A Robust, Multi-Criteria Customer Satisfaction Analysis Framework for Airline Service Provider Evaluation

Abstract

This research introduces a novel framework that allows the comparative evaluation of airlines based on passengers’ flight experiences. The proposed framework combines a typical and a simulation-based extension of the AHP in a group decision-making environment to elicit rankings of various airlines. The first option (T-AHP) generates rankings by combining individual passengers’ preferences using the geometric mean synthesis rule. The second option (S-AHP) simulates the stochastic characteristics of the responses, aiming to handle the inherent uncertainty and the variety of preferences obtained by the customers. The rankings are derived by mapping the decision space according to the evaluation criteria implemented and passengers’ preference dimensions. The proposed options are illustrated through a case study where four airlines are evaluated using 51 satisfaction dimensions (sub-criteria). Although the derived results indicate similar rankings, those obtained by the S-AHP option are more stable and robust, with greater discriminatory capacity compared to those of its typical counterpart (T-AHP).

1. Introduction

In the current turbulent times, airlines struggle to respond to the barriers of various global factors, such as the COVID-19 pandemic and the recent dramatic increase in fuel prices. Airlines have long realized that the provision of high-quality services is one of the few battles that is almost solely in their hands and can be used as their main weapon against the competition [1,2], since it significantly affects passengers’ attitudes, behaviors [3,4], satisfaction [4,5,6] and, in the long run, loyalty—a significant parameter of service effectiveness for the airline industry [3,7,8] and market share [9]. Therefore, it is crucial for their survival, as airlines need to be able not only to understand the factors that contribute to customers’ satisfaction but to also realign their strategies in order to increase their passenger numbers and long-term profitability [10]. Quality is a rather confusing term that is usually interpreted in various ways, based on the conceptual context in which it is addressed. Further, service quality refers to the difference (positive or negative) that exists between customers’ initial expectations and their perception of the actual service they received [11]. As far as the aviation industry is concerned, service quality refers to all the interactions (before, during and after the flight) between the airline and its customers, which will shape customers’ perceptions (overall experience) and enhance the image of the carrier [12].

Previous comparative studies have confirmed that passengers flying with a FSC (full-service carrier) are generally more satisfied (with the services they receive) than passengers traveling with a LCC (low-cost carrier) [13]. Although this is an expected finding, it is important to understand the factors that contribute to this result. In particular, Chen and Chang [14], investigating the differences in the factors affecting passengers’ choice between a Chinese FSC and LCC, found that the provided service was not an important factor for those passengers who chose LCCs, in contrast to those choosing FSCs. Further, Jiang and Zhang [15] also focused on the Chinese aviation sector (they analyzed four Chinese airlines), studying the links between service quality, customer satisfaction and confidence in the airlines. They concluded that, although service quality indeed affects customers’ satisfaction, this is not always accompanied by greater confidence. Actually, for LCCs, “service quality may not be a good indicator for predicting customer loyalty” [16]. Furthermore, in contrast to ticket pricing, FSCs fell short of expectations. Actually, there was a significant difference in the perception of value for money between passengers of FSCs and LCCs [17,18]. Thus, although low traveling cost offered by LCCs might be a crucial parameter affecting the selection of these carriers by a considerable number of customers [19], as it was expected, most LCCs’ passengers select their flight also on the basis that these airlines have a high safety reputation [19,20,21].

In addition, Rajaguru [11], using the means–end chain theory and the price sensitivity theory, compared the quality of services to the money that passengers of FSCs and LCCs had paid, and confirmed the sensitivity of LCC passengers to the value-for-money factor. This is also suggested by Shen and Yahya [22] who claim that FSC passengers are less price-sensitive. Further, Han et al. [23] found that although lounge facilities are affecting the selection of an airline, luxury lounges are considered necessary for passengers flying with an FSC, in contrast to the anticipation of LCC passengers. Similarly, although tangibles and in-flight service quality are important for FSC passengers [24], the expectations of LCC passengers for the same services are rather low [25]. This is actually the main reason why LCCs pay less attention to these factors [24]. However, it seems that given the post-flight service offered by FSCs, the frequent-flyer program—which provides to its members a number of benefits and discounts—makes up lost ground against LCCs [26] and increase passengers’ loyalty [27]. Finally, there are empirical studies which have found that significant differences do exist between FSCs and LCCs in all the pre-, in-, and post-flight services offered [28]. However, passengers’ intentions in traveling with either FSCs or LCCs are not directly affected by value for money and/or service quality, “but they are mediated through the chronological path of customer satisfaction and airline image” [18,22]. It should be stressed, though, that the impact of satisfaction on image and behavioral intention is higher in LCCs [18].

When it comes to multiple-criteria decision analysis (MCDA) methods, Tsaur et al. [29] introduced a hybrid Fuzzy AHP-TOPSIS to deal with imprecise evaluator knowledge, using 15 evaluation criteria in order to evaluate the performance of three airlines. In the same direction, Liou and Chuang [30] integrated a Fuzzy AHP-Fuzzy Rating option to evaluate the performance of eight airlines incorporating the responses of 446 passengers. The group extension of the typical AHP has been implemented by Singh [31] to obtain the ranking of three candidate airlines considering 23 evaluation criteria. The 171 responses to an AHP standard-type questionnaire were combined in terms of geometric mean to generate single pairwise comparison matrices. In the same line, Budimčević et al. [32] integrated the responses of 200 customers to evaluate three airlines. A hybrid Fuzzy AHP-TOPSIS model was also utilized by Bae et al. [33] to rank ten airlines according to their performance in financial and operational ratios. Finally, without specifying the passenger sample interviewed, nor the method for combining their preferences, Al Awadh [34] evaluated three airlines using twenty-two evaluation criteria.

In this research, the problem of customer satisfaction in the airline industry is also treated as a Group Multi-Criteria Decision-Making (GMCDM) problem using the Analytic Hierarchy Process (AHP) method. AHP has been selected among other well-established MCDM methods due to its capacity to address a/problem formation, b/criterion weight elicitation and alternative standardization in a unified environment and c/its ability to sufficiently assist integration with simulation options. AHP is used to combine passengers’ opinions and perceptions of various evaluation criteria to produce satisfaction indices (SIs) that allow airlines to be ranked. The decision framework developed allows the transformation of standard questionnaire survey responses into relative judgments and examines two AHP options. For the first typical AHP (T-AHP), pairwise comparison matrices are obtained using the geometric mean of passenger responses and a single rank is obtained without further investigation of the stochastic decision environment. In the second option, local weights are established using Monte Carlo simulation (S-AHP), where multiple rounds of AHP estimation are performed according to the stochastic characteristics of the derived responses. In this way, S-AHP identifies possible decision outcomes and generates various indices that support coherent decision-making in stochastic environments by examining the stability and the robustness of the rankings obtained with respect to the simulation trials. Both T-AHP and S-AHP are implemented in a real case study, supported by a questionnaire survey conducted at the two main international airports in Greece, and passengers were asked to indicate their preferences at arrival. The analysis performed and the results discussed in detail identify the S-AHP option as more efficient in terms of the quality of rankings generated and its ability to provide decision-makers with significant insights into the performance of candidate airlines.

2. Materials and Methods

2.1. Analytic Hierarchy Process

The proposed methodological framework addresses the problem of airline provider evaluation as a multi-criteria decision-making framework based on passengers’ judgments according to their recent traveling experience. For that reason, the Analytic Hierarchy Process (AHP) [35] has been utilized due to its ability to estimate absolute preference measurements (priorities) using ratio judgment scales. In that manner, AHP is capable of allowing the evaluation of specific alternatives using both tangible and intangible attributes [36].

