Designing Airline Hub-and-Spoke Network and Fleet Size by a Biobjective Model Based on Passenger Preferences and Value of Time

. Tis study presents a biobjective hub-and-spoke (HS) network design model for the global air passenger networks. Te model explores the tradeof between the total airline cost (airline preference) and lost time cost for passengers (user preference) as the model’s objectives. Most previous studies have focused on airline objectives and established HS networks based on the viewpoint of airlines, despite the importance of passenger objectives. Poor passenger service and inconvenience and dissatisfaction may lead to network breakdown. Te major criteria for passenger dissatisfaction in HS networks are schedule and trip delays caused by nondirect fights. Tese delays (the lost time cost for passengers) are multiplied by the passengers’ value of time (VOT) and minimized as one of the model’s objectives. Another objective that is minimized is the transportation costs of the airline depending on the services provided (short-, medium, and large-haul fights). Te model is solved in a case study (Iranian Aeronautics Network) that is applied to the well-known yearbook of tourism statistics data. Pareto frontier was found for all candidate airports. Also, the number of aircraft required (short-, medium, and large-haul), as well as the average load factor for diferent types of aircraft in various weights of the frst objective (airline costs), was presented. Te results of Pareto frontier indicated that Imam Khomeini International Airport should be selected as the global hub airport for Iran international fight network. Otherwise, Shiraz International Airport and Tabriz International Airport (as the frst alternative), as well as Isfahan International Airport and Mashhad International Airport (as the second alternative), would be the best choices. Te weight of the frst objective (airline costs) seems to be between 0.7 to 1, a practical and logical weight that can reduce passenger costs (as the second objective) by 20% on average by adding only 15 long-haul, 40 medium-haul, and 37 short-haul aircraft to the airline’s feet. Also, in this range, the average load factor for medium-and long-haul aircrafts is greater than 0.9, which seems to be ideal.


Introduction
Hub-and-spoke (HS) confguration is extensively used in airline and airport industries, emergency services, post delivery services, rapid delivery packing systems, telecommunication services, message delivery networks, and transportation networks [1].Te reasons for the growing use of HS confguration in transportation networks are as follows.First, HS networks, particularly in road and rail transportation, shorten the established links to fully connected networks, reducing fxed established costs [1].Te second reason is the economic scale of the fow of cost between hub nodes and even between nonhub and hub nodes so that with increased fow density, the costs decline [2].Te third beneft is related to resource management.For transportation networks with limited resources, HS confguration can provide service to more nodes with greater efciency compared to a fully connected network [3].In addition to the benefts, this system sufers from drawbacks such as increased travel time of users, sensitivity to congestion in hub nodes and links, and sensitivity to network disruptions [4].
In an air transportation network, HS confguration can save airline operational costs and increase the system capacity [5].In this type of network, due to the use of indirect connections, fewer fights, on-service aircraft, and crew staf are needed [3].However, if users' preferences (e.g., delay, travel time, fare, and service frequency) are overlooked in designing the network by an airline, the system utility deteriorates and the airline sustains irrevocable damages [6,7].
Delays in airline operations impose billions of dollars in additional costs to airlines, passengers, and the economy [8].According to the NEXTOR study conducted by the University of California, Berkeley's Institute of Transportation Studies reported that in 2007, the US economy has incurred a $32.9 billion loss due to fight delays across the US airspace system.Te US Federal Aviation Administration sponsored a report on the analysis of a variety of cost components induced by fight delays, including expenses incurred by airlines and passengers, as well as costs of lost demand and the indirect impact of delays on the US economy.According to this study, the direct cost of fight delays is $28.9 billion more than half of which is borne by passengers.Te cost of passenger time lost due to airline and passenger schedule bufers, delayed fights, fight cancellations, and missed connections was estimated at $16.7 billion.Te NEXTOR study estimated that air transportation delays shrank the US GDP by $4 billion in 2007 [9].
In addition to the fnancial losses resulting from the delays, fight delays on a route reduce passenger demand and raise airfares, wreaking havoc on both consumer (passenger) and producer (airline) welfare [10,11].Terefore, airlines strive to diminish delays in decisions by taking various strategies.As airlines need to reduce delays at all levels of decision-making, it is a good idea to prioritize delays in longterm decisions.Terefore, this research addresses tactical decisions (feet planning) and strategic decisions (hub Locating) together.
Hence, in a real-world application, the system (airline) and users' (passengers) preferences should be taken into account when designing HS networks [12].Aside from hub location, feet planning is another strategic decision whereby the airline can design its future feet (the number and type of aircraft needed) for servicing demand over long periods [13].Hub location without feet planning (i.e., feet size and diversity determination) can raise airline operational costs due to inappropriate allocation of aircraft to fight legs (e.g., long-haul aircraft on short-fight legs) and investment costs related to the purchase or rent of new aircraft to meet network demand [14].Terefore, to enhance the performance of HS networks and reduce an airline's operational and investment costs, hub location and feet planning should be simultaneously optimized.
Tis study proposes a biobjective uncapacitated single allocation p-hub median problem integrated with a feet planning problem to satisfy the preferences of the system and users at the same time.Te frst objective function minimizes the airline's operational costs while the second objective decreases the passengers' lost time costs attributed to passenger delays.In the latter, two types of delay, planning delay and delay caused by the time diference between HS network and direct fight, as the most ideal travel type, are used.Te hub location and feet planning are performed simultaneously where fight frequencies and aircraft types are determined for the fight legs.One of the best methods for modelling such an approach is the biobjective model, which can consider both objective functions (airline costs and passenger costs) simultaneously.Also, to fnd the optimal solution, two objective functions can be converted into a single-objective function using the weight-sum method, and then it can be solved exactly and the optimal solution is obtained.

