [17–22]. Variations in these factors can have a significant impact on total boarding time [23], which is considered the most critical measure of an airline’s boarding success. While infrastructure changes or the introduction of new technology – often expensive and time-consuming – are options for reducing total boarding time, a more immediate solution is to adopt more efficient boarding strategies. To date, the scientific literature on airplane boarding has focused primarily on reducing total boarding time by evaluating alternative boarding strategies. Several strategies have been proposed [17,24–29] that take into account factors such as passenger diversity [19,20,30,31], amount of luggage on board [32–36], groups traveling together [17, 26,33,35,37], and COVID-19-related social distancing [38,39]. The methodologies used in these studies have been diverse, including integer programming [36,40–42], pedestrian dynamics [43], discrete event simulation [44,45], machine learning [46], experimentation [47,48], physics and optics [31,49], cellular automata [50,51], and agent-based modeling [28,52–54]. Results so far have shown that no strategy is universally the most effective in terms of total boarding time across all possible boarding scenarios, although group boarding has consistently been shown to be slower than others [28,44,53,55,56], while some authors emphasize that random boarding performs poorly [57,58]. From an airline perspective, outside-in boarding is generally considered the most efficient strategy due to fewer interference events [55,57,58], despite being considered a group boarding strategy. As previously mentioned, fewer studies have focused on individual passenger metrics. Nevertheless, these studies have indicated that back-to-front boarding results in the longest individual boarding times (IBT) [20,28,44]. In practice, when an airline is selecting a boarding strategy to adopt, it must consider not only operational efficiency but also customer satisfaction. This aspect has so far received little attention from the scientific literature. A recent online survey of 1500 passengers found that while passengers value fast overall boarding times, getting to their seats quickly is even more important to them [59]. The modeling studies so far which considered individual passenger interest have indicated that back-to-front boarding strategy is the worst option because it results in the longest individual boarding times [20,28,44]. The present work proposes a spatially-explicit agent-based model (ABM) to compare the performance in a commercial airplane of alternative boarding strategies with respect to balancing airline revenue with customer satisfaction. Here three main-stream boarding strategies are compared: outside-in, back-to-front and random. The model represents single-aisle airplanes, like the B737 or A320, which may accommodate varying passenger capacities. Such airplanes are typically utilized for shortand medium-haul flights, in which boarding time is particularly critical compared to long-haul flights [16]. Here, the airline’s interest is assessed via measurements of the total boarding time (TBT), defined as the time interval from the first passenger entering the airplane to the last passenger sitting. Passenger preference for faster seating is assessed with two measures: individual boarding time (IBT), here defined as the time interval between a passenger entering the airplane and sitting, i.e., the total time walking or standing inside the airplane, and the maximum individual boarding time (MAXIBT) per boarding process. MAXIBT was included to allow for the assessment of the disproportionately large negative effect on an airline that a few extremely dissatisfied customers might impose, in terms for example of judicial problems or negative social media campaigning. In a real flight situation, the passenger demographics may change depending on the route. For example, air shuttle flights are typically flown by individuals who travel frequently and alone, and are therefore familiar with the boarding procedure. In contrast, tourist flights are largely made up of families or elderly passengers who may take longer to sit down. This study does not consider any particular type of flight and assumes that individuals travel alone, carrying or not a standardsized piece of luggage. Based on input from airline executives and information obtained from Boeing’s website [60], the overhead bins in the present simulation are modeled with limited capacity. In other words, there is insufficient space for every passenger to bring and store a piece of luggage on board. To the best of our knowledge, this aspect has not been addressed in scientific literature before. The usual approach involves increasing storage time in order to account for the number of bags passengers carry [18,33,44,61,62]. This makes the proposed model more realistic, as limited storage space may force some passengers to stow their luggage farther from their seats, causing aisle congestion. The main contribution of this work lies in the development and analysis of an agent-based model that differs from previous models in that it takes into account the physical limitation of overhead bins, and enables the comparison of the performance of alternative boarding strategies in terms of measures that reflect the interests of both airlines and passengers. In addition, this study examines how passenger seat locations affect individual boarding times, which is an important factor in customer satisfaction. The remainder of the paper is organized as follows: First, we describe the research problem and our model. In Section 3we present our simulation scenarios and the results. These are discussed in Section 4 before we conclude the paper in Section 5. 