The hierarchical structure of the decision problem is of significant value as it allows consistent comparative evaluation of the decision elements since they belong to the same level of importance. Using decision hierarchies, AHP is capable of estimating local weights ($w_i$) by comparing their elements in pairs (criteria, sub-criteria and alternatives). In detail, this is achieved by forming pairwise comparison matrices $B_{ij}={\left[b_{ij}\right]}_{n\times n}$ to evaluate the child elements of the hierarchy with respect to their importance in satisfying their parent element. Each position of the $B_{ij}$ facilitates the importance $b_{ij}$ of the row element $i^{th}$ when compared with the element of the $j^{th}$ column. Although evaluations are performed using linguistic variables, the AHP fundamental scale of preferences assigns a numeric value to each one of them using the odd values in the range 1–9, where 1 denotes equal importance and 9 extremely strong importance, respectively. Additionally, the intermediate values denote moderate ($b_{ij}=3$), strong ($b_{ij}=5$) and very strong ($b_{ij}=7$) importance [37]. As a result, pairwise comparison matrices are positive and reciprocals to their diagonal since $b_{ii}=1$ and $b_{ji}=1/b_{ij}$. Then, local weights can be obtained by solving the system of Equation (2). According to AHP, a single solution exists when the criteria weight vector equals the principal eigenvector of pairwise comparisons matrix ($egen\left(B_{ij}\right)$). Various options exist to estimate the eigen vector of $B_{ij}$. Among them, the option of the row average normalized by the sum of the columns (Equation (2)) is the most popular principally due to its simplicity [38].

Local weights provide the importance of the decision elements with respect to their parent node satisfaction. To obtain the importance for the goal of the analysis, local weights of the child nodes are weighted with the local weights of their parent nodes for each one of the hierarchy’s branches using Equation (3). Since the hierarchies developed do not have the same number of levels for every criterion examined, $W_{c\in C}$ denotes the elements sited in the last position of each one of the hierarchy’s branches (Figure 1) and form the evaluation criteria set $C$ of the analysis. Their number $c$, along with the alternatives number $m$, defines the dimension of the multi-criteria decision matrix.

$${\left[b_{ij}\right]}_{n\times n}\times {\left[w_i\right]}_{n\times 1}={\lambda }_{max}\times {\left[w_i\right]}_{n\times 1}$$

(1)

$$w_i=egen\left(B_{ij}\right)={\displaystyle \frac{\sum _{j=1}^n{b}_{ij}/{\sum }_{i=1}^n{b}_{ij}}{n}}$$

(2)

$$W_{c\in C}=w_i\times w_{i,j}\times \dots \times w_{i,j,\dots ,c}$$

(3)

When the transition property holds, Equation (4) is validated for every one of the elements of the pairwise comparison matrix $B_{ij}$. In such cases, $A_{ij}$ is perfectly consistent and the eigenvalue ${\lambda }_{max}$ equals the dimension $n$ of the $B_{ij}$. Thus, their normalized difference (Equation (5)) provides a measurement that indicates the existence of inconsistent judgments, named consistency index (CI). Consistency ratio (CR) provides a normalized expression of CI (Equation (6)) taking into consideration $A_{ij}$ dimension by dividing CI with the random inconsistency ratio (RI) provided in relation to $n$. An overall average $\overline{CR}$ for the decision problem can be estimated by dividing the weighted average $\overline{CI}$ by the corresponding weighted average $\overline{RI}$ (Equation (7)) [39]. Although AHP adopts different acceptable CR levels, based on the $B_{ij}$ size, the generic rule of $CR,\overline{CR}<10\%$ is widely implemented [40].

$$b_{ij}=b_{ir}\times b_{rj}$$

(4)

$$CI={\displaystyle \frac{{\lambda }_{max}-n}{n-1}}$$

(5)

$$CR={\displaystyle \frac{CI}{RI}}$$

(6)

$$\overline{CR}={\displaystyle \frac{\overline{CI}}{\overline{RI}}}={\displaystyle \frac{\sum _{c=1}^C{w}_{c-1}\times {CI}_c}{\sum _{c=1}^C{w}_{c-1}\times {RI}_c}}$$

(7)

$$S_a=\sum _{\forall c\in C}{W}_c\times x_{ac}^s$$

(8)

$$x_{ac}^s={\displaystyle \frac{x_{ac}}{\sum _{a=1}^m{x}_{ac}}}$$

(9)

$$x_{ac}^s={\displaystyle \frac{1/x_{ac}}{\sum _{a=1}^{m}1/x_{ac}}}$$

(10)

$$S_a=\sum _{\forall c\in C}{W}_c\times r_{ta}^c$$

(11)

In AHP, the per-criterion performances are combined using the weighted linear combination as a decision rule. For an alternative $a\in A$ that belongs to the set of feasible alternatives $A$, the weighted sum of their standardized performances is obtained allowing address selection, sorting and ranking decision-making problematics [41]. For quantitative criteria, conventionally AHP is implemented using pairwise comparisons matrices, where alternatives are evaluated according to their importance for each one of the evaluation criterion $c$. Additionally, for quantitative criteria, AHP uses the percentage score by dividing the individual performances by their sum [42]. In detail, for $m$ evaluation alternatives, Equations (9) and (10) provide the standardized performance for ascending and descending criterion types, respectively [43]. In that manner, the standardized performance occurs as a relative measurement since it is estimated in relation to the performances of every considered alternative. However, this approach should be considered for closed decision-making environments where the set of alternatives is considered fixed and no other alternatives are expected to be considered in the future. On the other hand, the ratings normalization option is adopted in open systems where the set of examined alternatives is subject to change [44]. Using ratings, a scale of preference intensity levels ($t$) is introduced and every alternative is allocated a level of intensity according to DMs’ preferences. Consequently, the predefined value $r_t$ is assigned to the alternative. To ensure commensurability, a single scale should be adopted for all the analysis evaluation criteria. In accordance with Equation (8), the overall performance of an alternative $a$ is obtained using Equation (11), where $r_{at}^c$ denotes the rating value $r_t$ assigned to $a$ because it is rated at the $t^{th}$ intensity level when evaluated for the $c^{th}$ criterion.

2.2. Proposed Framework

Commonly, customer satisfaction evaluation studies are implemented by conducting questionnaire surveys. Such surveys aim to collect information from users of a product or a service based to their responses to various aspects that are considered significant. In doing so, customers convey their satisfaction using an ascending scale of linguistic variables. In that manner, a business gains significant insights to assist decision-making. The current research proposes a framework that aims to evaluate the performance of airline service providers in terms of multi-criteria evaluation. The implemented analysis criteria correspond to the aspects evaluated by the passengers, while the passengers correspond to the decision-makers of the analysis. Thus, the framework is designed to assist GMCDM processes where a single score should be obtained for every examined provider based on the opinions of their customers. Moreover, the framework is developed to transform the responses gathered from questionnaires into comparative judgments in order to estimate local and global criteria weights using AHP. On the other hand, aviation provider evaluation is obtained using a rating option where passengers evaluate the performance of the provider they have just used against the analysis criteria, which avoids the collection of responses for services they have not experienced by the time they have been questioned. As a result, airline firms are evaluated based on the recent travel experience of their customers.