Literature Review
Tere are two aspects of the literature covered below.In Section 2.1, hub location problems (HLPs) are reviewed in the context of air transportation, and in Section 2.2, multiobjective HLPs are classifed in terms of their objective functions and compared to the current research.

HLP in the Aviation
Industry.In this section, HLPs in the aviation industry are reviewed based on three main elements of HS networks: hub airport, passengers, and airlines.
2.1.1.Hub Airport.Some researchers studied HLPs by accounting for specifc characteristics of hub airports such as hub capacity, hub congestion, and disruption in hubs.Yang and Chiu proposed a two-stage stochastic HS network design model by considering seasonal demand variations and hub congestion efects [15].Te capacity of hub airports was investigated in the HLPs proposed by Mohri et al. and Yang [16,17].Mohri et al. measured the capacity of hub airports by drawing an envelope curve on daily inbound and outbound fight statistics [16].Teymourian et al. proposed a novel model for a virtual hub-routing problem.A virtual hub is a predetermined replacement satellite node that can act as the main hub under certain situations to compensate for the service disruption in the main hub [18].

Passengers.
Here, research on variations of the passenger demand matrix and its impact on designing hub airports' locations are investigated.Carmona-Benítez et al. proposed an econometric dynamic model for estimating passenger demand in the airline industry, which was subsequently used for locating hub airports [19].Kawasaki explored the efects of scheduling in a monopoly airline market for hub location and their efect on demand and the trafc of passengers traveling between two cities [20].Yang presented a stochastic HLP under seasonal demand variations [21].
2.1.3.Airlines.Competition, merging, or alliance of airlines are some characteristics of HLPs related to airlines.Martıń and Román proposed the HLP as a spatial competition game that is played in two phases.Te hub location is selected sequentially in the frst phase while the competitive strategies are utilized in the second phase of the game [5].Eiselt and Marianov studied the efect of competition between two 2 Journal of Advanced Transportation airlines in an HLP, where the passengers' utility function of airlines was estimated according to the fying duration and ticket price [22].Te efect of code-share alliance agreements on designing HS networks was studied by Wen and Hsu [23].Wang et al. included feet size and allocation of various types of aircraft to air routes in an HS network.For the objective function, the net beneft of the feet was maximized by accounting for the least feet purchasing cost of six types of aircraft [24].Hsu and Wen investigated the efect of various aircraft types of diverse capacities on maximizing the benefts of code-share alliance agreements for airlines using an interactive biobjective model [7].Wei and Hansen looked into the efect of aircraft size and airline service frequency on minimizing airline operational costs in an HLP [25].Sina Mohri et al. designed a hub network for an airline or a group of airlines to cover international fights between countries considering the feet size and diversity on a global scale [26].Table 1 summarizes recent HLP studies in the aviation industry based on the scope of their research.