2. Research question and methodology This study addresses a fundamental question for aviation: among the most common boarding strategies employed today, which one should an airline adopt for a given specific flight in order to improve operational efficiency and customer satisfaction? This question is addressed for two large commercial airplanes, 132 and 160 passengers, taking into account constraints such as limited space for carry-on luggage along with factors such as the airplane’s passenger capacity, the quantity of carry-on items on board, passenger walking speed, as well as the time required to store luggage and resolve seat interferences. The agent-based modeling (ABM) approach was selected for investigating this question because it allows for the quantification of airline performance and customer satisfaction from observations of virtual passengers behaving similarly to real passengers boarding a virtual airplane to scale. The ABM approach offers numerous advantages relevant to the present study, including: (i) a high level of interaction between entities and their environment [63], (ii) some degree of unpredictability and uncertainty [64], and (iii) the ability for entities to adapt their behavior and decision-making processes [65]. These features allow for the visualization of emerging behaviors and patterns, enabling a more thorough investigation of complex real-world systems [66]. Operations Research Perspectives 12 (2024) 100301 3 B.H.P. Fabrin et al. Fig. 1. Example of a boarding simulation run. Arrows indicate the passengers and their facing directions; white cells represent open spaces where passengers can walk freely, such as aisles and legroom; brown cells represent seats in the economy class; gray cells represent seats in the business class; blue cells represent airplane internal structures; the green cell represents the door. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 2.1. The agent-based model The methodology adopted to build the simulation model follows the Overview, Design concepts and Details (ODD) protocol [67], which is frequently used for describing agent-based models (ABMs). The details are given next. The model was developed using Netlogo [68], an opensource programming software. For further information on the model, please refer to [69]. In the supplementary material, videos of the simulation are available. 2.1.1. Model purpose and patterns The general purpose of the spatially-explicit agent-based model (ABM) presented here is to compare the performance of alternative airplane boarding strategies in terms of balancing airline revenue and customer satisfaction. Its specific purpose is to compare the performance of random, back-to-front and outside-in boarding strategies in 132-passenger and 160-passenger airplanes with respect to (i) total boarding time (TBT), (ii) individual boarding time (IBT) and (iii) maximum individual boarding time (MAXIBT). 2.1.2. Entities, state variables and scales There are two types of entities in the model: (i) passengers, represented by mobile agents, and (ii) airplane structures, represented by stationary patches. The state variables of the passengers are: (i) the passenger’s walking speed (SPEED), (ii) the time needed to store their luggage in the overhead bin (TIMELUG), and (iii) the time needed to resolve a seat interference, also known as seat shuffle time (SHUFFLE). These variables have identical values for all passengers. There are two additional characteristics that vary for each agent: (i) seat location (SEATPATCH), and (ii) luggage possession upon entering the airplane (LUGGAGE?); these variables are both randomly assigned according to a Bernoulli process, and describe that each passenger has a final destination in the cabin, and may or may not have exactly one piece of carry-on luggage. The airplane model is based on a A320/B737 airplane cabin, which corresponds to a single-aisle layout of 3-3 seat configuration. A representation of the NetLogo interface is shown in Fig. 1. Some parameters defined by the user are: the maximum seat capacity (CAP), the number of rows reserved for business class passengers (BUSROWS), and the overhead bin capacity (BINCAPAC), defined as the maximum number of luggage pieces that a bin could hold per half-row. The time step in Netlogo is referred to as a ‘tick’ and is defined as 1/10 of a second (1 s = 10 ticks). Additionally, a patch in Netlogo, which corresponds