The proposed framework facilitates two options, and their implementation step sequence is illustrated in Figure 2. The first option consists of the typical AHP (T-AHP) implementation for GMCDM, while the second (S-AHP), using Monte Carlo Simulation, is a robust extension. Steps not included in the dashed frames are common to both options. The process is initialized with the definition of the analysis goal and the identification of the factors that contribute the most to the analysis goal satisfaction. Then, a decision hierarchy is developed to form a decision structure of objectives (criteria) and subobjectives (sub-criteria) that represent the decision analysis dimensions of the satisfaction aspects. At the last step, a questionnaire is developed to assist the evaluation based on passengers’ perceptions. Given that the evaluation process aims to estimate criteria importance (weights) and candidate alternative performance relative to the evaluation criteria, two Likert scales were developed (

Table 1. Criteria and alternatives’ evaluation scales.

Criteria Importance Intensity Levels *			Satisfaction Intensity Levels
$\mathit{t}$	Linguistic Variables	Value Scale (vt)	Linguistic Variables	Value Scale (rt)
1	Very Low Importance	1	Very Dissatisfied	1
2	Low Importance	3	Dissatisfied	2
3	Moderate Importance	5	Neutral	3
4	High Importance	7	Satisfied	4
5	Very High Importance	9	Very Satisfied	5

* If needed, even values can also be considered to assist compensation among the linguistic variables.

). The criteria evaluation intensity scale $v_t$ is used to assess the analysis criteria in terms of importance to their parent node, while the under-evaluated airline providers are rated using the satisfaction intensity scale $r_t$.

Using the T-AHP, relative judgments for every pair $i,j$ of the analysis criteria are estimated as the ratio of the derived response values for every $k$ questioned customer (Equation (12)). Thus, pairwise comparison matrices are reciprocals (Equation (13)) of the principal diagonal whose elements equals to 1 (Equation (14)), while $b_{ij}^k\in \left[1/9-9\right]$ holds the properties of the original AHP. Then, pairwise comparison tables $B_{ij}$ are established with the estimation of the group-based judgments $b_{ij}^g$, using the geometric mean of the $k$ decision-makers’ opinions that are involved in the process (Equation (15)). Since every evaluation is expressed in quantitative terms, pairwise comparison matrices present zero inconsistency, and local weights are estimated in terms of their percentage performance using the elements of the first column (Equation (16)) [45]. Global weights of the evaluation criteria with respect to the analysis goal are then estimated using Equation (3).

$$b_{ij}^k=v_{it}^k/v_{jt}^k$$

(12)

$$b_{ji}^k=v_{jt}^k/v_{it}^k=1/b_{ij}^k$$

(13)

$$b_{ii}^k=v_{it}^k/v_{it}^k=1$$

(14)

$$b_{ij}^g=\sqrt[K]{\prod _{k=1}^K{b}_{ij}^k}=\sqrt[K]{\prod _{k=1}^K{v}_{ti}^k/v_{tj}^k}=1/\sqrt[K]{\prod _{k=1}^K{v}_{tj}^k/v_{ti}^k}=1/b_{ji}^g$$

(15)

$$w_i={\displaystyle \frac{b_{i1}^g}{{\sum }_{i=1}^n{b}_{i1}^g}}$$

(16)

On the other hand, passengers express their satisfaction to the evaluation criteria using satisfaction intensity scale $r_t$. Thus, for the $k^{th}$ passenger the aviator $m$ receives a score $r_{ti}^{km}$, which corresponds to the value $r_t$ of the satisfaction level received $t$ for the $i^{th}$ evaluation criterion. Consequently, for every aviator and for each one of the evaluation criteria, a discrete probability density function can be obtained (Equation (17)), where $p_{ti}^m$ is the probability that an aviator $m$ receives the satisfaction value $r_t$ to the $i^{th}$ criterion. Under the concept of probabilistic additive weighting [46], the expected per-criterion satisfaction $S_{mi}$ and the overall satisfaction $S_m$ of the examined aviators can be estimated using Equations (18) and (19), respectively.

$$p_{ti}^m=p\left(r_{ti}^m\right)=p_{ti}^m\left(X=r_{ti}^m\right)={\displaystyle \frac{N{r}_{ti}^{km}}{Nk}}$$

(17)

$$S_{mi}=\sum _{\forall t}{p}_{ti}^m\times r_{ti}^m$$

(18)

$$S_m=\sum _{\forall i}{W}_i\times S_{mi}=\sum _{\forall i}\sum _{\forall t}{W_i\times p}_{ti}^m\times r_{ti}^m$$

(19)

The second option (S-AHP) is a robust decision-making framework which takes advantage of the feedback provided by the passengers and aims to evaluate the stability of the examined airlines’ performances based on the stochastic characteristics of the derived responses. Criterion weights are obtained by performing Monte Carlo simulation, where relative judgments in each trial are randomly generated using the density distribution functions as estimated by the responses to the questionnaires selected. From the responses collected, the density distribution function of the importance intensity scale values $v_{ti}$ can be derived as the ratio of the passengers $k$ that selected the intensity level $t$ (to denote the importance $v_{ti}$ of the $i^{th}$ criterion) divided by the total number of responders (Equation (20)). Equivalently, the cumulative distribution function $P_{ti}$ is obtained using Equation (21) and provides the basis for generating sample value scale numbers. The latter is achieved using the inverse cumulative distribution function to match randomly generated $P_{ti}$ values in the field $\left[0,1\right]$ with their corresponding values of the criterion importance scale $v_{ti}^{rand}$ (Equation (22)).

$$p_{ti}=p\left(v_{ti}\right)=p_{ti}\left(X=v_{ti}\right)={\displaystyle \frac{N{v}_{ti}^k}{Nk}}$$

(20)

$$P_{ti}=P\left(v_{ti}\right)=\sum _{\forall t}{p}_{ti}=P_{ti}\left(X\le v_{ti}\right)$$

(21)

$$v_{ti}^{rand}=\left\{\begin{array}{cc}1,& P_{ti}^{rand}\le {\sum }_{t=1}^1{p}_{ti}\\ v_t,& {\sum }_{t=1}^{t-1}{p}_{ti}<P_{ti}^{rand}\le {\sum }_{t=1}^t{p}_{ti}\\ 9,& {\sum }_{t=1}^4{p}_{ti}<P_{ti}^{rand}\le 1\end{array}\right.$$

(22)

For every trial, random pairwise comparison matrices $B_{ij}^{rand}={\left[b_{ij}^{rand}\right]}_{n\times n}$ are formed and, like the T-AHP option, random relative importance is estimated using Equation (23). Then, the local weights for every pair of criteria in the same cluster are derived using Equation (24), while the global weights can be obtained using Equation (3). Since $b_{ij}^{rand}$ are randomly generated, the overall weighted average consistency ratio $\overline{CR}$ is estimated and trials that present consistency ratios greater than 10% are rejected. For the rest of the trials, the score of an examined alternative is estimated adopting the concept of the previous options using Equations (18) and (19), with the difference that the global weights equal the weight generated in each one of the simulation trials. As soon as a sufficient number of trials are implemented, the expected satisfaction index ${SI}_m^{exp}$ of the $m^{th}$ alternative is estimated as the average score of the performances obtained in every trial $r$ (Equation (25)).

$$b_{ij}^{rand}=v_{ti}^{rand}/v_{tj}^{rand}$$

(23)

$$w_i^{rand}={\displaystyle \frac{\sum _{j=1}^n\frac{b_{ij}^{rand}}{{\sum }_{i=1}^n{b}_{ij}^{rand}}}{n}}$$

(24)

$${SI}_m^{exp}={\displaystyle \frac{\sum _r\sum _i\sum _t{W_{ri}\times p}_{ti}^m\times r_{ti}^m}{R}}$$

(25)

3. Case Study

3.1. Flight Service Satisfaction Dimensions

Olya and Al-ansi [47] emphatically stress that travelers take into consideration a rather large number of factors (mainly concerning pre- and post-flight services) [48] before they take their final decisions, thus highlighting the complexity of their behavior and actions. This view is in line with complexity theory which is found to be useful in describing the behavioral responses of travelers [49,50]. Further, the utility theory suggests that passengers buy airline services having a given level of expectations which are formed on a number of implicit service promises, such as “fair” price, tangibles and intangibles [51].

