A Review of Data Envelopment Analysis in Airline Efficiency: State of the Art and Prospects

/e rapid development of the aviation industry has brought about the deterioration of the climate, which makes airline efficiency become a hot issue of social concern. As an important nonparametric method, Data Envelopment Analysis (DEA), has been widely applied in efficiency evaluation. /is paper examines 130 papers published in the period of 1993–2020 to summarize the literature involving the special application of DEA models in airline efficiency. /e paper begins with an overall review of the existing literature, and then the radial DEA, nonradial DEA, network DEA, dynamic DEA, and DEA models with undesirable outputs applied in airline efficiency are introduced. /e main advantages and disadvantages of the above models are summarized, and the drivers of airline efficiency are analyzed. Finally, the literature review ends up with future research directions and conclusions.


Introduction
In the past half-century, the airline industry has undergone a lot of changes. On the one hand, from the deregulation and liberalization of the airline industry in the US and Europe to the adoption of "Open Sky" policies in Asia and Latin America, market global competition has greatly stimulated the development of air transportation. According to International Air Transport Association (IATA), the global air transport passenger traffic has grown from about 300 million to 4.5 billion from 1970 to 2019. Total airline revenue has doubled in the past 20 years, reaching 507 billion dollars in 2019. On the other hand, airlines have been faced with a greater cost challenge and a more complex business environment. e rising fuel prices, labor prices, and the cost of infrastructure together have exerted greater pressure on airlines. It has been reported that the fuel cost and labor cost are the two largest costs of global airlines. In addition, as the competition among airlines has continually intensified, especially after the entry of low-cost airlines, the global airline market structure and competition situation have been changing. At the end of the last century, there were only 3 low-cost carriers (LCC) in the world (Southwest Airline, Ryanair, and Easy Jet), but the number has increased to about 200 now. And the market share of LCC in the global market has reached nearly 30%, which becomes a huge challenge and threat to traditional air carriers. Acquisition, mergers, and alliances among airlines further complicate the airline market environment.
Under this context, boosting operational efficiency has become the key for airlines to survive and develop in the rapidly changing environment. Plenty of scholars have paid much effort in evaluating airline efficiency and have achieved rich results. Among these researches, parametric methods and nonparametric methods are usually applied. Parametric methods mainly involved production function, cost function, and regression analysis, while nonparametric methods are mostly based on Data Envelopment Analysis (DEA). DEA is a method to measure the relative efficiency of a series of multi-input multioutput Decision-Making Units (DMUs) [1]. For decades of studies, DEA models have been rapidly evolved and enriched to adapt to different conditions in various fields. Reference [2] summarized the early studies of DEA models, while [3] provided a detailed review of DEA models over the last three decades. With the continuous enrichment of the research results of DEA methods in various fields such as finance, transportation, environment, and education, it is quite necessary to summarize the relevant research results from specific fields. On the one hand, it is helpful to understand the issues that the DEA method mainly solves in related fields. On the other hand, the applicable DEA models can be further extended according to problems in specific fields. Reference [4] examined work of the application of DEA on hospitals and health care. e study in [5] and presented the efficiency studies on rail transport and ports, respectively. e authors of [6][7][8] investigated the DEA method and its applications in financial services.
e study in [9][10][11] reviewed the application of DEA on energy and environment aspects from different respect.
However, few surveys are available to review systematically the status of studies and to discuss the future research direction of DEA application in the airline industry. As the studies on airlines are enriched and deepen, it is necessary to make a review and summary of relevant researches. erefore, this paper aims at sorting out the literature of DEA applications in the airline industry, analyzing the research status, and pointing out the possible future research directions. We collect 130 relevant papers over the past 27 years (1993-2020) in the Web of Science (WOS) database and Google Scholar. e rest of this paper is as follows. Section 2 provides the overall review. Section 3 describes the application of DEA and its extended methods in airline efficiency research. Section 4 presents the future research directions and the conclusions of this study.