Multiobjective HLP. Tis section reviews multiobjective
HLPs.Various researchers have minimized the total operational and fxed costs as the cost objective function [12,[27][28][29][30][31][32][33].Some researchers only minimized operational costs [6,[34][35][36]; however, some previous research decreased operational and fxed costs using two separate objective functions [35].Tis study contributes to the literature by integrating feet planning and hub location decisions in a strategic problem.Hence, this is the frst study to investigate the minimization of total operational costs and feet planning costs (i.e., aircraft purchasing costs) as an objective function.
Other objectives investigated in HLPs are mostly related to time (i.e., service time in hubs or travel time in the network) or the number of intermediate stops in trips.Tese objectives can account for customer satisfaction in designing HS networks.As Table 2 shows, fve diferent types of objectives have been explored in the literature, minimizing the total service time in hubs [27,30,33,35,37], minimizing the maximum service time in hubs [27,34,37], minimizing the maximum travel time between origin and destination (OD) pairs [28,31,32,38], minimizing the total travel time between OD pairs [29], and minimizing the total number of intermediate stops [12].Table 2 outlines the objectives of the previous studies.As Table 2 indicates, operational or/and fxed costs are usually minimized as one of the HLP's objective functions.
Tis study looks into a new time-related objective refecting the passengers' satisfaction with the hub services.It minimizes the subtraction of total travel time in the hub network from total travel time in a direct point-to-point network, where the passengers' value of time (VOT) and the schedule delay in hubs are also investigated.VOT is important because passengers with high VOT are more sensitive to the quality of services, such as service time in hubs and travel time in routes.Hence, if an airline provides services with a high delay time in hubs or on routes, these passengers are more likely to receive services from other airlines, which consequently contracts the airline market share.

Problem Definition and Formulation
Tis study presents a biobjective uncapacitated single allocation HLP for a global air passenger network to satisfy passengers' preferences.Te proposed objective functions include: (a) minimizing the airline costs, including transportation costs and expenses of purchasing aircraft, and (b) minimizing costs incurred by the passengers due to the delay in routing and the use of HS network.In the designed global HS network, passengers on OD pairs may be scheduled for an indirect fight with an intermediate stop in a hub airport.
To estimate the costs incurred by the passengers, the passengers' VOT in each OD pair is also considered.Te model aims to fnd the optimal HS network confguration and the optimal feet size, where the aircraft type, load factor, and fight frequency for servicing network fows are determined.

Mathematical Formulation.
Before introducing the model, the mathematical notations, including sets and indices, input parameters, and decision variables, are presented in Tables 3-5.
Te proposed mathematical model is a mixed integer nonlinear model that is converted into a mixed integer linear model by the linearization of nonlinear terms.Te initial mixed integer nonlinear model is as follows: Journal of Advanced Transportation