to the unit area, is equivalent to 0.5 m ×0.5 m. Table 1 lists the main variables used in the simulation, as well as their descriptions and units. The flow rate (FLOWRATE) is defined here as a constant number of passengers entering the airplane door per minute, measured in pax/min. Our approximation to this rate is based on data from the literature [23]. Using the number of passengers and the times at which the first and last passengers boarded the airplane for each flight observation, it was possible to estimate an average flow rate for each occurrence. With the calculated flow rates, a regression curve Table 1 Entities and state variables used in the boarding process simulation. Entity State variable Unit Description Global CAP passenger Maximum seat capacity in the airplane PAX passenger Number of passengers OCC – Flight’s occupancy level LUGPERC % Percentage of passengers carrying luggage at the beginning of boarding process BUSROWS row Number of rows designated to business class SPEEDREDUCT – Walking speed reduction factor for passengers walking in counterflow BINCAPAC piece Number of luggage pieces that an overhead bin can hold per half-row STRATEGY – Entering order of passengers FLOWRATE pax/min Number of passenger entering the airplane door per minute based on occupancy level Passenger SPEED m/s Maximum passenger’s walking speed TIMELUG s Time needed to store luggage in the overhead bin by a passenger SHUFFLE s Time needed to solve a seat interference by a passenger LUGGAGE? boolean Defines if passenger carries luggage SEATPATCH patch Patch referring to seat location Airplane BINCUR pieces Current number of luggage pieces in a overhead bin above a seat of the flow rate versus expected flight’s occupancy level (OCC) was constructed (Fig. 2). The fixed value of flow rate used throughout the entire simulation is calculated at the beginning of each simulation run. However, and importantly, if there are passengers queuing close to the entrance door, for example because one or more are stowing their luggage, no new passengers will enter until there is free space. Thus, during the model run, the actual flow rate varies depending on local conditions. In real life, this rate is controlled at the boarding gate, where the agents check passengers’ tickets and IDs. Occupancy level is defined as the expected total number of passengers on the flight (PAX) over the seat capacity (CAP). For more information, please see [69]. Eq. (1) shows the function of the flow rate used in the model. 𝐹 𝐿𝑂𝑊 𝑅𝐴𝑇 𝐸(𝑂𝐶𝐶) = {16.797 − 9.015 ∗ 𝑂𝐶𝐶, if 0≤𝑂𝐶𝐶 ≤1 0,otherwise. (1) Operations Research Perspectives 12 (2024) 100301 4 B.H.P. Fabrin et al. Fig. 2. Flow rates in terms of flight’s occupancy level. The blue line represents the approximated regression function obtained and the black points are data from the observational study [12]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) The simulation produces the following outputs: (i) total boarding time (TBT), (ii) individual boarding time (IBT), and (iii) maximum individual boarding time (MAXIBT), as previously defined. All three variables are analyzed in this paper, but we give special focus to TBT and MAXIBT because we believe they are the most predominant when comparing airline and passenger interests around the boarding process. It is important to mention that in [59], IBT describes the entire time interval taken by a passenger from the moment he or she passes through the ticket check until he or she takes the assigned seat inside the cabin. However, since standing in the aisle of the airplane is the part of the boarding process that most bothers passengers [59], in the present paper, IBT only considers the time passengers wait standing in the cabin before taking their seats. 2.1.3. Process overview The model’s high-level algorithm proposed in this study is presented in Fig. 3. The simulation starts with an empty airplane with the defined characteristics. Then, the following actions take place: •At the beginning of the simulation, all passengers are generated, each being assigned to a random seat (SEATPATCH). Whether a passenger carries one piece of luggage or not is determined randomly according to a Bernoulli process. Then, all passengers are gathered and await their turn to board. •In accordance with the selected boarding strategy and expected flight occupancy, the first passenger boards the airplane following the flow rate (Eq. (1)). Each passenger proceeds to their seat without making any mistakes (the passenger does not get lost inside the cabin, for example). •Upon reaching their assigned row, the passenger carrying luggage checks the overhead bin of the same row and side where their seat is located. If there is space available, the passenger stands in the aisle for a certain period of time (herein TIMELUG) while stowing their luggage. During this time, other passengers cannot pass and must wait behind the person storing their luggage. •If, conversely, the passenger reaches their assigned row and verifies the overhead bin above their seat is full, they will immediately discover the location