Overall Review
We initially use "airline efficiency" as a keyword to search the studies in the WOS database and Google Scholar. "DEA" and "data envelopment analysis" were applied as keywords to filter the list. After excluding the unrelated papers by reading the abstract of these papers, we got a final sample of 130 papers published from 1993 to 2020.
In recent years, studies on airline efficiency with DEA methods were flourished and active. e annual times cited have reached a sharp growth rate after 2013, which is consistent with the growth in the number of publications. It is not hard to predict that the number will be further increased soon. Figure 1 presents the top 12 journals that 72 of the 130 papers were published in. Among these, the Transportation Research Series (including Part A: Policy and Practice, Part D: Transport and Environment, and Part E: Logistics and Transportation Review) and the Journal of Air Transport Management published most articles, both over 20 ones. Other journals published 2 to 5 papers, respectively.

Applications of Radial DEA.
Among the papers applying the radial DEA models, there are about 3 classes of methodologies, one is to directly apply the standard CCR or BCC models, and the other is to combine standard DEA models with other methods, especially the combination of parametric and nonparametric methods. And the last is the application of modified or extended DEA models.
In early researches, the traditional radial DEA models including CCR and BCC models were typically employed for evaluating the technical efficiency and scale efficiency of airlines (Table 1). e factors affecting the technical and scale efficiency were further identified.
Initially, when applying DEA models to assess the performance of airlines, financial index, such as total revenue and total cost, was usually selected as the input and output index. e study in [12] considered that it is difficult to assess the performance of international airlines with financial information for the lack of uniformity in statistics across countries. e author proposed adding nonfinancial indexes (such as available ton-kilometers, available seat kilometers, and fleet capacity) as input or output indexes for the DEA approach. Since then, nonfinancial indicators have been extensively developed and popularly applied in the evaluation of airline efficiency with the DEA model. For a long time, the combination of DEA models and other methods was the most popular way to study airline efficiency. Among the previous researches, the common methods combined with DEA models are (1) regression methodologies, which include Tobit regression [21][22][23], bootstrapping truncated regression [24,25], and GLS regression and time-series regression [26,27]; (2) productivity index, such as Malmquist productivity index [28,29], Total Productivity Index [30], and Fisher Productivity Index [31]; (3) other methods such as stochastic frontier approach [32,33], free disposal hull [34,35], and balanced scorecard [36]. e detailed ones are shown in Table 2.
Regression methodologies are often used as the second step following the DEA methods to identify the cause of high or low efficiency, through the correlation of efficiency scores and the contextual factors. Productivity indexes, especially the Malmquist productivity index, are frequently applied to attribute the measured change in productivity. Stochastic frontier approach and free disposal hull, which are semiparameter and nonparameter methods, respectively, are usually applied as a complementary contrast or robust examination of the results derived from the DEA method. Reference [36] uniquely combined standard DEA with a balanced scorecard to assess the efficiency by incorporating leading and lagging factors.
ere is a tendency that the extended DEA models for different situations are integrated to deal with the more complex situations in a deep extension, as shown in Table 3, for example, the network dynamic DEA models and the stochastic network DEA models.