Airport
Yang and Chiu [15] Air trafc congestion in hub airports Mohri et al. [16] Te real capacity of hub airports using envelope curves Teymourian et al. [18] Predetermining an alternative hub in the disruption situation Passengers Carmona-Benítez et al. [19] Estimation of passenger demand using an econometric dynamic model Kawasaki [20] Scheduling efect on the demand side and the number of passengers Yang [21] Hub location and fight route planning under seasonal demand variations Airlines Martin and Román [5] Airline's HLP through a spatial competition game in two phases Eiselt and Marianov [22] Te efect of competition between two airlines in an HLP Wen and Hsu [23] Te efect of code-share alliance agreements on designing HS networks Wang et al. [24] Maximizing the net benefts through feet size and feet assignment Hsu and Wen [7] Maximizing the benefts through code-share alliance agreements for airlines Wei and Hansen [25] Minimizing airline operational costs through feet planning and airline service frequency Sina Mohri et al. [26] Fleet planning to locate optimal global hubs 4 Journal of Advanced Transportation   Set of airports with hub potential Parameter Description Cost of purchasing an aircraft of type s ($) q s Maximum seat capacity of an aircraft of type s (passenger) VOT of passengers planning to travel from i to j ($) Desirable frequency from i to j to remain competitive c s Maximum fight hours of an aircraft of type s n ′ s Number of aircrafts of type s that is currently owned by the airline M, M ′ A large positive number (it is set in the model as 2 × size(N)) T Desired time horizon: 24(hours/day) × 365(days/year) � 8760(hours/year) Objective 1 (O 1 ) minimizes the total operational cost of the airline, which is comprised of three terms.Te frst and second terms denote routing operational costs from origins to hubs and from hubs to destinations, respectively.Te third term indicates the cost of purchasing new aircrafts.Objective 2 (O 2 ), which minimizes the total delay imposed on passengers, includes two terms.Te frst term represents the on-route delay caused by taking an indirect fight with a stop in a hub airport as opposed to a direct fight.It is calculated from the diference between the direct trip time and HS trip time multiplied by the number of passengers and their VOTs.Te second term represents the waiting time of passengers in the hub airport to receive service, which is called scheduling delay (SD).Also, passengers' VOTs are multiplied by SD.
Equation ( 3) ensures that only one hub node in the network is selected.Equations ( 4) and ( 5) ensure that nodes i and j can only be allocated to the located hub airport.
Equations ( 6) and ( 7) guarantee passenger fow in the hub-and-spoke network.Equation ( 6) ensures that the passenger fow is established from all origins to the hub and equation (7) ensures that the passenger fows are maintained from the hub to all destinations.
Equations ( 8)-( 11) represent a range restriction.According to equations ( 8) and ( 9), short-haul and mediumhaul aircrafts are not allowed to service long-fight legs, and based on equations ( 10) and ( 11), short-haul aircrafts are not authorized to service medium-fight legs.
Equation ( 12) calculates the frequency of fights departing from origin i and arriving at hub k, and equation ( 13) computes the frequency of fights departing from hub k and arriving at destination j.In the selected hub airport for each OD pair (e.g., i to j), SD is estimated by equation ( 14), which is commonly used for SD estimation in the literature [7,[39][40][41].Equation ( 15) makes sure the frequency of fights departing from each origin node is suitable and competitive.In this relation, F ij is the biggest fight frequency between i and j ofered by the other airlines.
Equation ( 16) accounts for the number of short-haul, medium-haul, and large-haul aircrafts in the designed hub networks.Equation ( 17) also determines the number of new aircrafts that must be purchased.
Finally, the variation range and type of decision variables are specifed by equations ( 18)- (20).
Equation ( 14) is nonlinear.Te values of SD ij ∀i, j are illustrated in Figure 1(a).Using piecewise-linear programming, the values of the equation are approximated by two linear functions represented by Equation ( 21) as illustrated in Figure 1(b).

Journal of Advanced Transportation
According to equations ( 22) and ( 23), if 24) and (25) ensure that the value of SD ij is equal to − 122f j arrival + 1340, which refects the frst if-then condition in (21).Also, if Y � 0, equations ( 26) and (27) ensure that the value of SD ij is equal to − 0.57f j arrival + 81, which indicates the second if-then condition in equation ( 21).

Converting the Biobjective Function into the Single-Objective Function.
To solve the biobjective model, the normalized weight-sum method is used to convert the biobjective model into a single-objective model [42][43][44].Accordingly, objectives (1) and ( 2) are replaced by equation (29). where

Case Study and Model Set-Up
To test this biobjective model, a real-world case study is conducted for the international fight network of Iran.Te objective is to expand Iranian airlines' operational span in the Middle East and increase their market share by designing an optimal HS network and feet.Hence, we seek to locate the optimal hub airport in Iran and design the optimal feet for the leading Iranian airline.Given that the Iranian airline is deemed as a newcomer and its services should be highly competitive, it needs to consider a competitive frequency for its fights and assess customer satisfaction by minimizing delay.Accordingly, the necessary data (i.e., input parameters) for the above model is prepared in the following.

