AIRLINE CHOICE MODEL FOR AN INTERNATIONAL ROUND-TRIP FLIGHT CONSIDERING OUTBOUND AND RETURN FLIGHT SCHEDULES

This paper quantified the impact of outbound and return flight schedule preferences on airline choice for international trips. Several studies have used airline choice data to identify preferences and trade-offs of different air carrier service attributes, such as travel time, fare and flight schedule. However, estimation of the effect return flight schedules have on airline choice for an international round-trip flight has not yet been studied in detail. Therefore, this study introduces attributes related to return flight characteristics and round-trip flight schedule interaction into the airline choice models, which have not previously been reported in the literature. We developed a stated preference survey that includes roundtrip fares based on flight schedule combinations and the number of days prior to departure fares was purchased. We applied modelling techniques using a set of stated preference data. A mixed logit model was tested for the presence of heterogeneity in passengers' preferences. Our results indicated that models with attributes related to return flight and its interaction with outbound flight attributes have a superior fit compared with models only based on attributes reported in the literature review. The model found shows that airfare, travel time, arrival preference schedule in the outward journey, departure preference in the return journey and the schedule combination of round-trip flight are significantly affecting passenger choice behaviour in international round-trip flights. Sensitivity analysis of airline service characteristics and their marketing implications are conducted. The analysis reports seven policies with the greatest impact on each airline choice probabilities. It shows that by reducing travel time and airfare and by adopting an afternoon and night schedule preference for outbound and return flight, respectively, the highest probability on airline choice would be reached. This research contributes to the current literature by enhancing the understanding of how passengers choose airlines, considering both outbound and inbound journey characteristics. Thus, this study provides an analytical tool designed to provide a better understanding of international round-trip flight demand determinants and support carrier decisions.


Introduction
According to IATA's latest World Air Transport Statistics publication, North America is the main market to which air transport in Latin America is moving (IATA, 2019). This market transported during 2019 to 10,038,856 million passengers, implying a 1.60% growth compared to 2018 (ALTA, 2020). In fact, the Federal Aviation Administration (FAA) has predicted South America to be the fastest-growing region for commercial air transport over the next two decades. Colombia is the third best-connected country in Latin America behind Mexico, and Brazil and its air connectivity have increased by 34% in the last five years (World-Bank, 2019). This represents a substantial growth performance, broadly in line with the world average over the same period. Colombia, with its advantageous geographical location and its potential to act as a regional centre stands out as a very important network of international connections. To which can be added the fact that Medellin is the Latin America centre for the fourth industrial revolution, making it a particularly attractive destination. International air transportation has undergone substantial changes in the last decade, one of which has been the increased number of airlines offering commercial flights. This growth in numbers of air carriers has led to an increase in competition among them. Thus, airlines must develop effective marketing and operating strategies that can meet travellers' needs. This raises the need to understand what influences passengers to fly with one air carrier versus others. However, the choices air travellers make for international round-trip flights are complex and involve varying decisions related to the two journeys. Balobaba, Odoni and Barnhart (2015) defined the typical air trip as consisting of two steps: an outbound air trip and an inbound air trip. Therefore, passenger choices for a round-trip flight should be based on the outward and return journey characteristics to a better reality understanding. Although many studies have estimated the factors that influence a round-trip flight preferences (Freund-  Theis et al., 2006), most have focussed on outbound flight attributes. Thus, to fill the research gap, this study introduces attributes related to return flight characteristics and round-trip flight schedule interaction into the airline choice models, which have not previously been reported in the literature. This study intends to ascertain what influences the process of deciding which air carrier to fly. To attain this objective, we analyse the most important route connecting the United States and Colombia, which is currently served by four airlines: Avianca, Viva Air, American Airlines and Copa Airlines. All airlines offer non-stop flights except for Copa Airlines, which only has one-stop flights. A stated preference (SP) experiment was conducted to analyse passenger choice behaviour with respect to an international round-trip. The SP experiment considered six attributes: round-trip fare, travel time, flight frequency, arrival schedule preference at the destination and departure schedule preference from the destination on the return flight. The main goal here is to develop airline choice models that enable air carriers to identify traveller preferences on international round-trip flights. Multinomial logit (MNL) and mixed logit (ML) models were used to identify important explanatory variables affecting airline choice. These models measure travellers' trade-offs among roundtrip fare levels, travel time, schedule convenience offered by outbound flight and return flight. Sensitivity analysis was calculated from the estimated coefficients of the airline choice models. These estimations provide valuable insights into how best to develop strategies. This study contributes to the current literature by improving the understanding of how travellers choose airlines, considering both outbound and inbound journey characteristics. Thus, this research provides an analytical tool designed to provide a better understanding of round-trip flight demand determinants and support carrier decisions on operating, pricing, yield management, and marketing strategies.  Zhang (2012) and Wen, Chen and Fu (2014) examined the relationship between schedule delay and passenger's choice behaviour. They defined schedule delay as the difference between preferred and actual departure time of flight. Their results indicated that air travellers are willing to pay a high amount to have a preferred departure time. Based on the literature review of air round-trip flights, airline attributes were based only on outbound flight characteristics. To fill up this gap, we integrated attributes related to return flight characteristics and attributes related to the interaction between outbound and return flight variables. Thus, the aim research is to find a model with a better Goodness-of-Fit in comparison to the models that not consider round-trip attributes. In other words, this is the first study to consider the outbound and inbound flight schedules preference in an airline choice. The above studies indicate the importance of including airline attributes, passenger characteristics and trip experience variables into the airline choice models. Therefore, in this study, we show how a roundtrip fare, trip duration, departure and arrival schedule attributes affect the passenger choice behaviour in an international round-trip flight.