Applications of Nonradial DEA and Epsilon-Based
Measure (EBM) Models. Although the radial models have been modified in many papers and are popular in evaluating airline efficiency, it has some shortcomings. Firstly, it neglects the effects of nonradial slacks in the efficiency, which means when an airline's efficiency is 1 but the slacks are not 0, we cannot identify the airline to be fully effective. When applying the radial model, it is difficult to distinguish a strong effective DMU and a weak effective DMU. Most importantly, radial models assumed that inputs and outputs of DMUs change in the same proportion, but in airline efficiency, inputs such as employees and fuels cannot be substituted completely and may not change proportionally. erefore, many nonradial models such as slack-based measures and range-adjusted measures have been recently employed in the airline efficiency assessment, as shown in Table 4.
Since the "black box" of airline efficiency has been opened, there is an increasing need to evaluate multistage aviation efficiency, including the overall efficiency and the subefficiency across sectors. Nonradial measures have been popular in network DEA methods. e study in [70] proposed a novel slack-based measure network DEA model (SBM-NDEA) and firstly applied it to airlines efficiency evaluation. ey believed that the model represents both the nonstorable feature of transportation service and production technology and can measure the overall efficiency and subefficiency of airlines, even in the presence of shared input. e authors of [72,73] also use SBM-NDEA to evaluate the efficiency of LCC and European airlines. Some papers extended the SBM-NDEA model to Virtual Frontier Network SBM [74]; metadynamic SBM [75]; and network SBM with weak or strong disposability [69,71,77]. Apart from the slack-based measure, range-adjusted measure is also introduced into evaluating airline efficiency in recent years [76,78], but the papers are relatively limited. e detailed ones are shown in Table 4.
Since the slacks in these nonradial models may not be necessarily proportional to the inputs or outputs, the projected airlines may lose proportionality in the original inputs or outputs. When evaluating airline efficiency during different years, if the slacks are significantly different, it is difficult to determine the direction of efficiency improvement. us, a new model, EBM, proposed by [86] to be a combination of both radial and nonradial models, has been applied in airline efficiency evaluation [80,81,85]. It has been also gradually employed in network or dynamic situations.
In addition, these nonradial DEA models have also been combined with other methods such as simple regression analysis, Tobit analysis, and Malmquist-Luenberger index, grey model to explore the factors of airlines efficiency, or the cause of productivity growth.

Network DEA in Airline Efficiency.
Before the application of network DEA, each airline was treated unit with multiple inputs and outputs, and the evaluation of airline efficiency was limited to the overall efficiency, which did not reveal the internal relations inside the "black box." Network DEA models break down the system into multiple processes and divisions, taking into consideration the component processes and the relations between them via intermediate  products. Different systems have different structures, which are mainly classified into the series structure, parallel structure, and series-parallel structure. In the application for the airline industry, the series structure was the most popular and suitable network model, as shown in Table 5.
Regarding series structure, some papers considered the airline system a two-stage process, which usually comprises productivity process and consumption process, calculating the technical efficiency and marketing efficiency, respectively; some studies broke down the system into three stages, usually consisting of operation stage, service stage, and sales stage. A few studies divided the airline system into several parallel divisions, such as passenger subproduction and cargo subproduction in [70] and operating stage and fleet maintenance stage in [80]. Figures 2 and 3 illustrate the two divisions and two-stage series-parallel structure in [70] and Figure 3 presents the three-stage series structure in [91]. For the inputs and outputs, most papers assumed that the intermediate products produced in the former process would be consumed by the next process. However, some studies have considered the final (usually undesirable) outputs produced in the intermedia stages, such as the delays in [50], the greenhouse gases in [77], and the carbon dioxide in [69]. e exogenous inputs for the second stage or third stage have also been taken into account in many papers, such as the selling cost [73,74,77]; the fleet size and destination [56,74,77,80]; and the abatement expense in [69]. In addition, as the allocation of shared inputs in different divisions and stages, a few studies took into account the shared inputs such as the number of employees in [70] and in [70,91] took the number of employees as a shared input for different parallel divisions (Figure 4), while [91] assumed the number of employees (NE) as a shared input for different stages (Figure 2). In Figure 2, NE is the number of employees, AK is aviation kerosene, FS is fleet size, SC is sales cost, and TR is total revenue.
It should be noted that most researchers paid attention to the mainstream process which eventually produces revenue and took the undesirable outputs as additional outputs. Reference [69] focused on the carbon abatement process of airlines, taking the RPK and RTK as additional desirable outputs.