(i) OD fow matrix
To form OD matrix (h ij ), the historical passenger fights originating from/destined to 30 diferent world countries are studied.Tese 30 countries have had the highest passenger trafc to/from Iran.Apart from Iran which has fve nominated airports in OD matrix, other countries only have one nominated airport, and therefore, |N| � 34.Te countries considered in the demand matrix and their airports are shown in Figure 2 and their details are tabulated in Table 6 [45].OD fow matrix is designed for 2025.Te volume of OD fows (h ij ) in these matrices are projected by equations ( 30) and ( 31) based on 2015 tourism data 8 Journal of Advanced Transportation [45] and the gross domestic product (GDP) of the 34 countries between 2000 to 2019.
where  the aircraft size [48].As for the maintenance check, check A is due after 65 fight hours, check B is required between 300-600 fight hours, and checks C and D are conducted yearly [49,50].According to the 2014 to 2018 statistics taken from MIT's Airline Data Project, which was carried out for USA airline companies, the longest average daily block hour utilization for long-, medium-, and short-haul aircrafts were 13.02, 14.78, and 13.91 hours, respectively.Terefore, in this study, the maximum fight hours (c s ) would be 4800, 5400, and 5000 hours per year for short-, medium-, and long-haul aircrafts, respectively.(vi) Maximum seating capacity of s-haul aircrafts One of main features of an aircraft is its maximum seating capacity, which is variable between aircrafts.In this study, the average maximum seating capacity (q s ) for short-, medium-, and long-haul aircrafts is estimated as 80, 150, and 300 seats, respectively [51,52] In this study, VOT is estimated using the production-based method according to equation (32) [53].
where GDP m is the gross domestic product of country m, A m is the average working hours per year in country m, which is estimated at 2920 hours for all countries, and P m is the average number of people employed in the country m.GDP m and P m Figure 4 shows VOT m ∀m ∈ M, which is equal to In this study, three discredited levels are considered for the load factor: maximum, half, and minimum.Hence, the ρ l volume is equal to 1, 0.5, and 0.1 when l is set to its maximum, half, and minimum values, respectively.Table 7 outlines the initial values for the models' parameters.

. Result and Discussion
In the model, the Imam Khomeini International Airport in Tehran was selected as the hub airport in all Pareto solutions.However, a sensitivity analysis was conducted to calculate the values of model's objectives when another nominated airport (e.g., Isfahan International Airport, Mashhad International Airport, Tabriz International Airport, and Shiraz International Airport) is selected as the hub airport.Given that there are 11 scenarios for the weighting system in which w 1 varies from 0.0 to 1.0 by an incremental step of 0.1, and 5 scenarios for the location of international airport, the model is solved for 55 scenarios.Te raw output data obtained from solving the model is outlined in Table 8. Figure 5 demonstrates the Pareto fronts when each of the fve nominated airports is selected as the hub airport.
As Figure 5 shows, the Pareto fronts of Shiraz International Airport and Tabriz International Airport are identical.Hence, they can be selected as the frst alternative hub airport for Imam Khomeini International Airport by the government.Also, since the Pareto fronts of Isfahan International Airport and Mashhad International Airport are identical, these airports could be introduced as the second alternative hub airport for Imam Khomeini International Airport.Te Pareto front for Imam Khomeini International Airport is approximated with several linear functions to demonstrate the percentage by which passenger costs (the second objective) will drop for a percent increase in the optimal value of the airline costs (Z * 1 ).Equation ( 33) represents the Pareto front as a multisegment function.
where (zZ 1 /zZ 2 ) is the percentage of changes in variable Z 1 for one percent of changes in variable Z 2 , (∆Z 1 /Z * 1 ) is the range of variations in variable Z 1 , and R 2 is the coefcient of determination.
According to the results, more than 6.8% movement from the optimal solution for the airline costs will cause an insignifcant improvement in the frst objective.Hence, the optimal distance from the optimal solution for the airline costs should be between 0% and 6.8%.Tis distance will improve passenger costs by nearly 15 percent.
In the optimal solution, when Imam Khomeini International Airport is selected as the hub airport, the following numbers of aircrafts are required, as shown in Figure 6.As the fgure shows, with a decrease in the weight of the frst objective (airline costs), the total number of short-, medium-, and long-haul aircrafts increases.Hence, if the airline intends to decrease passenger costs, it should raise the number of aircrafts in its feet but this growth is not uniform and keeps fuctuating.If the diagrams of this fgure are combined with the optimal passenger costs in the Pareto front of Imam Khomeini International Airport, the increased number of feets can be divided into three ranges.In the frst range, where the weight is between 0.7 and 1, the feet expansion seems justifable, so that the addition of 15 long-haul, 40 medium-haul, and 37 short-haul aircrafts on average will reduce passenger costs by 20 percent.Tis growth feet expansion is practicable and logical for the airline due to passenger convenience and satisfaction.In the second range, which covers 0.5 to 0.7 weight of the frst objective (w1), there is a signifcant increase in the number of feets, particularly in medium and long aircraft.Accordingly, adding 300 long-haul, 260 medium-haul, and 50 short-haul aircrafts on average would cut passenger costs by 50 percent.In the third range, where 0 ≤ w 1 ≤ 0.5, the passenger's objective function has a greater weight, the feet is expanded signifcantly, and there will be 568 longhaul, 370 medium-haul, and 67 short-haul aircrafts y = 2.76E+09e -1.42E-11x R 2 = 9.71E-01 y = 2.92E+09e -1.36E-11x R 2 = 9.77E-01 y = 2.94E+09e -1.39E-11x R 2 = 9.80E-01 y = 3.13E+09e -1.30E-11x R 2 = 9.90E-01 y = 3.28E+09e -   14 Journal of Advanced Transportation approximately.It is clear that the second and the third ranges do not present an appropriate choice for the airline due to the large number of feets imposed on the airline.In addition, the number of short-haul aircrafts has a low tolerance between 37 and 67 on average; therefore, the airlines are advised to avoid huge investments in purchasing short-haul aircrafts.
As shown in the Figure 7, in all alternative hubs (the frst and second alternatives), long-haul aircrafts surpass the number of medium-haul aircrafts and the medium-haul aircrafts outnumber the short-haul aircrafts.Also, the diagram of long-haul aircrafts encloses that of medium-haul aircrafts and the same rule applies to the diagram of medium-haul and short-haul aircrafts.In addition, the number of long-haul aircrafts does not vary by changing alternative hubs (especially in the frst alternative hub where the maximum number of long-haul aircrafts is about 800).Also, by increasing the weight of the frst objective, the number of long-haul aircrafts would take a gradual downturn but the number of short-haul aircrafts, dependent on the alternative hub, follows a particular pattern in the alternative hub.
Another major characteristic of the obtained Pareto solutions is the average load factor for short-, medium-, and long-haul aircrafts as shown in Figure 8.
As shown in Figure 8, by decreasing the weight of the frst objective (airline costs), the average load factors of diferent types of aircrafts drop.It suggests that should the