Model structure
Several studies have researched traveller choice behaviour, many of which have applied discrete choice models to obtain useful information on how travellers select trip alternatives. Previous air travel choice behaviour studies have been based on random utility theory (Domencich and McFadden, 1975) and various discrete choice models have been developed. MNL models have the simplest structure and are the most used model formulation for travel choice. Nested logit (NL) models are complex and allow correlation between different alternatives. Flexible ML models allow the capture of heterogeneity, which is referred to as differences between consumers. The ML model uses a random parameter specification to explain unobserved heterogeneity across travellers and solves the MNL and NL models' main limitations. Discrete choice models are often used in the air transportation market to analyse airline marketing problems. This study adopts the random utility theory, which represents the theoretical basis of discrete choice modelling, to assess choice behaviour for four airline alternatives (Avianca, American Airlines, Viva Air and Copa Airlines). The random utility theory is an econometric instrument for empirical estimation of the demand function (Domencich and McFadden, 1975). The discrete choice model measures the attractiveness of each airline based on a utility function consisting of two components: a systematic component observed by the researcher and a random error component that includes unobservable effects. Thus, the utility function of airline i for passenger q can be expressed as: Where Viq is equal to the representative or systematic utility and εiq represents the error component for airline i and passenger q. The random utility function, Viq, depends on airline i's observable attributes and the socioeconomic characteristics of a passenger q. Viq can be expressed by a linear equation that includes parameter vector k (e.g., airfare, travel time, arrival time, departure time, age, education level and gender) The random utility function, Viq, depends on airline observable attributes, trip experience variables and the socioeconomic characteristics of a passenger q. Viq can be expressed by a linear equation: Where are parameters related to outbound flight attributes ( ) (e.g., travel time, arrival schedule, flight frequency).
are parameters related to return flight attributes ( ) (e.g., departure schedule, flight frequency).
are parameters associated with attributes related to the interaction between outbound and return flight variables ( ) (e.g., round-trip fare, flight schedules interaction).
are parameters related to travellers characteristics ( ) (e.g. age, education level). ℎ are parameters related to trip experience attributes ( ℎ) (e.g. membership in FFP, trip purpose). The assessment of and parameters are the contribution of this research that had not been covered by other studies within this field. Coefficient vectors , , , , ℎ can be estimated using maximum likelihood methods. Given equations (1) and (2), the probability that passenger q chooses alternative i can be expressed as: Piq depends on the distribution on the random vector of error terms. The MNL model is the simplest random utility model and assumes that errors of the utilities are independent and identically follow Gumbel distributions, with a mean of zero and a scale of one (which implies a variance of π2/6) (Domencich and McFadden, 1975). Under those assumptions, the probability that alternative i will be chosen is given by:  Train, 2000) that should be set by specifying a random distribution defined by the mean and standard deviation. Thus, the utility of airline i for passenger q can be expressed as: where: ′ : random parameters that vary over air passengers : vector of observed variables of airline i for passenger q : independent and identically distributed as Gumbel ′ varies over passengers in the population with the continuous probability density ( / ), where θ characterises density with mean and variance parameters. The unconditional probability of passenger q choosing airline i can thus be expressed as (Train, 2009): Train (2009) also indicated that ML probability does not have a closed-form and can thus be approximated using simulation methods.