Dynamic DEA in Airline Efficiency.
In this section, we will introduce the application of dynamic DEA models as well as dynamic network DEA models in airline efficiency. Although there were plenty of previous studies evaluating intertemporal performance of airlines in the application of Malmquist productivity index or window analysis, they ignored the transition elements existing in airline operations. For example, the fleets and capital stock of an airline can be carried over from one period to another. In order to model the intertemporal features of these transition elements, scholars have established many dynamic DEA models considering the carryover, including the basic dynamic DEA model in [92]; the dynamic SBM model in [93]; the dynamic network DEA in [94]; the dynamic multiactivity network DEA in [95]; and the dynamic network SBM in [86].
As for the carryover activities, opinions varied in the carryover element selection. For papers that did not take network structure into consideration, dynamic factors like capital stock, fleet size, stockholder equity liabilities, and intangible assets were assumed as carryovers, that is, the outputs of the whole process in the previous term and the   Journal of Advanced Transportation inputs of the whole process in the subsequent period [58,61,76,81,97,[99][100][101]. For papers combining dynamic and network models, the selected carryovers are different in substages. e study in [75] selected net revenues and accident occurrence as desirable and undesirable carryovers, respectively, to the consumption division between consecutive periods. e authors of [59,64] also assumed that carry activities existed in consumption division and selected the number of fleet seats as a carryover. e study in [83] considered a self-owned fleet as a carryover to production division and waypoints as a carryover to service division in consecutive terms. Figures 3 and  5 present the dynamic structure in [58] and the dynamic network structure in [83], respectively. In Figure 3, NE is the number of employees, AK is aviation kerosene, and CS is capital stock. In Figure 5, ASK is available seat kilometers, and FATK is freight available ton-kilometers.

DEA Models considering Undesirable Outputs.
When assessing the efficiency of airlines, it is necessary to consider the generation of undesirable outputs in the DEA models. According to [9], there are about five approaches in modeling pollution-generating technologies at present: (1) Free disposability (strong disposability), an approach to treat undesirable outputs as free disposable inputs for the argument that the environment capacity is strong enough to dispose of bad outputs of environmentally detrimental products. (2) Weak disposability, in which the reduction of undesirable outputs requires a proportional reduction of desirable outputs. (3) Byproduction model. In this model, the inputs producing undesirable outputs are separated from the ones producing desirable outputs, and the two sets of efficiency scores are   averaged. (4) Weak G-disposability. With direction vectors included in the model, it indicates that with more inputs it is possible to produce less desirable output and more undesirable outputs. (5) Natural disposability and managerial disposability. Natural disposability is equal to free disposability, while managerial disposability treats inputs as outputs and the undesirable outputs are modeled as inputs.
Papers with these models employed in airline efficiency evaluation are limited at present. When considering the environmental efficiency of airlines, the Virtual Frontier Benevolent DEA Cross-Efficiency model [62]; Benevolent DEA cross PAC (Pollution Abatement Costs) model [102]; network SBM with weak disposability [69]; network SBM with weak disposability and with strong disposability [77]; RAM with weak disposability and with strong disposability [103]; Virtual Frontier Network RAM models with weak disposability [88]; network EBM with managerial disposability [85]; dynamic RAM with unified natural and managerial disposability [99] have been established to evaluate the energy efficiency of airlines. Among these researches, it was found that the model with weak disposability is more reasonable in distinguishing efficiency differences and confirming benchmarking airlines, while strong disposability is a more reasonable way in treating undesirable outputs. Further, under natural disposability, the indices related to undesirable output have a larger role in deciding benchmarking airlines.
On the other hand, with the increasing attention to the emissions control costs, there is a tendency to focus on the impact of environmental pressure on PAC. e study in [85] defined the pollution abatement cost as the ratio of the outputs when the undesirable outputs are freely disposed to the outputs when the undesirable outputs are weakly disposed of. is novel definition which utilized the two approaches modeling undesirable outputs can express the output loss of different disposability modes of undesirable outputs