The model that has been most widely used for measuring service quality in the industry is “SERVQUAL” [52]. It includes twenty-two sub-criteria divided into five main criteria (tangibles, reliability, responsiveness, assurance and empathy) [53]. Based on this model, quality is based on subjective evaluation, since a service is perceived by the customer as an experience rather than as a physical component. However, SERVQUAL is not an airline sector-specific model. Thus, Ali et al. [54] assessed a modified version called AIRQUAL in Pakistan and found that passengers’ satisfaction can be explained by all five main service quality dimensions of the model. At the same time, Hussain et al. [55] used an altered model to assess an airline operating from Dubai, as Rahim [56] did for the Nigerian airline sector and Jiang et al. [57] also did for China’s domestic airline sector. AIRQUAL was also used by Shen and Yahya [22] in Southeast Asia. Further, Al Ghamdi [58] used another modified version, the nine-dimensional ASQUAL, to assess the service quality of Saudi Arabian Airlines. Finally, Gupta [2] attempted to rank the criteria of service quality using the best–worst method and, then, to classify airlines based on these criteria while applying the VIKOR (Vlse Kriterijuska Optimizacija I Komoromisno Resenje) methodology. It emerged that “tangibles” is the main dimension/feature of an airline and that service quality has a significant impact on the number of passengers attracted by a carrier.

In an attempt to assess the features that affect airlines’ attractiveness, Medina-Muñoz et al. [26] found that passengers place safety, punctuality and cost high in their list of priorities, as well as services provided during the flight. Similar are the results of the study of Kurtulmusoglu et al. [59], who found that prices, punctuality and booking convenience are among the most significant factors for choosing an airline. However, Namukasa [1] found that not only the services offered during the flight but also those offered before and after the flight, significantly affect passenger satisfaction and loyalty. It is not surprising that ticket prices and extra charges (e.g., in the case of changing seat or flight date, charges for luggage size or weight) are considered as two of the main reasons for selecting an airline [60]. Passenger behavior and loyalty, as well as the image of an airline, are all directly affected by the value-for-money perception of passengers [11,12,15].

Turning, first, our attention to the pre-flight services, Medina-Muñoz et al. [26] suggest that passengers’ rating of an airline is affected by the routes and the airports that the airline flies from/to. This is also confirmed by other studies [61], where two more factors, frequency and availability of flights, are found to play a significant role in the assessment of an airline by passengers. Further, many studies have highlighted the importance of the natural environment of an airport [62,63], its general attractiveness [64], the clear queuing instructions [65], accurate terminal information [66], lounge facilities [23] and, of course, the speed and comfort of the check-in process [62]. Finally, the use of information technologies can make passengers’ pre-flight experience more convenient and save them time and money [67].

As far as the in-flight service quality is concerned, it is found that it has a direct and significant effect on passenger satisfaction [68], especially the “tangibles” (comfort, cleanliness, and quality of food and beverages) [28,69]. However, the most important are still reliability and, mainly, safety [26,28,70], which obviously is the most fundamental and the one that provides airlines with a significant competitive advantage. Further, staff behavior (courtesy and responsiveness), appearance and professionalism also affect passenger satisfaction [69,71]. Moreover, focusing on the post-flight service quality, it has been confirmed by many studies that disembarkation, the speed of luggage collection [72], handling of personal belongings (lost or damaged luggage, etc.) [73], and the handling of passenger complains, refunds [74] and benefits [75] also affect passengers’ overall flight experience and carriers’ brand name/image, which, in turn, affects airline selection [19,76]. Finally, travel choices are also affected by the previous experiences that passengers have had [77,78], their personal characteristics (socio-demographics, etc.) [79,80], as well as whether they are members of a frequent-flyer program [70] (members usually perceive the airline of their choice as safer).

3.2. Evaluation Model

The proposed framework was implemented in a real-world case study to assist customer satisfaction analysis for aviators (service providers). The decision models take into consideration 51 evaluation criteria organized in a four-level hierarchical structure (Figure 3). The decision hierarchy is formed using five principal criteria. The first and the fifth criterion directly consists of the parent nodes of the evaluation criteria selected for the evaluation of the alternatives examined. On the contrary, the second, third and fourth criterion are further subdivided into three sub-criteria in order to subdivide decision elements into dimensions that can be efficiently handled by the AHP. It is noted that AHP suggests that pairwise comparison matrices should not exceed the ninth dimension [81]. The adopted formation demands the development of fifteen pairwise comparison matrices in total to obtain the local weights of the decision elements.

The fifty-one evaluation criteria for measuring both the first- and second-level features of the study have been adopted from various sources. More specifically, for pricing policy we have adapted the dimensions used by Rajaguru [11] and Tsafarakis et al. [82], for pre-flight service quality those used by Tsafarakis et al. [82] and Chou et al. [74], for in-flight service quality those used by Gupta [2], Rajaguru [11], Perçin [69], Namukasa [1] and Nejati et al. [83], for post-flight service quality those used by Gupta [2], Tsafarakis et al. [82], Namukasa [1] and Chou et al. [74], and for past experience those used by Babbar and Koufteros [84]. The questionnaires used by some of the airlines were also taken into consideration. For the collection of the necessary primary data, a structured questionnaire was developed. It included sixty-five close-ended questions for measuring the importance ($v_t$) of the criteria, sub-criteria and evaluation criteria incorporated into this study, and fourteen more questions for recording the demographic characteristics of the participants. Finally, satisfaction related to the evaluation criteria was measured including fifty-one questions using the satisfaction intensity scale $r_t$.

The data collection took place at the two largest Greek international airports (Athens and Thessaloniki). The sampling approach adopted was the judgment sampling approach [85]. The sample size consisted of 675 passengers, mainly women (53.8%) and well educated (64% hold a bachelor’s degree). They have permanent residency in Greece (60.9%), Germany (14.7%), the U.K. (6.2%) and the USA (3.6%). Further, their last flight was with Aegean Airlines (44.4%), Ryanair (19.6%) and Lufthansa (12.9%), while they fly on average once every three months (37.3%) or every six months (29.8%), mainly for pleasure/holidays (63.1%). Finally, they stated that the main reason for selecting the airline of their last trip was the ticket price (26.2%), availability (12.4%), quality (9.3%) and safety (7.1%), or a combination of these (security and quality 10.2%). Those who are members of a frequent-flyer program corresponded to only 28.4% of the total.

The five principal criteria are (a) pricing policy (C1), (b) pre-flight service quality criterion (C2), (c) in-flight service quality (C3), (d) post-flight service (C4) and (e) past experience (C5). Considering their opinions (

Table 2. The probability distribution function of the importance preference scale for the primary analysis criteria.