Empirical investigation
We examine choice behaviour on the route from Medellin (MDE) to Miami (MIA), which is one of the most important routes connecting Colombia with an international destination. The MDE-MIA-MDE round-trip is currently served by The MDE-MIA-MDE round-trip flight is currently served by three full-service carriers: Avianca (AVA), American Airlines (AAL), and Copa Airlines (CMP) and one lowcost carrier: Viva Air (VVC). We chose this route based on three criteria. First, the Colombia to Miami route has the most passengers carried per year on in-ternational flights in the Colombian air market. Second, both cities are served by a low-cost airline. Additionally, the MDE-MIA route is the only non-stop flight route served by VVC. Third, VVC and AAL have the highest numbers of passengers carried between MDE and MIA yearly compared to other journeys from Colombia to MIA. Table 1 shows some passenger flow values. This route is particularly relevant because VVC, AVA, AAL and CMP compete over it by providing passengers with options regarding airfares, travel time, frequencies, departure and arrival schedules and other attributes. Our interest focuses on analysing the main factors passengers consider when buying a ticket for an MDE-MIA round-trip.

Variables and levels
We identified factors that air travellers consider when deciding which airline to choose using two steps. First, we reviewed previous airline choice behaviour studies to identify pertinent attributes for our research. Second, we conducted qualitative research using focus groups. We selected two focus groups representing frequent fliers, travel agents, academics, airline and airport managers and government officials who helped define airline attributes that could be analysed. This research conducted an SP experiment to examine traveller preferences. The experiment involved four alternatives. The first airline was VVC, which is a low-cost carrier. The second carrier was AVA, which represents the dominant domestic and international air carrier in Colombia. The third and fourth alternatives were AAL and CMP, respectively, and they only cover international flights to and from Colombia. The attributes used in the experiment are round-trip fare (FARE), travel time (TTIME), flight frequencies (FREQ), arrival schedule from MDE to MIA and departure schedule from MIA to MDE. Table 2 shows the set of attributes and levels used in the choice experiment. FARE and FREQ were determined so the values would be like current air carrier operations. By basing on the days prior to departure day, we calculated mean fares for each airline and for each schedule combination and these were set to be the median level. Seelhorst   The orthogonal design allows all attributes to be uncorrelated and attribute levels to be balanced. However, an efficient design method has been used to minimise standard errors in recent years. An efficient design disadvantage is the need for prior knowledge of estimated parameters. This makes the experimental design sensitive to a misspecification of previous parameters. Choosing an orthogonal design reflects our preference for statistical independence over efficiency. A full factorial design for four airlines described by five attributes, each of which is further described by three attribute levels, produces 3 4x5 possible combinations. An orthogonal fractional factorial design was applied to reduce the huge number of combinations into a manageable size using NGENE software (ChoiceMetrics, 2014). The smallest possible experimental design consists of 64 treatment combinations. Four scenarios were identified as dominant options. Furthermore, a block design was used to split the remaining 60 scenarios into 10 subsets to limit respondent burden, thus each respondent needed to assess only six randomly assigned subsets. A pilot study of 60 members was performed prior to full administration of the survey to detect potential problems regarding factors such as questionnaire length, respondent fatigue and survey clarity.