of the nearest empty overhead bin, assuming perfect information about its location, as if they saw it straight away or cabin crew members were assisting them. The passenger walks towards this nearest empty overhead bin, stores the luggage following the usual procedure, turns back towards their assigned seat and returns to it. •When a passenger without luggage reaches their assigned row, they check for seat interference; in positive case, the passenger stands in the aisle for another period of time (called SHUFFLE) while the interference is resolved, meanwhile blocking the way of others. •After resolving luggage storage and seat interference, the passenger is allowed to enter the row and to take their seat. •If all overhead bins in the cabin are full, a passenger that is carrying a piece of luggage drops it and moves directly towards their seat without any time penalty, as if airline employees were at the entrance of the airplane controlling the bin capacity and checking in bags before the passenger enters the airplane. •By default, passengers move along the cabin at maximum speed (SPEED). However, this speed can be adjusted. For example, if a passenger is standing in the aisle, the others must also stop and wait until this interference is resolved. If there is counterflow, i.e., two passengers passing each other in opposite directions in the aisle, SPEED is reduced by a factor given by SPEEDREDUCT for both passengers, until both have completed the passage. •The next passenger is allowed inside the cabin according to FLOWRATE, which specifies a uniform rate of passengers entering the airplane door per minute, and follows the same process as the previous passenger. This process is repeated iteratively until all passengers have boarded. •If the aisle is congested up to the door of the airplane, i.e., passengers are standing at the door and not moving forward, the passenger’s boarding will be interrupted until the congestion is cleared and space is available inside the cabin. Passenger boarding will then resume. •When all passengers are seated, the simulation ends. 2.1.4. Main model assumptions The main assumptions are: (i) passengers enter the airplane one at a time, so there are no families or groups traveling together, (ii) passengers board over the bridge and only through one door at the front of the airplane, (iii) every passenger has an assigned seat, (iv) passengers cannot overtake each other when moving in the same direction, i.e., if there is a slower passenger ahead, the next passenger Operations Research Perspectives 12 (2024) 100301 5 B.H.P. Fabrin et al. Fig. 3. Model’s high-level algorithm. All passengers move at a maximum speed (SPEED), which is reduced by a factor (SPEEDREDUCT) when two passengers are in counterflow. must follow behind, (v) passengers make no mistakes regarding path or seat location; there are no delays either, which means that all passengers follow the rules and come on board at their assigned time and with their group, (vi) all carry-on luggage have the same size and format, and each passenger may or may not have one piece of luggage, (vii) the space in the overhead bin is limited, meaning that it may be insufficient for all passengers to store one luggage piece, (viii) as long as there is space available, carry-on luggage is always stowed in the overhead bins; as soon as all bins are full, the remaining passengers carrying luggage leave it at the airplane door so that it is transported to the airplane’s trunk, (ix) passengers have perfect information, i.e., if looking for available space, passengers always know where the closest empty bin is, (x) business class is not considered and passengers can only take a seat at economy class. 2.1.5. Output verification The model has been thoroughly verified to ensure that it works as conceptually designed. The existing procedures in the code were verified by individually testing code parts to check functionality and to make it as simple as possible. Verification was also done visually, given the visual element of the coding software, by checking whether the overall behavior of the passengers reflected what was expected of them. 2.2. Output validation Simulation predictions were compared with results obtained from observations of real boarding processes in airplanes [23]. In this paper, the authors performed a statistical analysis of boarding times with respect to factors such as airplane capacity and number of luggage items on board. The data were collected by observing real boarding processes at a European airport. A total of 58 observations were obtained within several different airplane models and configurations. Considering only flights with occupancy above 50%, there are 13 observations for the 132-seat passenger airplane and six observations for the 160-seat passenger airplane, which are one of the largest data Operations Research Perspectives 12 (2024) 100301 6 B.H.P. Fabrin et al. Fig. 4. Total boarding time for a 132-seat passenger airplane at different levels of occupancy. Points in red correspond to occupancy observations in the literature [23], and points in black are results obtained in the present simulation. Black bars shows the interval including 95% of simulation points. