Measurement of airlines’ capacity utilization and cost gap: Evidence from low-cost carriers

Journal of Air Transport Management 53 (2016) 186e198

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Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman

Measurement of airlines’ capacity utilization and cost gap: Evidence from low-cost carriers Ming-Miin Yu, Yu-Chun Chang*, Li-Hsueh Chen Department of Transportation Science, National Taiwan Ocean University, No. 2 Pei-Ning Road, Keelung 20224, Taiwan

a r t i c l e i n f o

a b s t r a c t

Article history: Received 29 September 2014 Received in revised form 7 February 2016 Accepted 8 March 2016 Available online 19 March 2016

The aim of this paper is to evaluate the capacity utilization and cost gap between actual and global longrun minimum costs. Based on the data for thirteen low-cost carriers around the world for the year 2010, an input-oriented data envelopment analysis model is used to estimate the physical capacity utilization and cost gap between actual and global long-run minimum costs. The empirical results show that more than half of low-cost carriers should improve their capacity utilization, and all low-cost carriers should enhance their market efficiency and reduce their excess costs. Of the thirteen low-cost carriers, three should improve their technical efficiency, four should re-distribute the mix of variable inputs, all thirteen should pay lower prices for all variable inputs, and ten should enhance the utilization rate of their fixed factors. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Low-cost carriers Data envelopment analysis Efficiency Capacity utilization

1. Introduction Low-cost carriers (LCCs) have existed in the airline industry for over 30 years. Since the LCCs have cost advantages over traditional airlines, they have grown rapidly. Their growth has promoted competition in the airline industry, and induced a sustained increase in passenger numbers and a larger network in recent decades. According to Airport Council International (2013), the European network had fewer than 6000 routes in 2001, but more than 10,000 in 2013. However, the cost advantages of LCCs are threatened by worsening economic conditions (International Air Transport Association, 2009). Hence, not all LCCs can achieve sustainability. Pearson and Merkert (2014) indicated that there were 27 LCC failures in their samples covering the 1993e2012 period. The International Air Transport Association and other international airline associations have warned that, in the airline industry, higher performance is the only way to achieve sustainability in the tough competitive environment (Assaf & Josiassen, 2012). Therefore, the operational performance assessment of LCCs should be a fundamental management activity. Capacity utilization and the cost gap between actual and global long-run minimum costs can provide useful information on how to improve LCCs’ performance. Therefore, this paper aims to analyze capacity utilization, the cost gap

* Corresponding author. E-mail address: [email protected] (Y.-C. Chang). http://dx.doi.org/10.1016/j.jairtraman.2016.03.005 0969-6997/© 2016 Elsevier Ltd. All rights reserved.

between actual and global long-run minimum costs, and their decomposition for LCCs. The results are expected to contribute to improvement in overall management of LCCs. Since the degree of capacity utilization depends on the ability of firms to utilize their fixed factors in the short run, and cost inefficiency often results from the inability to adjust fixed factors, capacity utilization is an important economic parameter of performance when analyzing firms’ behavior (Sahoo & Tone, 2009). Capacity utilization is generically defined as the ratio of actual output to potential output. The potential output can be defined in two alternative ways: physical concept and economic concept. Using the physical concept, the capacity output is defined as the maximum potential output when the variable inputs are fully utilized with existing plants and equipment (Johansen, 1968). In contrast, based on the economic concept, there are three definitions of capacity output. The first definition is the output level at the short-run minimum average cost (Cassel, 1937; Hickman, 1964; Berndt & Morrison, 1981). The second definition is the output level at which the short-run and long-run average cost curves are tangent (Klein, 1960; Segerson & Squires, 1990). The third definition is the output level at the maximum profit (Coelli et al., 2002). The main difference between physical and economic measures is that the physical measure of capacity output does not require information regarding input prices. Since the physical measure can eliminate the effect of input prices, this paper adopts the physical concept of capacity output to measure the capacity utilization. However, we measure physical capacity utilization in terms of