	Importance Levels
	Low Importance Values 1 to 3	Moderate Importance Values 4 to 6	High Importance Values 7 to 9
C1—Pricing policy evaluation criterion	0.89%	11.16%	87.95%
C2—Pre-flight service quality criterion	2.67%	22.67%	74.67%
C3—In-flight service quality criterion	1.33%	12.89%	85.78%
C4—Post-flight service criterion	4.52%	14.48%	81.00%
C5—Past experience criterion	1.35%	13.45%	85.20%

), the vast majority of the passengers agree on the importance of these factors (87.95%, 74.67%, 85.78%, 81.00% and 85.20%, respectively).

3.3. Analysis Criteria

Pricing policy criterion (C1) is formed using four evaluation variables (items). Probabilities for the importance scale levels of the answers provided by the passengers interviewed are illustrated in

Table A1. Importance preference scale probability distribution function.

	Importance Levels
	Low Importance Values 1 to 3	Moderate Importance Values 4 to 6	High Importance Values 7 to 9
Pricing Policy
C1.1—Ticket price (in relation to the seat)	11.56%	28.00%	60.44%
C1.2—Quality/price (value for money)	7.56%	26.22%	66.22%
C1.3—Additional charges (e.g., baggage charges)	37.33%	28.89%	33.78%
C1.4—Seasonal offers and discounts (loyalty miles)	21.78%	33.78%	44.44%
Pre-flight Service Quality
C2.1—Information included in the website	4.89%	16.00%	79.11%
C2.1.1—Travel information	4.00%	22.67%	73.33%
C2.1.2—Online booking process	2.22%	12.00%	85.78%
C2.1.3—Online check-in procedure	4.89%	7.56%	87.56%
C2.1.4—Security of financial transactions	1.78%	8.00%	90.22%
C2.2—Flight schedule and routes (destinations)	1.78%	8.44%	89.78%
C2.2.1—Destinations	3.56%	18.67%	77.78%
C2.2.2—Distance between airport and city center	12.00%	25.78%	62.22%
C2.2.3—Flight schedules	8.00%	28.00%	64.00%
C2.2.4—Frequency of flights	10.22%	28.44%	61.33%
C2.3—Pre-flight experience	2.67%	23.11%	74.22%
C2.3.1—Waiting time for check-in	9.33%	22.22%	68.44%
C2.3.2—Services provided during the check-in	8.44%	21.33%	70.22%
C2.3.3—Airport services (e.g., lounges, shops)	11.56%	22.67%	65.78%
C2.3.4—Efficiency of the boarding process	66.67%	33.33%	0.00%
C2.3.5—Efficiency of the embarkation process	8.44%	21.33%	70.22%
C2.3.6—Services during the embarkation procedure	11.11%	28.89%	60.00%
C2.3.7—Response to emergencies (e.g., cancelations, delays)	19.56%	27.11%	53.33%
In-Flight Service Quality
C3.1—Airplane	0.44%	9.33%	90.22%
C3.1.1—Physical characteristics of the aircraft (e.g., size, age)	9.33%	22.22%	68.44%
C3.1.2—Available legroom	8.44%	21.33%	70.22%
C3.1.3—Cabin cleanliness	11.56%	22.67%	65.78%
C3.1.4—Bathroom cleanliness	66.67%	32.89%	0.44%
C3.1.5—Seat comfort and cleanliness	9.33%	25.33%	65.33%
C3.1.6—In-flight entertainment (e.g., newspapers, screens)	11.11%	28.89%	60.00%
C3.1.7—Quality of the food or snacks on board	19.56%	27.11%	53.33%
C3.1.8—Available cabin baggage space	4.44%	24.89%	70.67%
C3.2—Crew	1.33%	10.22%	88.44%
C3.2.1—Crew appearance and elegance	9.33%	22.22%	68.44%
C3.2.2—Professional skills (e.g., use of foreign languages)	8.44%	21.33%	70.22%
C3.2.3—Courtesy	11.56%	22.67%	65.78%
C3.2.4—Willingness and speed of response	66.67%	32.89%	0.44%
C3.2.5—Approach in unexpected situations	9.33%	25.33%	65.33%
C3.3—Security	0.45%	2.68%	96.88%
C3.3.1—Compliance with safety rules during take-off and landing	0.44%	7.11%	92.44%
C3.3.2—Absence of in-flight problems	5.33%	8.89%	85.78%
C3.3.3—Necessary safety equipment on board	2.22%	10.22%	87.56%
C3.3.4—Safety instructions given by the crew	1.33%	6.22%	92.44%
Post-Flight Service Quality
C4.1—Frequent-flyer program	13.27%	25.59%	61.14%
C4.1.1—Rewards	32.44%	30.67%	36.89%
C4.1.2—Updates for offers and discounts	27.11%	26.67%	46.22%
C4.1.3—Network of international partners	28.89%	27.56%	43.56%
C4.2—Disembarkation	3.11%	17.78%	79.11%
C4.2.1—Efficiency of the disembarkation process	5.33%	23.56%	71.11%
C4.2.2—Baggage collection time	27.11%	26.67%	46.22%
C4.2.3—Luggage management (e.g., damage, lost luggage)	28.89%	27.56%	43.56%
C4.3—Complaint handling	1.81%	12.67%	85.52%
C4.3.1—Management of personal complaints	28.89%	24.89%	46.22%
C4.3.2—Speed of response to personal concerns	28.00%	24.44%	47.56%
C4.3.3—Compensation policy in case of loss or damage	33.78%	26.67%	39.56%
Past Experience
C5.1—I enjoy flying with this airline	11.11%	23.56%	65.33%
C5.2—I get good value for money from this airline	9.33%	23.11%	67.56%
C5.3—I am satisfied with the way the airline takes care of me	12.00%	23.11%	64.89%
C5.4—I am satisfied with the airline’s member of staff	4.44%	14.67%	80.89%
C5.5—This airline values customer feedback	10.53%	22.81%	66.67%
C5.6—My expectations from the airline were met	12.00%	14.67%	73.33%

. An interesting finding concerning this set of variables is that passengers are almost equally divided into three parts, since low to very low importance recorded a probability of 37.3% (item C1.3).

Further, pre-flight service quality is defined by measuring an aviator’s performance against various criteria that are grouped in three second-level criteria. Satisfaction is ascertained regarding the services and information obtained from the aviators’ websites (C2.1) (measured using four items), the flight schedule and routes (destinations) (C2.2) (measured using four items), and the pre-flight experience (C2.3) (measured using seven items). In general, both second-level criteria and evaluation criteria are considered of high importance by the majority of the passengers. The only exception was the efficiency of the boarding process (C2.3.4), indicating that this criterion does not contribute significantly to airline evaluation.

In total, seventeen evaluation criteria were taken into account for the evaluation of the airline performance based on the satisfaction derived from their in-flight experience. Evaluation criteria are grouped into three categories forming the “Airplane” (C3.1) (8 items), “Crew” (C3.2) (5 items) and “Security” (C3.3) (4 items). In general, the implemented criteria are considered of high importance by the passengers. However, criteria C3.1.4 and C3.2.4 do not achieve significant importance since either the majority of the passengers did not use the aforementioned services, or they had no experiences which warranted mentioning the behavior of the crew members.

As far as the post-flight quality of the provided services is concerned, it was measured using nine evaluation variables (items) organized into three sub-criteria. In detail, passengers were asked to evaluate the frequent-flyer program (C4.1) (3 items), disembarkation (C4.2) (3 items), and complaint handling (C4.3) (3 items). In general, the total of the implemented criteria is considered of moderate to high importance. Finally, aiming to bring into the analysis how passengers value previous experiences of using the same airline, six evaluation criteria were considered. Their goal was to counterbalance dissatisfaction exclusively owed to passengers’ last traveling experience with the specific airline company.