Data
This section describes the process used to obtain the data and assesses our analysis database's representativeness. Cochran (1977) developed the following expression to calculate the sample size for an infinite population where n is the sample size, p is the estimated proportion of an attribute present in the population, q is calculated as 1-p and z represents the z-value that accumulates a probability in the standard normal distribution of α/2, where (1-α) x 100% is the confidence level. In this research, the population is assumed to be a large population with an unknown degree of variability. We assumed the extreme case, where p and q are both 0.5 and taking 95% as the confidence level with ±5% precision. Thus, the sample size (n) is 384. In our research, we decided to conduct at least 480 surveys (n + 96) because of the probability of inconsistent or missing data. In order to draw a representative sample of all air passengers and reflect the real airline usage pattern for the MDE-MIA journey, quota sampling was necessary for the surveys. Table 3 is based on relative frequencies of airlines market share and the sample size found by equation 7. The total sample was stratified by sample size in each category, as shown in Table 3. Therefore, the data employed in this study may be representative of the population of customers in the MDE-MIA journey.

Data collection
Surveys were performed face-to-face since the scientific literature indicates that this sampling method delivers better results in terms of representativeness (Szolnoki and Hoffmann, 2013). Data were collected at MDE airport, near the international flight boarding gate. Passengers who travelled to MIA airport were asked to fill out the questionnaire. All MDE-MIA flights over October and November 2018 were sampled. Passengers who were travelling as part of tourist packages were excluded as they would not be aware of the air travel portion of their cost.
The questionnaire consisted of four sections. In the first section, travellers were asked about socioeconomic characteristics, such as age, gender, individual monthly income, education level and employment status. The second section collected information on traveller experience, including air trip frequency, journeys taken over the last year by each airline, membership in FFP, airline chosen for the last international flight and airline chosen for the last domestic flight. In the third section, passengers were asked about their current trip, including the airline chosen for the MDE-MIA-MDE trip, the number of connections, airfare paid, trip purpose, the number of people flying together, who paid the trip and ticket payment method. In the last section, prior to the SP experiment, passengers were asked about preferred arrival and departure schedules (to and from MIA) and the number of days prior departure that the flights were booked. These questions provided information needed to assign travellers to a specific type of questionnaire related to schedule combinations and airfare. Respondents conducted six SP games in which each respondent chose one alternative among four air carriers. Fig 3 shows an example of the choice card presented to the respondents.

Data description
The travellers interviewed yielded 480 valid responses.

Model estimation and empirical results
Multivariate outlier detection is an important task in statistical analysis. A classical approach for detecting outliers in a multivariate framework is Mahalanobis distance (MD). We used MD to find the outliers in the sample using SPSS software (Pérez, 2004). The MD score for each subject is considered an outlier if it exceeds a critical value. The probability level set for this test was p < 0.01. The MD method was applied to illustrate multiple outliers. The dataset for international flights contained 480 respondents, with only seven outliers identified using the MD (p < 0.01). Therefore, the new sample size for modelling was 473 respondents.
To explore choice behaviour, we applied the MNL (equations (1) to (4)) and ML (equations (5) and (6)) models. The dataset contained 2838 observations. Estimation was performed using BIOGEME software and numerous specifications were tested. We identified that FREQ was not significantly different from zero at the 0.1 level in the first estimations. Therefore, we used the log-transform for FREQ. The log-transform has been widely used by Seelhorst and Liu (2015), Hess, Adler and Polak (2007), Theis et al. (2006) and Hess and Polak, (2005), suggesting that a non-linear transformations approach leads to significant model performance improvements.
To verify the presence of endogeneity, we implemented a two-stage least squares instrumental variable model (Greene, 2003). First, we used a diagnostic test to verify that the Hausman-type instrument is valid. The result of the ordinary least squares regression for the Hausman instrument indicates that the parameter associated with the airfare instrument is significantly different from zero at a 95% confidence level. Finally, we tested the null hypothesis that airfare is an exogenous regressor using the t-statistic associated with the residual. The result was not significant at the 0.05 level, thus the null hypothesis was not rejected, indicating that airfare should not be treated as endogenous. Therefore, endogeneity was not present in our model. Table 5 lists the results of the MNL and ML models. The MNL_1 and ML_1 models do not include both return flight attributes ( ) and attributes related to the interaction between outbound and return flight variables ( ). The final versions of MNL and ML include all parameters set out in equation (2). Additionally, the panel effect was taken into account given that responses of the same individual to an SP survey may be correlated, thus it is necessary to include an additional term for panel effect (Cantillo, Ortúzar and Williams, 2007).