16
Journal of Advanced Transportation airline decides to prioritize optimization of the second objective (passenger costs) over the frst objective (airline costs), it needs to decrease the aircraft load factor due to the increase in the number of aircraft's empty seats.Tis reduction can be categorized into three ranges.In the frst range, when 0.7 ≤ w 1 ≤ 1, the average load factor for longand medium-haul aircrafts is larger than 0.9.Also, for shorthaul aircrafts, the average load factor is greater than 0.6.In the second range, where the weight of the frst objective (w1) is between 0.5 to 0.7, the average load factor for long-, medium-, and short-haul aircrafts is 0.6, 0.6, and 0.4, respectively.In the third range, where 0.5 ≤ w 1 ≤ 0, the average load factor for all three types of aircrafts drops to 0.4.As the fgure shows, the declining average of load factors for longand medium-haul aircrafts is gradual while the load factor of short-haul aircrafts tolerance is approximately between 0.6 and 0.4.In addition, the second and third ranges are not economical for the airline due to the number of the aircraft's empty seats (40% to 60% capacity) though it can save 50 to 80 percent of passenger costs (the second objective).Hence, the airlines are recommended to avoid setting the weight of the frst objective to less than 0.7.
Moreover, as Figure 9 shows, in all alternative hubs, by increasing the weight of the frst objective (airline costs), the load factor surges for long-and medium-haul aircrafts.As demonstrated by Figures 7 and 9, increasing the weight of the frst objective (airline costs) will reduce the total number of medium-and long-haul aircrafts, which will lead to a high load factor (in all of the alternative hubs, where 0.8 ≤ w 1 ≤ 1, medium-and long-haul aircrafts are approximately at full capacity).Also, the diagrams of load factor of long-and medium-haul aircrafts have identical patterns (especially for Shiraz, Tabriz, and Mashhad international airports), but it is not the case for short-haul aircrafts even if the weight of the frst objective is high.For example, in Isfahan international airport, where w 1 � 1, the maximum load factor of shorthaul aircraft is 0.8.Journal of Advanced Transportation