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 2 Airplane models used for validation of the boarding process simulation [23]. Parameter A319 A320neo Maximum seat capacity 138 168 Maximum number of passengers 132 160 Number of business rows 3 4 Maximum number of passengers in economy class 120 144 Table 3 Nominal values of parameters used in the validation of the boarding process simulation. Parameter Value Source CAP 138 and 168 pax [23] OCC According to Hutter et al. (2019) [23] LUGPERC 75% [23] BUSROWS 3 and 4 rows [23] SPEED 0.5 m/s [70] TIMELUG 13.9 s [71] SPEEDREDUCT 0.1 SHUFFLE 10 s [71] BINCAPAC 2 pieces/half-row [60] STRATEGY random [23] sets available. In order to validate the simulation built in this paper, two airplanes with the same configuration as those considered in the literature were examined, as shown in Table 2. The data included flights with different numbers of passengers. In line with the adopted Ref. [23], business class seats were not considered in our simulation model because the boarding process only considered regular passengers, not including priority passengers. All observed boarding events used the random boarding strategy, which means that passengers did not follow any particular order and boarded on a first-come, first-served basis. Other parameter values used in our simulations are given in Table 3. Nominal values were taken from the literature and have not been calibrated. The simulations were run 1000 times for each instance, giving a total of 12,000 runs for the 132-seat passenger airplane and 5000 runs for the 160-seat passenger airplane to ensure statistical relevance, due to the randomness introduced by passengers boarding order and seat assignment. Each data point used for validation was selected based on the flight data with unique occupancy levels above 50%, resulting in 12 data points for the 132-seat passenger airplane and five data points for the 160-seat passenger airplane. Compared to real observations, the simulation results showed a tendency to speed up boarding (Figs. 4 and 5). To assess the agreement between the simulation results and the data points, we quantified how different the average of each analyzed case was from its respective observation. On average, the results for the 132passenger airplane differed by 17% and for the 160-passenger airplane by 16% from the observed data. Although the simulated results do not fully match the real data, a similar trend can be observed. Although our simulation results are in good agreement with the real data, because the sample is rather small we recommend the results herein to be interpreted with caution. Additional input data are available in the literature, such as flow rate [71,72] or walking speed [44,71,73]. Various validation scenarios for different values of walking speed (SPEED) were considered in order to investigate the impact of different parameter values on the results, as well as to showcase our model’s capability to produce results that are closer to reality (Figs. 6 and 7). Nonetheless, we opted for using as the nominal values for the simulations input data from sources that provided a well-documented description of their experimental data collection processes. 3. Simulation scenarios and results This section presents the results obtained from the simulated scenarios and the sensitivity analysis. The results in the main text refer to a 132-seat passenger airplane, while those for the 160-seat passenger airplane are presented in Appendix A. Each scenario was run 1000 times. The parameters used for this assessment are shown in Table 4. The data post-processing was performed in RStudio, using the R programming language. In order to do that, the output file generated by Netlogo was read into RStudio. Besides the standard RStudio builtin functions, the following libraries were used: (i) tidyverse and dplyr, for data manipulation, (ii) ggplot2 and ggpubr for plot creation, (iii) colorBlindness and viridis, for plot color manipulation, and (iv) FSA, for hypothesis testing. To compare distributions, non-parametric statistical tests were used, including: (i) the Wilcoxon test to compare two distributions, (ii) the Kruskal–Wallis test to determine if one of the analyzed distributions differed from the others, and (iii) Dunn’s test, to determine which of the non-parametric distributions differed from Operations Research Perspectives 12 (2024) 100301 7 B.H.P. Fabrin et al. Fig. 5. Total boarding time for a 160-seat passenger airplane at different levels of occupancy. Points in red correspond to occupancy observations in the literature [23], and points in black are results obtained in the present simulation. Black bars shows the interval including 95% of simulation points. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig. 6. Total boarding time for a 132-seat passenger airplane at different levels of occupancy and walking speed. Points in black correspond to occupancy observations in the literature [23]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 4 Nominal values of parameters used in the boarding process simulation. Parameter Value Source CAP 138 and 168 pax [23] OCC 100% Worst case scenario LUGPERC 75% [23] BUSROWS 3 and 4 rows [23] SPEED 0.5 m/s [70] TIMELUG 13.9 s [71] SPEEDREDUCT 0.1 SHUFFLE 10 s [71] BINCAPAC 2 pieces/half-row [60] STRATEGY random, back-to-front and outside-in [23] each other. The significance level was considered to be 5% (𝛼= 0.05). Local Sensitivity Analysis [74] was performed in order to evaluate how changes on a particular input affect a given output. It was carried out by applying small perturbations around nominal values of inputs, one-factor-at-a-time. 3.1. Simulated scenarios Following the verification and the validation stages of the simulation model, we explored various scenarios in order to investigate the effect of the boarding strategy on total boarding time and individual boarding time. Three different boarding strategies were examined: (i) random, (ii) back-to-front, and (iii) outside-in. These strategies were selected because they are among the most commonly used boarding strategies used by airlines today. Operations Research Perspectives 12 (2024) 100301 8 B.H.P. Fabrin et al. Fig. 7. Total boarding time for a 160-seat passenger airplane at different levels of occupancy and walking speed. Points in black correspond to occupancy observations in the literature [23]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig. 8. Total Boarding Time (TBT) in terms of boarding strategy on a 132-seat passenger airplane (RAND = random, BTF = back-to-front, OI = outside-in). Random boarding means that no specific order is used and passengers enter on a first-come-first-served basis. When back-to-front boarding strategy is adopted, it means that passengers are separated into three groups, and come on board in an order dependent on their seat locations: the passengers on the group that will board first have seats assigned to the back of the cabin; the next group of passengers have their seats in the middle of the cabin and, finally, the last group to enter the airplane are those passengers assigned to seats at the front of the cabin. Within each group, the order is random. When outsidein boarding strategy is used, passengers are also separated into three groups based on their seat locations; however, in this case, the groups are separated according to the seat locations relative to their proximity to the windows: the first group to board is the window seat group; then, the group of passengers assigned to middle seats; and, finally, the last group to come on board are those passengers assigned to aisle seats. Again, within each group, the order of passengers is random. For all these three strategies, passengers always enter through the front door of the airplane. 3.2. Simulation results Concerning total boarding time, random boarding was the slowest strategy, with the largest median time, followed by back-to-front and then outside-in (Fig. 8). A Dunn’s hypothesis test showed that the medians of all distributions differed (p-value <2.2e−16, 𝛼= 0.05), though by a small amount. Random boarding had a median of 978.85 s, while back-to-front and outside-in had practically the same result (960.07 s for back-to-front and 958.40 s for outside-in, with a difference of about 2 s between them). The averages of TBT for each strategy were: 961.37 s for outside-in, 972.25 s for back-to-front and 982.86 s for random. As the distributions are highly skewed, we decided to evaluate the results through the median because it is a centrality statistics, giving a more accurate interpretation. Also, results suggested that the outsidein strategy presented the smallest deviation (15.56 s in comparison to back-to-front’s 33.52 s) and the shortest upper tail among the three strategies. Operations Research Perspectives 12 (2024) 100301 15 B.H.P. Fabrin et al. Fig. A.17. Total Boarding Time (TBT) in terms of boarding strategy (STRATEGY) for a 160-seat passenger airplane (RAND = random, BTF = back-to-front, OI = outside-in). Fig. A.18. Maximum Individual Boarding Time (MAXIBT) in terms of boarding strategy (STRATEGY) for a 160-seat passenger airplane (RAND = random, BTF = back-to-front, OI = outside-in). Operations Research Perspectives 12 (2024) 100301 16 B.H.P. Fabrin et al. Fig. A.19. Individual Boarding Times (IBT) in terms of boarding strategy (STRATEGY) for a 160-seat passenger airplane (RAND = random, BTF = back-to-front, OI = outside-in). Fig. A.20. Individual Boarding Times (IBT) in seconds per seat for random boarding on a 160-seat passenger airplane. Operations Research Perspectives 12 (2024) 100301 17 B.H.P. Fabrin et al. Fig. A.21. Individual Boarding Times (IBT) in seconds per seat for back-to-front boarding on a 160-seat passenger airplane. Fig. A.22. Individual Boarding Times (IBT) in seconds per seat for outside-in boarding on a 160-seat passenger airplane. Operations Research Perspectives 12 (2024) 100301 18 B.H.P. Fabrin et al. References [1] IATA Economics. 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