MNL model results
As expected for models in Table 5, the coefficient estimates for TTIME, FARE, ARR and DEP had negative signs. Travel time is considered a fundamental factor in both transport modelling and economic appraisal (Juhász, Mátrai and Koren, 2017). The model shows that the t-value was the highest (tvalue = −20.55) for TTIME in the MNL_final model, indicating that this attribute has the highest statistical significance in the model and that higher TTIME values would reduce the probability of choosing an airline. FARE also has a negative relationship with airline utility. Based on statistical significance levels, FARE was the next most significant attribute in the model. ARR has the expected negative effect on airline utility and was significantly different from zero at the 5% significance level. Furthermore, we found that DEP for the return flight is a significant driver in airline choice; however, this effect is smaller in magnitude than ARR. Several observations can be made from the results of schedule difference variables in Table 5. First, as expected, passengers prefer itineraries that get them to their destination close to their preferred time of arrival. Second, travellers were primarily concerned about ARR rather than DEP. Third, schedule time differences coefficients in both models indicate that when the time difference increases, the utility of travellers decreases. This is intuitive as passengers are likely to have more schedule constraints if they have short stays, and in our research the stay was for two weeks on average. In addition, in our model, schedule time differences did not differentiate between early and late.
The analyses of previous models revealed that the log-transformed frequency's coefficient is positive, meaning that the probability of travellers choosing an airline increases when FREQ increases; however, the log-transformed frequency was not significantly different from zero at the 10% significance level for MNL and ML models. This may simply be due to the fact that travellers choose flight schedules rather than frequencies. Previous studies have shown FFP membership having strong effects on airline choice (Wu and So, 2018); Hossain, Saqib and Haq, 2018; Seelhorst and Liu, 2015; Park, 2010; Proussaloglou and Koppelman, 1999). This finding is reinforced in the current research. The FFP membership coefficient is both highly significant and positive, indicating that travellers prefer flying with an airline with which they have FFP membership. In terms of travel purpose, the coefficient was also positive, indicating that respondents on business trips have a higher probability of choosing AAL, AVA or VVC airlines. The reason may relate to CMP airline currently not offering non-stop flights from MDE to MIA. Freund-Feinstein and Bekhor (2017) stated that business travellers are willing to pay more for nonstop flights. As indicated earlier, travellers were asked about their arrival and departure schedule preferences, and the MNL_final and ML_final models show a positive impact of MA, AN and NM schedule interactions on airline utility. MA schedule interactions preference significantly affect AAL, AVA and VVC airline choice, whereas the AN interaction preference significantly affects CMP and VVC airline choice. Table 5 indicates the statistical significance of DEP and flight schedule combinations in the models with return flight attributes. We applied the likelihood ratio test to compare the models shown in Table 5. The MNL_1 and MNL_final models can be formally tested by using the likelihood ratio test that is expressed as (Ben-Akiva and Lerman, 1985): The test value is -2(-3299.457 3282.558)=33.798, which is substantially larger than χ2 value with four degrees of freedom at any reasonable level of significance. Thus, the null hypothesis that departure flight schedule preference for the return flight and the schedule interactions do not play a role in airline choice can be strongly rejected.

ML model results
After estimating MNL models both without and with return flight attributes and flight schedule combinations, random coefficients were considered based on travel time and airfare. The final specifications of the ML model were based on eliminating statistically insignificant variables. Functional forms were tested, including linear effects, dummy variable effects and logarithmic transform effects for FREQ. In the first models, the standard deviation of FREQ, ARR and DEP were not significant, whereas the other variables had significant standard deviations. The final ML specification was selected based on statistical fit.