Conclusion
Tis study proposed a biobjective hub network design model to design global air passenger networks.Poor passenger service, inconvenience, and dissatisfaction may lead to network breakdown.Hence, this study adopted a usersystem approach to design global air passenger networks wherein two conficting objectives of the users and the system (i.e., passenger costs and airline costs) are optimized.Te passenger cost is a function of scheduling delay and time delay in the designed hub network.Te airline cost is also a function of routing costs for diferent types of aircrafts and the cost of purchasing new aircrafts of various types.In this study, as a case study, the model was solved for a leading Iran international fight network to identify the optimal HS network and feet in order to expand its operational span in the Middle East region and increase its market share.Solving the model and evaluating the results yielded the following insights: (i) Imam Khomeini International Airport should be selected as the global hub airport for Iran international fight network.Otherwise, the best alternatives would be Shiraz International Airport and Tabriz International Airport.(ii) Distancing up to 6.8% from the optimal solution for airline costs will signifcantly reduce passenger costs (nearly 15%).(iii) Giving priority to the optimization of passenger costs over airline costs will increase the frequency of fights with medium and low load factors in HS network.In this regard, the results suggested that to reduce the number of fights with a low load factor, the airline costs should be twice as important as the passenger costs.
Tis study had a number of limitations that could be addressed in future research.First, here, the tourist dataset was used to identify the fight demand between countries.Future studies can explore other means of data collection, such as fight statistics released by leading international airlines.Second, the model's parameters (e.g., demand as well as travel cost and time) are deterministic but uncertain in nature.Terefore, it is recommended that future research addresses this uncertainty.As another suggestion, incorporating the probability and consequences of disruptions in HS modelling approach can provide a robust HS network that is protected against unforeseen disasters.It should be noted that the proposed model is a singleperiod HS network design; hence, further research can be performed on its development into a multiperiod HS network design model.Moreover, statistical analysis can be incorporated into the proposed approaches [54][55][56].Also, various machine learning methods and optimization algorithms are also recommended for further investigation in future research [57][58][59][60].
w 1 and w 2 are weighting coefcients for the model's objectives, which are determined by the intrinsic knowledge of the decision maker (w 1 + w 2 � 1)solutions for the frst and second objective functions, respectively.Te mathematical model is solved using the commercial software GAMS/ Cplex.

Figure 1 :
Figure 1: SD function: (a) SD function and (b) approximation of SD function by two linear functions.

Figure 2 :
Figure 2: Locations of airports in Iran international fight network.

Figure 5 :
Figure 5: Comparison of Pareto fronts when diferent locations are selected as the hub airport.

Figure 6 :
Figure 6: Number of aircrafts of diferent types in each Pareto solution (Imam Khomeini International Airport).

Figure 7 :
Figure 7: Number of aircrafts of diferent types in each Pareto solution for (a) frst alternative and (b) second alternative.

Figure 8 :Figure 9 :
Figure 8: Average load factor for diferent types of aircrafts in each Pareto solution (Imam Khomeini International Airport).

Figure 9 :
Figure 9: Average load factor for diferent types of aircrafts in each Pareto solution for (a) frst alternative and (b) second alternative.
Short-haul Medium-haul Long-haul Short-haul Medium-haul Long-haul Short-haul Medium-haul Long-haul Short-haul Medium-haul Long-haul Short-haul Medium-haul Long-haulNumber of feets

Table 1 :
Summary of HLP recent studies in the aviation industry.

Table 2 :
Multiobjective hub location models in recent studies.

Table 3 :
Sets and indices.
k Binary variable, if X k � 1, then node k is a hub; otherwise, X k � 0Z ls ik Number of fights performed by an aircraft of type s with the load factor l from nonhub i to hub k Z ′ ls kj Number of fights performed by an aircraft of type s with the load factor l from hub k to nonhub j n s Number of aircrafts of type s available in the airline's feet ij is a growth factor for volumes of OD fows in 2015, which is used to calculate the volumes of OD fows in 2025.GDP2015 (check A, B, C, and D), weather conditions, and the number of airline pilots lead to delays in aircraft fights, thereby limiting the number of real aircraft fight hours during the year.Te average return time may vary from 30 to 60 minutes depending on

Table 7 :
Initial values of the model's parameters.
Travel time from i to j (t ij ) (hour) A matrix Load factor volume for index (ρ l ) (no dimension) Full Capacity ρ l � 1, Half − capacity ρ l � 0.5, minimum capacity ρ l � 0.1 Desired time horizon (T) (hour/year) 8760

Table 6 :
International airports in OD fow matrices.

Table 8 :
Raw outputs obtained from solving the model for 55 scenarios.

Table 9
indicates a summary results of the average load factor and the number of aircrafts of diferent types (shorthaul, medium-haul, and long-haul) in each Pareto solution for 55 scenarios related to 5 candidate airports (Imam Khomeini International Airport, Shiraz International Airport, Tabriz International Airport, Isfahan International Airport, and Mashhad International Airport).

Table 9 :
Summary of the numerical results related to the number of feets and average load factor.