M.-M. Yu et al. / Journal of Air Transport Management 53 (2016) 186e198

inputs. In other words, capacity utilization is defined as the ratio of potential fixed input to actual fixed input in this paper, in which the potential fixed input is the minimum fixed input given the current output levels. Furthermore, the effect of input prices is reflected in the measure of market efficiency. Hence, this paper can provide more accurate directions for improvement for managers. In the field of performance evaluation, few studies have developed frontier-based methods for estimating capacity utilization. €re et al. (1989) introduced the frontier-based method to define Fa and measure the physical measures of capacity and capacity utilization. Coelli et al. (2002) decomposed capacity utilization into technical efficiency, economic capacity utilization and optimal capacity idleness, and also measured the contribution of the unused capacity of 28 international airline companies. Their results showed that 70% of the profit gap may be attributed to unused capacity. Sahoo and Tone (2009) proposed radial and non-radial methods to assess the physical and economic measures of capacity utilization of the Indian banking industry. Their results indicated that since competition was promoted after the financial sector reforms, efficiency was enhanced and excess capacity was reduced. However, €re et al. (1989) results in a the capacity utilization measured by Fa downward bias because they consider technical inefficiency and unused capacity to be two mutually exclusive components. Although Coelli et al. (2002) eliminate the aforementioned problem and treat technical inefficiency as a component of unused capacity, they adopt the radial method, which results in an upward bias to the utilization rates when some slacks remain after the full radial projection is achieved. Since the non-radial method proposed by Sahoo and Tone (2009) further solves the problem of slacks and considers technical inefficiency as a component of unused capacity, this paper follows Sahoo and Tone (2009) to use the non-radial input-oriented slack-based measure data envelopment analysis (SBM-DEA) model to measure capacity utilization and its decompositions in the context of LCCs around the world. However, the point of full capacity utilization may be not the point of minimum cost. In order to capture the contribution of capacities, the global long-run minimum cost should be computed, and the cost gap between the actual and global long-run cost minimum should be decomposed. The DEA-based cost efficiency model can be used to estimate the long-run minimum cost. However, the traditional cost efficiency measure neglects the presence of price differences between the decision making units (DMUs) (Tone, 2002). Camanho and Dyson (2008) relaxed the common set of prices for all DMUs to develop a new framework for cost efficiency assessments, and used the DEA analysis to account for the conditions of not-fully competitive markets in real life. When considering economic efficiency, they distinguished between market efficiency and Farrell cost efficiency.1 Based on their interpretation, market efficiency reflected the differential between the minimum cost with the current input prices and the minimum cost potentially attained under the conditions of fully competitive markets as a baseline. This reflected the ability to pay the minimal input prices under the current conditions of their market. In the airline industry, the input price differences across LCCs are not exogenously defined for the DMUs, but can depend on negotiation in real-life markets. The cost efficiency measure should have a baseline under the conditions of fully competitive markets in DEA analysis. Hence, this paper applies the model proposed by Camanho and Dyson (2008) to reflect cost reductions achievable via price adjustments in non-fully competitive LCC markets which are not

1 Farrell cost efficiency measures the ratio of the minimal cost given the current price levels at each DMU to produce the current outputs to the actual cost (Camanho and Dyson, 2008).