3.4. Alternatives Profiles

The research examines the performance of four alternative airline services providers (Alt1, Alt2, Alt3 and Alt4) through the use of 568 (84.15%) questionnaires (out of the total 675 questionnaires initially collected). These airlines are those with a higher market share (flying from/to Greece). More specifically, two are local and two are foreign airlines, while three of them are FSCs and one an LCC. For each one of the analysis criteria, the expected satisfaction $S_{mi}$ performance was calculated in order to investigate whether an obvious solution exists and, if so, there was no need for further analysis. The results presented in Figure 4 show that there is no such ranking for all the analysis criteria. However, with the naked eye, it can be seen that Alt2 outperforms in the third and fifth evaluation criteria and records moderate performances with respect to the second and fourth criteria. The third alternative is competitive to options Alt1 and Alt4 in criteria 2, 3, 4 and 5, and falls short in the first criterion.

4. Results and Discussion

Initially, exploratory factor analysis was performed (using principal component analysis) with standard varimax rotation, using, as a selection criterion, an eigenvalue score greater than one. To validate the one-dimensional structure of the scales, Kaiser–Meyer–Olkin (KMO) was used to test the sampling adequacy, while convergent validity was tested using the item loadings and, finally, internal consistency of the factors was measured using Cronbach’s α. The scores for all tests and all factors and subfactors were within acceptable range, indicating that the factors and subfactors are valid and reliable (

Table 3. Exploratory factor analysis results.

	KMO	TVE	Factor Loadings	Cronbach’s α	Level of Satisfaction		Significance for Satisfaction
Factors					Mean	Std	Mean	Std
C1: Pricing Policy	0.716	55,230	0.579–0.858	0.776	3.46	0.731	8.35	1.600
C2: Pre-flight service quality	0.652	61,672	0.791–0.827	0.689	3.93	0.534	7.63	1.902
C2.1: Website	0.824	64,114	0.652–0.889	0.857	4.27	0.641	7.59	1.958
C2.2: Flight schedule and routes	0.842	62,455	0.631–0.876	0.840	3.78	0.657	8.37	1.573
C2.3: Airport services	0.878	62,300	0.719–0.827	0.987	3.73	0.739	7.65	1.846
C3: In-flight service quality	0.703	74,489	0.820–0.892	0.821	4.07	0.601	8.23	1.711
C3.1: Airplane	0.902	57,504	0.692–0.848	0.903	3.56	0.761	8.26	1.518
C3.2: Crew	0.869	74,904	0.853–0.904	0.933	4.26	0.716	8.36	1.653
C3.3: Security	0.883	71,505	0.811–0.891	0.896	4.39	0.617	9.36	1.180
C4: Post-flight service quality	0.690	72,564	0.797–0.883	0.811	3.68	0.699	7.68	1.857
C4.1: Frequent-flyer program	0.822	64,883	0.840–0.912	0.888	3.59	0.773	6.77	2.512
C4.2: Disembarkation	0.748	73,264	0.783–0.947	0.870	3.75	0.834	7.80	1.868
C4.3: Complaint handling	0.846	84,408	0.882–0.944	0.937	3.58	0.932	8.15	1.724
C5: Past experience	0.716	59,678	0.545–0.842	0.749	3.44	0.826	8.07	1.706

).

The descriptive statistical analysis shows (Table 3) that the quality of the services provided in-flight is that which passengers were more satisfied with (4.07). In contrast, the factor they were the least happy with was the pricing policy of the airline (3.46). As far as the subfactors are concerned, they were very satisfied with the level of security (4.39), the crew (4.26) and the website (4.27).

Finally, ANOVA analysis indicated that there is a significant difference in the arithmetic mean score of the factors and subfactors based on the reason (price, safety, quality and availability) each airline was chosen, as well as their membership (or lack thereof) in a frequent-flyer program. The country of permanent residency (Greece or elsewhere), the age group and the frequency of travel are also some characteristics that differentiate the mean score of some (relatively few) factors and subfactors.

A deterministic AHP option using the geometric mean operator (T-AHP) indicates that the overall global weights of the primary (first-level) criteria almost equally contribute to the analysis goal (

Table 4. Local weights generated by T-AHP and S-AHP versions for the analysis of first- and second-level criteria (%).

	T-AHP Local	S-AHP (Total Trials)			S-AHP (Accepted Trials)
Criteria		Min	Exp	Max	Min	Exp	Max
C1: Pricing policy	20.97	7.49	21.46	43.59	10.99	21.36	39.01
C2: Pre-flight service quality	19.01	6.94	18.58	37.46	7.74	18.74	33.28
C2.1: Website	31.86	6.25	31.04	60.14	8.37	31.13	60.14
C2.2: Flight schedule and routes	35.73	15.00	36.94	81.82	15.00	36.72	80.91
C2.3: Airport services	32.41	5.94	32.03	63.25	5.94	32.15	63.25
C3: In-flight service quality	20.57	7.73	20.75	39.27	10.90	20.82	35.33
C3.1: Airplane	33.05	14.24	33.16	63.27	14.24	32.98	63.27
C3.2: Crew	31.97	11.40	31.27	62.84	12.81	31.34	62.84
C3.3: Security	34.98	12.71	35.57	63.27	14.17	35.67	60.31
C4: Post-flight service quality	19.19	7.29	18.69	37.82	7.48	18.73	36.67
C4.1: Frequent-flyer program	28.19	5.52	25.31	56.05	5.52	25.56	55.80
C4.2: Disembarkation	35.13	8.96	36.18	78.44	8.96	36.07	78.44
C4.3: Complaint handling	36.68	9.56	38.51	77.78	9.56	38.36	77.78
C5: Past experience	20.25	10.96	20.52	41.82	11.28	20.34	33.47

). The simulation trials were executed by generating 5000 trials, where the differences in the obtained expected performance results remained constant up to the fifth decimal place. Estimations of the average overall inconsistency ($\overline{CR}$) in every simulation trial indicated that the maximum acceptable threshold of 10% was violated in 1.963 (39.26%) of the total trials implemented. The expected ${\overline{CR}}_{exp}$ (average of the per-trial $\overline{CR}$) in the total and in the accepted trials has been found (9.83% and 7.51%, respectively). However, on the first occasion, $\overline{CR}$ falls into the range $\left[3.16\%, 49.6\%\right]$, while for the accepted trials $\overline{CR}$ ranges between $\left[3.16\%, 10\%\right]$. Although the analysis should be performed on the accepted trials, results for both S-AHP variants will be generated to investigate the quality of the derived rankings with respect to both the number of rounds generated and the impact of inconsistent judgments.

Table 4 also reveals that the expected criteria weights, estimated by averaging the weights generated in the trials of both S-AHP variants, are almost equivalent to those derived by using the geometric mean option (T-AHP). In detail, the root mean square of the deviations among the T-AHP and S-AHP variants are 1.091% and 0.985%, respectively, while the simulation variants produce more closely related results with a 0.143% root mean square deviation. However, the minimum and maximum derived criteria weight values indicate that the decision space has a significant range in each dimension (criterion).

According to the T-AHP option, Alt3 is ranked first, recording an SI of 3.717, followed by Alt4 with an SI of 3.675. Alternatives 1 and 2 are in third and fourth place, registering a performance of 3.602 and 3.181, respectively (

Table 5. SIs for the estimation options examined.