Sensitivity analysis
This research used ML model results to conduct a sensitivity analysis considering the impacts of TTIME, schedule combinations, travel purpose and FFP membership. A case strategy scenario is determined by multiplying the appropriate βk from Table  5 by each attribute's value. This represents the deterministic portion of the utility function (Vi) (Ortúzar and Willumsen, 2011). The results obtained produce overall choice probability for any given value. The ML model considers random coefficients; therefore, market shares are computed by simulating the distribution of random coefficients. Table 6 reports the change in market shares concerning different travel times, as well as the assessment of different schedule combinations considering if travellers are business passengers with or without FFP membership. For all individuals, the values of TTIME, FARE, ARR and DEP were based on the choice experiment. If passengers are for business purposes, travellers book tickets three weeks before the trip on average. Therefore, airfare for this kind of passenger was based on a booking time of three weeks for each schedule combination. The base scenario when travellers are business passengers reported in Table 6 shows that CMP currently offers one-stop flights (6 hours), whereas AVA, AAL and VVC all have non-stop flights (3.5 hours). Table 6 also shows that airline choice probabilities are influenced by TTIME. In fact, shifting TTIME to the best attribute level (non-stop flight) could produce an increase of 12% (18%-6%) in CMP airline choice probability. This probability increase is achieved for travellers having an FFP membership and preferring to fly in AN schedule combinations (case 3 and case 4).

Discussion
In this research, we investigated the effects of schedule combinations on airline choice using MNL and ML models. The ML model results indicated that MA could produce the highest choice probability for AVA; whereas for AAL, NM schedule interaction increases its choice probability. For VVC and CMP, AN schedule combinations increase their choice probabilities. Hence, offering an FFP membership, non-stop flights and MA, NM and AN schedule combinations are the most effective strategies to increase market share. The ML model results also showed that ARR and DEP have negative and significant impacts on the utility of airlines. We also identified that ARR and DEP have similar effects on the utility of airlines for international trips. We determined that random heterogeneity exists for TTIME and FARE. Like previous study of round-trips by Theis et al. (2006), the analysis presented in this research has highlighted the important role airfare plays in airline choice. The results from this SP study have shown TTIME to be the variable with the most explanatory power for an international roundtrip flight. The analysis also revealed significant effects in response to FFP. ML model results indicate that FFP membership is a strong driver of airline choice. We can conclude that we do find evidence that some travellers who have FFP membership with at least one air carrier tend to place little focus on FFP membership when choosing airlines. Therefore, airline marketing managers should carefully design benefits provided by FFP membership, as an efficiently developed FFP membership might improve competitive advantage by retaining loyal travellers, which becomes a source of steady revenue.

Conclusion
This study contributes to the literature by introducing the effect of schedule preferences on airline choice for a round-trip flight. Return flight schedule preference had not been covered by other studies within this field. Problems with departure schedule preferences in the return flights could be mitigated if an airline could increase flight frequency to reduce the difference between preferred and offered departure times and thus improve passenger welfare. This paper discussed the findings of research making use of innovative survey design for understanding air passenger travel choice behaviour. In the survey design, airfare for the international round-trip flight was the result of fare combinations depending on schedule interactions and number of days prior to departure day flights was booked. This design improves realism on how people handle airline choice context for round-trip travel. The model results clearly demonstrate the importance of arrival and departure schedules as well as schedule combinations. In addition, our study's results indicated passenger preference for flying non-stop. In keeping with this, air carriers could design alternative travel arrangements using the proposed model to improve travellers' perception and not affect their loyalty. The strategy implications deriving from this research can be distinguished in two main categories: one general and one specific to the case study analysed. The study conducted reveals that, in general, one cannot a priori assume that similar policies will produce similar effects in different airlines. With specific reference to the four air carriers studied one can say that the most relevant strategy attributes influencing choice probabilities are TTIME, FARE, ARR, DEP and schedule preference combinations. The results reported in this paper can be extended and improved by acquiring detailed information concerning travellers satisfaction with airline service quality in order to increase model explanatory power.