187

fully competitive. In addition, an LCC competes not only with other LCCs in the same market, but also with other LCCs in different markets. In order to achieve global cost efficiency, an LCC seeks not only the minimum input prices in its market but also the minimum input prices in the whole world. Hence, in examining global cost efficiency, this paper distinguishes between market efficiency and the current short-run cost efficiency. It also measures the local market efficiency and global market efficiency to capture the extent to which the LCCs succeed in incurring the minimal input prices under the current conditions of their local market or global market as well as the inefficiencies associated with the overpayment of resources. The contributions of this paper are threefold. First, we explore the capacity utilization of LCCs based on the SBM-DEA model. Second, we consider the input price and market differences to assess the local and global market efficiency of LCCs. Third, we decompose the cost gap between actual and global long-run minimum costs into the cost gaps between actual and technically efficient costs, between technically efficient and short-run minimum costs, between short-run minimum and local short-run minimum costs, between local and global short-run minimum costs, between global short-run minimum and local long-run minimum costs, and between local and global long-run minimum costs. The advantage of our approach in the measurement of LCCs’ capacity utilization and cost gap is that it not only provides more information for cost reduction target setting, but also overcomes the shortcomings of the Farrell cost efficiency measure when prices differ between LCCs. The method we propose provides information that is meaningful to managers. The rest of this paper is organized as follows. Section 2 presents a literature review on airline performance analysis using DEA models. Section 3 describes the methodology. Section 4 examines the capacity utilization and cost gap between the actual and global long-run minimum costs of LCCs, and also explores the market efficiency measure when prices differ between LCCs in markets. Section 5 concludes the paper. 2. The use of DEA in performance analysis of airlines Although various methods have been adopted to measure the performance of airlines (e.g. ratio indicators; cost models; total factor productivity approach; stochastic frontier approach), contemporary research has applied the DEA methods to evaluate airline performance in recent years. However, most DEA studies of performance evaluation of airlines focused on computing technical efficiency scores or productivity change. In terms of technical efficiency, Schefczyk (1993), Barbot et al. (2008) and Cheng (2010) used traditional DEA models to measure the efficiency of airlines. Tofallis (1997) did not consider inputs to be substitutes for each other, and proposed a modified DEA approach to study the input efficiencies of 14 major international passenger carriers for the year 1990. Scheraga (2004), Barros and Peypoch (2009), Assaf and Jossiassen (2011), Wu et al. (2013) and Lee and Worthington (2014) applied DEA models to assess technical efficiency of airlines, and used regression models to investigate the impact of environmental variables on the estimated efficiency. Chiou and Chen (2006) used the perspective of cost efficiency, cost effectiveness and service effectiveness to evaluate the performance of 15 domestic air routes in Taiwan by separate DEA models. Jang et al. (2011) used an SBM model to assess the technical efficiency of 15 major US airlines for the period of 2000e2006. Zhu (2011), rrez (2014), Gramani (2012), Lu et al. (2012), Lozano and Gutie Tavassoli et al. (2014), Li et al. (2015) and Mallikarjun (2015) developed various network DEA (NDEA) models to analyze the sub-process and overall efficiencies of airlines. Yu (2012) developed

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the Enhanced-Russell measure NDEA model for simultaneously evaluating the production efficiency, service efficiency and operational efficiency of 11 air routes of a domestic airline in Taiwan. Arjomandi and Seufert (2014) utilized bootstrapped DEA models to analyze the technical efficiency of 48 major airlines around the world from 2007 to 2010. Chang et al. (2014) studied the efficiency of 27 airlines around the world in 2010 by using an extended environmental SBM-DEA model. Chang and Yu (2014) used the SBM-NDEA model to assess the efficiency of 16 LCCs around the world on the basis of concurrently considering the production and consumption processes. Choi et al. (2015) investigated the efficiencies of 12 US airlines from 2008 to 2011 with a service qualityadjusted DEA model. In terms of productivity, Semenick Alam and Sickles (2000) used DEA to examine the productivity changes of US airlines between €re et al. (2007) estimated the productivity 1970 and 1990. Fa changes of 13 US airlines after deregulation from 1979 to 1994. Greer (2008) applied DEA to calculate the productivity changes of the major US passenger airlines from 2000 to 2004. Chow (2010) used DEA to study the productivity changes of Chinese airlines after the entries of these non-state-owned airlines. Assaf (2011) applied a bootstrapped DEA model to measure productivity changes of 18 major UK airlines during the period 2004e2007. Jang et al. (2011) also used DEA to evaluate the productivity changes of 15 major US airlines for the period 2000e2006. Pires and Fernandes (2012) applied DEA to assess the productivity changes of 42 airlines around the world from 2001 to 2002. Barros and Couto (2013) used DEA to evaluate productivity changes of European airlines between 2000 and 2011. Cao et al. (2015) adopted DEA to measure the productivity changes of China's airlines in the period of reform. Lee et al. (2015) applied DEA to measure the productivity growth of 35 airlines for the period 2004e2011, taking both desirable and undesirable outputs into consideration. Scotti and Volta (2015) proposed a biennial MalmquisteLuenberger index to measure the productivity changes of 18 major European airlines over the 2000e2010 period, and investigated the main determinants of airlines' productivity changes. Recently, a few studies have also appeared covering issues such as energy efficiency of airlines (Cui and Li, 2015), profit efficiency of airlines (Coelli et al., 2002; Lee & Johnson, 2012), cost efficiency of airlines (Merkert & Hensher, 2011) and capacity utilization of airlines (Coelli et al., 2002). In addition, some studies have investigated the performance of LCCs. Most of them aimed at comparing the performance of full service airlines and LCCs (e.g. Barbot et al., 2008; Cheng, 2010; Jang et al., 2011; Lu et al., 2012; Arjomandi & Seufert, 2014; Lee & Worthington, 2014; Choi et al., 2015). However, Chang and Yu (2014) indicated that the operations of LCCs and full service carriers were very different. Hence, their data set only included the LCCs. Although capacity utilization of airlines is a big issue (Coelli et al., 2002), according to the authors’ knowledge, no study assesses the capacity utilization of LCCs. Hence, this paper tries to fill this void and further investigate the cost gap between actual and global long-run minimum costs. 3. Methodology 3.1. Production technology and capacity utilization In this paper, we use the non-radial input-oriented SBM-DEA model and the definition of physical capacity utilization proposed by Sahoo and Tone (2009) to evaluate the performance of LCCs. It is assumed that there are K LCCs, and that each LCC uses a vector of M inputs, x ¼ ðx1 ; …; xM Þ2RM þ , to produce a vector of S outputs, y ¼ ðy1 ; …; ys Þ2RSþ . The M inputs can be divided into I variable inputs and J fixed inputs. Denote the variable and fixed