Geometric Mean Option	Airline 1	Airline 2	Airline 3	Airline 4
Satisfaction Index	3.602	3.181	3.707	3.675
Ranking	3rd	4th	1st	2nd
Simulation Option (Total Trials)	Airline 1	Airline 2	Airline 3	Airline 4
Satisfaction Index (Minimum)	3.537	2.802	3.468	3.442
Satisfaction Index (Expected)	3.716	3.182	3.707	3.676
Satisfaction Index (Maximum)	3.864	3.368	3.906	3.814
Ranking	1st	4th	2nd	3rd
Simulation Option (Accepted Trials)	Airline 1	Airline 2	Airline 3	Airline 4
Satisfaction Index (Minimum)	3.592	2.952	3.536	3.522
Satisfaction Index (Expected)	3.717	3.184	3.707	3.677
Satisfaction Index (Maximum)	3.821	3.336	3.847	3.778
Ranking	1st	4th	2nd	3rd

). On the other hand, estimation of the expected SIs for each alternative, generated as the average of the values estimated at the simulation trials (Equation (25)), yielded the same ranking order for the simulation variants no matter if the consistency check was omitted or not. In detail, both variants indicate that Alt1 is ranked first, followed by Alt3, while Alt4 and Alt2 are ranked in third and fourth place. Summarizing, the difference in the observed ranking orders is because Alt1 manages to climb to the first-rank position in S-AHP variants although the specific airline was ranked third using T-AHP.

Table 5 indicates that the T-AHP-estimated SIs fall between the minimum and maximum estimated values of the simulation trials generated. Thus, there is evidence that T-AHP ranking may also occur in the simulation trials. Moreover, the estimated SI magnitude for Alt1, Alt3 and Alt4 remains too close for both T-AHP and S-AHP especially, leaving space to develop an argument regarding the existence of practically equivalent alternatives. In contrast to the geometric mean option (T-AHP), where a single SI is obtained, S-AHP variants are capable of investigating the stability of the results to various changes regarding both criteria and alternative performances. A simulation of passengers’ responses enables an investigation with respect to both the stability of the derived solution and the quality of the ranking orders obtained.

An approach to quantify the stability related to the performance of the examined alternatives in simulation trials is to estimate the distribution of the expected score that will be generated. Such an analysis, focused on the 3037 consistent trials, is highlighted in

Table 6. Examined alternative scenarios’ SI distributions.

			Satisfaction Index (N of trials)
Range			Airline 1	Airline 2	Airline 3	Airline 4
2.9	to	3.0	-	0.03% (1)	-	-
3.0	to	3.1	-	5.60% (170)	-	-
3.1	to	3.2	-	56.87% (1727)	-	-
3.2	to	3.3	-	36.65% (1113)	-	-
3.3	to	3.4	-	0.86% (26)	-	-
3.5	to	3.6	0.03% (1)	-	0.49% (15)	1.09% (33)
3.6	to	3.7	30.29% (920)	-	41.82% (1270)	75.70% (2299)
3.7	to	3.8	68.98% (2095)	-	56.34% (1711)	23.31% (705)
3.8	to	3.9	0.69% (21)	-	1.35% (41)	-

. The results presented in percentages and the counted trials indicate the following: (a) Alt2 is not a competitive alternative as its maximum performance is lower than the other alternatives’ minimum. Its most counted performances fall into the range $\left(\left.3.1,3.2\right]\right.$; (b) Alt4 is ranked third since its most counted performances fall into the range $\left(\left.3.6,3.7\right]\right.$; Alt4 records a significant number of trials that fall into the range $\left(\left.3.7,3.8\right]\right.$. Τhis number is lower than that of Alt3, which is ranked second although it records the highest observed performance (3.878); (c) Alt1 is ranked first since it dominates the satisfaction level in the range $\left(\left.3.7,3.8\right]\right.$. At the same time, its performances remain, with only one exception, constantly above 3.6 and it records the highest minimum and expected observed $SI$ performances.

To address the previous issues, the S-AHP option also allows further investigation of the extent to which high satisfaction performance ensures higher rankings by examining the rankings derived in each trial. In particular, the unique rankings derived from the 5000 trials of the simulation can be obtained in order to investigate the stability of the result derived and to estimate the robustness of the ranking obtained by both T-AHP and S-AHP.

Table 7. Simulation ranking appearance probability analysis.

	Unique Simulation Ranking Analysis
Ranking ID	Airline 1	Airline 2	Airline 3	Airline 4	# of Trials	Probability of Appearance (%)
R1	1	4	2	3	1785	58.78
R2	2	4	1	3	916	30.16
R3	1	4	3	2	291	9.58
R4	2	4	3	1	35	1.15
R5	3	4	1	2	8	0.26
R6	3	4	2	1	2	0.07

summarizes the results of such an analysis and indicates that the 3037 consistent trials generate only six possible rankings. As expected, the most counted ranking order is the one already indicated by the S-AHP option, which occurs as a result of 1785 trials, corresponding to a percentage of 58.78%. The second most common ranking is the one where Alt3 prevails over Alt1 with a significantly lower appearance probability (30.16%). It is noticed that the ranking order of the T-AHP is assigned to only 0.26% of the simulation trials, highlighting that the T-AHP in the current analysis does not generate a robust solution to the evaluation problem.

The ranking appearance probability analysis also indicates that Alt1 is ranked first at R1 and R3 unique rankings. Thus, Alt1 is ranked first among a total of 2076 trials, which results in an overall 68.36% probability of a first-ranking appearance. Additionally, Alt1 records a 31.31% and a 0.33% probability of a second- and third-ranking appearance. The analysis also validates that Alt2 is constantly ranked in the last position. Alt4 is commonly ranked third (88.94%), while in the first position there has been found only 37 trials with a probability of 1.22%. Alt3 is ranked second for 58.84% of the trials and records the second highest number of trials for which it is ranked first (924). An overall index adopted to provide a synopsis of the simulation rankings order analysis can be reached as the satisfaction expected rank ($SER$) using Equation (26). The lower the index, the higher the level of customer satisfaction.

Table 8. Appearance probability of alternatives’ ranking order.

	Alternatives’ Ranking Order Probability (N of Trials)
Rank	Airline 1	Airline 2	Airline 3	Airline 4
Ranked 1st	68.36% (2076)	-	30.42% (924)	1.22% (37)
Ranked 2nd	31.31% (951)	-	58.84% (1787)	9.85% (299)
Ranked 3rd	0.33% (10)	-	10.73% (326)	88.94% (2701)
Ranked 4th	-	100% (3037)	-	-
$SER$ index	1.320	4.000	1.803	2.877

summarizes the results of the airline ranking appearance in the simulation trials.

$${SER}_i={\sum }_r{p}_r\times R_r$$

(26)

The proposed framework has the capacity to support sectorial analysis by partitioning the sample dataset in terms of gender, age, income, etc. Such an analysis can provide significant insights with respect to various aspects of satisfaction that may occur based on passenger profiles. To estimate different attitudes and differentiations in SIs among the genders, the dataset has been queried accordingly and both T-AHP and S-AHP were used to estimate the SIs and the ability of the examined alternatives to be ranked in a certain position. With respect to the simulation option, 5000 trials were implemented and SIs were obtained for both the total number of trials as well as for those that fall into the accepted level of inconsistency. The comparative analysis between the clusters studied, in relation to the overall estimates previously discussed, was applied to the accepted trials to ensure consistency. However, it is noted that the results derived from the total trials present strong similarities. From the total of 5000 trials, the corresponding number of accepted trials were 3925 for males and 2457 for females.

The analysis results (

Table 9. AHP-based group SIs and alternative ranking evaluation per gender.