Conclusions.
is paper reviews the application of DEA methods in airline efficiency with 130 articles in high-impact journals as samples.
e DEA models mainly consist of radial and nonradial models. For radial models, the standard CCR and BCC models, a combination of standard DEA and other methods, and extended and modified models are widely used in airline efficiency studies. For nonradial models, SBM and RAM models are popularly applied. In addition, the EBM model that unifies the features of radial and nonradial measures has been gradually employed in airline efficiency evaluation. In recent years, there is a trend that DEA models considering network structure and dynamic situation are constructed; with the increasing importance of environmental efficiency, approaches dealing with undesired outputs also arouse attention.
From the existing research results, we can know that the airline efficiencies are different for different periods and regions, different types of airlines, and different substages. But overall, the productivity of the international airline industry has been largely improved over the past 30 years, and the operational efficiency of airlines had tended to converge. Drivers of airline efficiency are from the firm level, industry level, and macroenvironment level, but there are slight differences in the results of these studies.
is review does not include airline efficiency papers using parametric methods and those investigating the efficiency of airports. We will expand the range of papers in the future.

Future Research Directions.
According to the review and combing of previous literature, we found that DEA and airline efficiency have the following main research directions in the future: Firstly, with respect to DEA models applied in airline efficiency, although numerous different DEA models have been developed and applied, there are also many DEA models that deal with more complex problems and tricky data that needed to be established. For example, models dealing with special types of data (such as ordinal data, negative data, and interval data) have not been applied in airline efficiency yet. But in practice, there are some special circumstances. For example, when airline profit is used as an indicator, it may be a negative value. Furthermore, sometimes the data may be an interval data rather than an exact value. Furthermore, with most airlines facing challenges from rising fuel prices and stricter environmental regulations, airline cooperation and alliance will become the trend. e application of DEA models considering airline competition and cooperation should be another important future topic.
In addition, radial and nonradial DEA models have been widely used in airline efficiency evaluation, but the application of EBM is still limited. Since the EBM model combines the feature of radial and nonradial measures to a unified framework, the extended DEA models based on EBM will be expected in the future. Secondly, regarding DEA network structure and dynamic structure applied in airline efficiency, there is room for further exploration. Apart from the production, service, and sales process, is there any other stage in the process of airline efficiency? And are there any other final outputs and independent or shared inputs at different stages that have not been considered? Upon dynamic DEA models, there are about three future research directions. First, since previous studies mostly took the past time periods as sample periods, it will be valuable and innovative if we can take advantage of other data prediction methodologies and dynamic DEA models to predict airline efficiency in the future time periods. Second, the carryovers found in previous literature are still limited (usually capital stock and fleet size). More transition elements that better reflect the dynamic efficiency of airlines need to be explored. Finally, the dynamic network DEA models with a longer time and more stages can be tried in airline efficiency research, which allows for a better exploration of the drivers of airline efficiency.
irdly, regarding the approaches considering undesirable outputs, only the free disposability, weak disposability, and managerial disposability approaches have been applied in the environmental efficiency evaluation of airlines, lacking the application of other pollution modeling approaches. What is more, since there is a tendency that the integrated DEA models will be more suitable for handling complex situations, the dynamic network DEA with approaches handling special types of data and with different pollution modeling approaches are needed in future research. Fourthly, apart from the model innovation and extension, there are several future research directions regarding the efficiency evaluation of airlines and the efficiency drivers. For example, the economic efficiency of airlines has been given much focus, but the social and safety efficiency of airlines have been paid much less attention. Since the development of airlines has a great impact on society, the related efficiency measurement will also be a hot research direction in the future. erefore, it can be more concerned with the noneconomic efficiency of airlines such as safety efficiency and carbon abatement efficiency. Fifthly, among the factors affecting airline efficiency, there is little research paying attention to the industry and macroenvironmental level factors. At present, most research focuses on the measurement and exploration of specific airline efficiency, which cannot assess impact in the context of the industry. As the pressure of environmental policies increases, it is necessary to further Journal of Advanced Transportation reveal the connection between environmental policies and airline efficiency, to answer questions like what is the impact of environmental policies on airline efficiency and how does it affect.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare no conflicts of interest.