f

f

J

input vectors by xv ¼ ðxv1 ; …; xvI Þ2RIþ and xf ¼ ðx1 ; …; xJ Þ2Rþ , respectively. The variable and fixed input price vectors are repref f J sented by wv ¼ ðwv1 ; …; wvI Þ2RIþ and wf ¼ ðw1 ; …; wJ Þ2Rþ , respectively. The production technology can be defined as T ¼ fðx; yÞ : x can produce yg. The respective output and input sets can be denoted by PðxÞ ¼ fy : ðx; yÞ2T cxg andLðyÞ ¼ fx : ðx; yÞ2T cyg. Following Sahoo and Tone (2009), the physical capacity utilization can be obtained by solving the following input-oriented SBM-DEA model with a variable returns-to-scale technology2:

0 *

q ¼ min

1 J sf  X 1 jo @1  A J j¼1 xf jo

s.t. K X

lk xfjk þ sfjo ¼ xfjo ; j ¼ 1; …; J;

k¼1 K X

lk ysk  yso ; s ¼ 1; …; S;

k¼1 K X

lk ¼ 1;

k¼1

lk  0; k ¼ 1; …; K; f

sjo  0; j ¼ 1; …; J:

(1)

where q* is the measure of the physical capacity utilization of LCC o.

3.2. Market efficiency Since the real airline markets are not perfectly competitive, input prices among LCCs are different. However, Koopmans (1951) indicated that a necessary and sufficient condition for Pareto efficiency was the existence of a common unit price by firms, i.e., the law of one price. Hence, in order to capture the levels of deviations from fully competitive settings leading to price differences across LCCs, we also assess market efficiency. In addition, in order to consider the situations where LCCs may serve different local markets and the fixed inputs cannot be adjusted in the short run, market efficiency is further decomposed into short-run local market efficiency, short-run global market efficiency, long-run local market efficiency and long-run global market efficiency. Following Camanho and Dyson (2008), these four market efficiencies can be respectively defined as follows: Short-run local market efficiency

MELSR ¼

C LSR ðyÞ ; C SR ðyÞ

(2)

Short-run global market efficiency

2 Metters et al. (1999) suggested that the variable returns-to-scale model should be chosen when modeling observations of largely varying size. Since LCCs have different sizes, the variable returns-to-scale technology constraint is adopted in the proposed model.