	Males				Females
	Airline 1	Airline 2	Airline 3	Airline 4	Airline 1	Airline 2	Airline 3	Airline 4
SI Option 1 *	3.717	3.001	3.733	3.544	3.525	3.269	3.481	3.690
SI Option 2 **	3.834	3.114	3.848	3.662	3.640	3.269	3.477	3.689
SI Option 2 ***	3.835	3.115	3.849	3.664	3.640	3.272	3.477	3.689
Ranked 1st	23.21%	-	76.79%	-	0.98%	-	-	99.02%
Ranked 2nd	76.79%	-	23.21%	-	99.02%	-	-	0.98%
Ranked 3rd	-	-	-	100%	-	0.04%	99.96%	-
Ranked 4th	-	100%	-	-	-	99.96%	0.04%	-
$SER$ index	1.768	4.000	1.232	3.000	1.990	4.000	3.000	1.010
Rankings	2nd	4th	1st	3rd	2nd	4th	3rd	1st

* T-AHP, ** S-AHP (total trials), *** S-AHP (accepted trials).

) indicate that similar SI estimations were generated for the geometric mean and the simulation options, which results in the same alternative ranking for every group of responders. However, these rankings are different for each group of respondents, and they also differ from those of the overall analysis. For the male passengers, the 3014 (76.79%) consistent trials indicate a single ranking according to which Alt4 and Alt2 are ranked third and fourth, while Alt1 and Alt3 are additionally ranked second and first. Nevertheless, for the remaining 23.21% (911 trials) Alt1 has better performance compared to Alt3, and they switch positions. Consequently, the $SER$ index stands in favor of Alt3 recording a performance of 1.232. The analysis of the female passengers returns almost (99.02%) a single ranking with Alt3 and Alt2 in third and fourth places with certainty. Alt4 is now in first place and Alt1 remains in second place. As observed, male passengers are most satisfied with Alt3 airline, while female passengers are most satisfied with Alt4. Irrespective of gender, both genders agree that Alt1 is the second-best option and Alt2 is in fourth place. The analysis at this stage verifies the overall analysis results, where Alt1 is ranked first, because the same alternative is consistently ranked second, while Alt3 and Alt4 switch places among the first- and third-ranking order. Finally, Alt3 outranks Alt4 in second place in the overall rankings since Alt3 is ranked first with respect to the male cluster, which provides more consistent judgments and, thus, it is overrepresented in the overall trial analysis.

5. Summary and Conclusions

This research proposes a novel decision framework for evaluating airline service provision based on passenger satisfaction. The proposed framework approaches customer satisfaction analysis as a multi-criteria decision analysis problem and uses AHP to estimate SIs. To support the implementation of the AHP, a modification was developed to allow the extraction of relative judgments from a single questionnaire survey, which is the most common way of collecting customer perceptions regarding the quality of the services they receive. The responses were then coded using a five-point Likert scale based on the AHPs’ fundamental scale of preferences, with the aim of maintaining the original properties of the methodology.

As a GMCDM approach, two options are integrated into the analysis. In the typical T-AHP option, global pairwise comparison judgments are estimated using the geometric mean of the individual judgments received, while in the second, the stochastic characteristics of the responses collected are used to build a Monte Carlo simulation-based AHP (S-AHP) version. To minimize the effect of the rank reversal phenomenon, the analysis is conducted as an open system using the ratings option based on which of the alternatives’ expected performance relative to the analysis criteria has been estimated.

The analysis is supported by the responses of a questionnaire survey conducted in the two main airports in Greece. Four airline service providers were examined; three of them are FSCs (Alt1, Alt3 and Alt4), and one an LCC (Alt2). According to the responses collected from 675 passengers, not a single ranking based on the analysis criteria has occurred. LCC airline (Alt2) is ranked first (along with Alt4) for the ticket price criterion (C1.1) and records moderate performance for the seasonal offers and discounts (C1.4) criterion. Apart from the online check-in (C2.1.3) and destination (C2.2.1) criteria, for which it is ranked third, Alt2 is constantly ranked fourth. Consequently, FSCs dominate the first three positions of the analysis. Alt4 is ranked first for 6 evaluation criteria, second for 17 and third for 26. Alt3 dominates the first ranking order regarding its expected performance since it is ranked first for 30 evaluation criteria. On the other hand, Alt1 is ranked first for 15 evaluation criteria, but it presents a more balanced performance at the second and third ranking orders. In detail, Alt1 is ranked second for 23 evaluation criteria and third for 13 of them.

Since the lack of an obvious solution has been verified, an alternative comparative evaluation could only be reached by combining criteria weights and their satisfaction performances. In the current research, both T-AHP and S-AHP have been implemented to obtain the rankings of the alternatives examined. The results derived indicate common rankings, similar SIs, and expected SI estimations for the T-AHP and the S-AHP with and without consistency constraint implementation in the trials under consideration. However, T-AHP implementation may lead to low differences in the SIs and that may provoke disagreement or doubts regarding the ranking obtained. In this research, T-AHP generates an efficient ranking order but not a robust solution, indicating that in a stochastic decision environment the simulation-based extension of the AHP is more efficient in generating candidate alternative rankings. In particular, the ranking order obtained by the T-AHP has been reached in only 8 out of the 3037 consistent rounds of the S-AHP and Alt1, which is ranked third, climbs to first place in the simulation-based extension since the specific airline company is ranked first in 68,36% of the accepted trials. Moreover, the introduced Satisfaction Expected Rankings (SER) index, which effectively summarizes the results of the simulation trials, also ensures the first position for Alt1, the second for Alt3, the third for Alt4 and the fourth for Alt2.

By exploiting the potential of the S-AHP to provide a mapping of the decision space, a family of indices can be extracted to ensure final decisions. Such indices have been included in the present research to ensure a robust decision framework. In particular, SI descriptive statistics and probability distributions, together with the rank order probabilities and SER index estimates obtained for each alternative considered, provide a clearer picture of their final rankings. In this way, the S-AHP produces more robust rankings, which is of great importance, especially when valuable companies are being evaluated. The proposed methodological framework can be used to produce reports on the breakdown of respondents by gender, age, etc., providing useful insights for managers and administrator officials of the airline sector. As a customer satisfaction methodology, it can be further enriched by SWOT-like analysis to highlight strengths, weaknesses, opportunities and threads in a criterion-by-criterion basis to enrich its potential as a decision-making tool.

5.1. Limitations

The sample size is relatively small and, consequently, it may not be representative of all airline passengers flying from/to Greece. Further, the data collection process took place in the two main Greek international airports and, as a result, a large percentage (2/3) of the sample mainly consisted of passengers with Greek origins. Thus, the findings may have been affected by cultural or other country-specific factors and, therefore, generalization should be made with caution.

5.2. Impact Statement

Air travel accounts for more than half of all international travel, so the contribution of airlines to the tourism industry is unanimously recognized as crucial. An important dimension that enriches the complementary nature of the tourism and air transport industries is the analysis of passenger satisfaction. Although it is very difficult to define passenger satisfaction, it is certain that satisfied customers ensure successful businesses. In the airline industry, satisfaction is related to different dimensions. This study builds a decision model that enumerates satisfaction dimensions and transforms them into criteria in order to treat airline evaluation as a multi-criteria decision analysis problem. The analysis performed acts as a benchmarking procedure, highlighting the strengths and weaknesses of the airlines studied, while also able to provide results by partitioning the sample dataset to support sectoral performance analysis. Combined with Monte Carlo simulation, it generates robust rankings based on the stochastic characteristics of passenger responses.