M.-M. Yu et al. / Journal of Air Transport Management 53 (2016) 186e198

MEGSR ¼

C GSR ðyÞ ; C SR ðyÞ

(3)

Long-run local market efficiency

MELLR ¼

C LLR ðyÞ ; C LR ðyÞ

MEGLR ¼

C GLR ðyÞ : C LR ðyÞ

h i h i h CðyÞ  C GLR ðyÞ ¼ CðyÞ  C TE ðyÞ þ C TE ðyÞ  C SR ðyÞ þ C SR ðyÞ i h i h  C LSR ðyÞ þ C LSR ðyÞ  C GSR ðyÞ þ C GSR ðyÞ i h i  C LLR ðyÞ þ C LLR ðyÞ  C GLR ðyÞ

(4)

Long-run global market efficiency

(5)

where C LSR ðyÞ is the local short-run minimum cost, which is the actual fixed cost plus the minimal variable cost given the minimum variable input price levels observed in these LCCs in the same local market to produce the current outputs; C SR ðyÞ is the short-run minimum cost, which is the actual fixed cost plus the minimal variable cost given the current variable input price levels observed at each LCC to produce the current outputs; C GSR ðyÞ is the global short-run minimum cost, which is the actual fixed cost plus the minimal variable cost given the minimum variable input price levels observed in all LCCs in the data set to produce the current outputs; C LLR ðyÞ is the local long-run minimum cost, which is the minimal cost given the minimum fixed and variable input price levels observed in these LCCs in the same local market to produce the current outputs; C LR ðyÞ is the long-run minimum cost, which is the minimal cost given the current fixed and variable input price levels at each LCC to produce the current outputs; and C GLR ðyÞ is the global long-run minimum cost, which is the minimal cost given the minimum fixed and variable input price levels observed in all LCCs in the data set to produce the current outputs. Due to space limitations, these functions of the local short-run minimum cost, shortrun minimum cost, global short-run minimum cost, local long-run minimum cost, long-run minimum cost and global long-run minimum cost are relegated to Appendix A. 3.3. Decomposition of the cost gap between actual and global longrun minimum costs Since the ratio decomposition of physical capacity utilization in the non-radial model is impossible (Sahoo & Tone, 2009), the cost gap between the actual and global long-run minimum cost, which is based on the concept of cost efficiency, is applied to capture various meaningful components. We extend the cost efficiency measurement method proposed by Camanho and Dyson (2008) to build a new decomposition framework of the cost gap between actual and global long-run minimum cost. Under the proposed framework, the cost gap between actual and global long-run minimum cost results from three factors: technical inefficiency, allocative inefficiency and market inefficiency.3 Due to the conditions of markets in the LCC sector which are not fully competitive, the impact of different prices between LCCs in the same local market or in the global one on cost efficiency can thus be investigated. Hence, we further capture the extent to which the LCCs succeed in incurring the minimal input prices under the current conditions of their local market or global market by measuring the local market efficiency and global market efficiency. Consequently, the cost gap between actual and global long-run minimum costs and its components can be shown as follows:

3 The measures of technical inefficiency and allocative inefficiency constitute the €re et al. (1985). This convenmeasure of Farrell cost inefficiency developed by Fa tional measure assumes that input prices are fixed.

189

(6) where CðyÞ is the actual cost, and C TE ðyÞ is the technically efficient cost where fixed and variable inputs are on the efficiency frontier. The first component refers to the excess cost due to technical inefficiency, the second component denotes the excess cost due to allocative inefficiency, the third component represents the excess cost due to not paying for the variable inputs at the local minimum prices, the fourth component refers to the excess cost due to not paying for the variable inputs at the global minimum prices, the fifth component indicates the excess cost due to the fixed cost not being adjusted to the local minimum cost level in the short run, and the sixth component represents the excess cost due to not operating at a global long-run cost minimizing level. The third and fifth components result from local market inefficiency, and the fourth and sixth components stem from global market inefficiency. In order to compute the cost gap between the actual and global longrun minimum cost and its components, the input-oriented models must be used to calculate the functions of the technically efficient cost, the short-run minimum cost, the local short-run minimum cost, the global short-run minimum cost, the local long-run minimum cost and the global long-run minimum cost in Eq. (6). To further save space, the technically efficient cost function is introduced in Appendix B.

4. Empirical implementation 4.1. Data and specification of inputs and outputss The data relate to 13 LCCs in operation in 2010 and are collected from annual reports of airlines. Although there are more than 13 LCCs in the airline industry, we only obtained 13 sets of observations for the model due to the confidentiality of business information (a list of 13 LCCs is presented in Appendix C). Following Barbot et al. (2008) and Chang and Yu (2014), staff and fuel consumption were selected as variable inputs for this paper. Staff is measured by the number of full-time employees on the payroll and by then dividing the total labor cost of the carrier by the total number of staff to obtain the price of staff. The fuel price is measured by dividing the total fuel cost by fuel consumption. As Doganis (2010) indicated, those costs which can be directly avoided in the short run such as fuel cost and labor cost are treated as variable costs. Therefore, staff and fuel are treated as variable inputs. In addition, Fageda et al. (2015) found that new LCC models applied different methods in fleet selection, such as by mixing the types of aircraft. In order to consider the differences in aircraft size, this paper has therefore selected the total number of seats of owned and leased aircraft provided by the LCCs as another input to represent fleet size. It includes owned and leased aircraft, with the owned aircraft involving maintenance and depreciation costs, and the leased aircraft involving maintenance and leasing costs. Since the numbers of leased aircraft essentially remain constant for a given period or level of activity, the total number of seats of owned and leased aircraft is treated as a fixed input. Furthermore, the maintenance and depreciation costs will increase as a fleet becomes older, and an LCC's aircraft may be leased. The cost of the fleet is obtained by dividing the sum of the maintenance,

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depreciation and leasing costs by the total number of seats. LCCs normally offer no interlinking with other carriers and avoid transfers between flights. Their focus is very much on a point-topoint network (Doganis, 2006). Hence, this paper has selected the network as another input. An LCC's network size maybe observed through the number of destinations. Therefore, a network is measured by the number of destinations provided by LCCs. The price of the network is measured by dividing total airport charges and other costs by the number of destinations. LCC's other costs include ground handling charges, advertising fees, commission fees, and so on. Although in an airline's annual report these costs are still regarded as operating costs, according to Boeing's network and hub analysis report (2015), network strategies must be accompanied by effective fleet plans. Airlines link their network strategies to their long-term requirements for airplane replacement and fleet growth to create the most efficient, capable, and flexible fleet. Since the network strategy is part of the long-term planning process, we therefore treat it as a fixed input in explaining the LCC's flight network effectiveness. Johansen (1968) defined “the maximum amount that can be produced per unit of time with existing plant and equipment, provided that the availability of variable factors of production are not limited’’ as the capacity of existing plant and equipment using the concept of the production function. However, since transportation services cannot be stored, there are two separate measures of outputs: the produced output type (e.g., available seatkilometers) and the consumed output type (e.g., revenue passenger-kilometers) (Karlaftis, 2004). Fielding et al. (1985) define the service effectiveness as the ratio of consumed output to produced output, which implies that the production process is different from the consumption process (Yu & Lin, 2008). This paper follows Johansen (1968)’s definition, whereby available seatkilometers (ASK) are selected as the produced output in the production process, since we can easily define the production technology and use distance functions to provide a functional representation of the boundary of the production sets. ASK is the sum of the products obtained by multiplying the number of seats carried on each flight stage by the stage distance. The data descriptions are summarized in Table 1. The descriptive statistics of 13 LCCs in 2010 are presented in Table 2. Since the exchange rate and real price among countries are different, we use the purchasing power parity (PPP) index obtained from World Bank to deflate these price variables to eliminate the difference in exchange rates and currency values. According to

Table 2, the maximum units of staff among the 13 LCCs is 349,017, meanwhile the minimum units is 16,147. The substantial difference in units of staff is due to the great variability in company sizes. Observing the units of a network is another way to understand the size of an airline. The maximum units in a network is 250 and the minimum units in a network is only 52. Furthermore, it is likely that different airlines have adopted different fuel hedging programs, which can be seen by the wide range of variation in fuel prices indicated by Table 2. Depreciation cost of the aircraft and the maintenance fee will influence the unit price of a fleet. The maximum fleet unit price is USD 31,000, but the minimum fleet price is only USD 7000. As for the output of this paper, the highest ASK is 157,512 and the lowest is 9170 among all the 13 LCCs. The input and output variables have quite large standard deviations relative to their sample means. Hence, it is suitable to adopt the DEA model under the assumption of variable returns-to-scale. In addition, price variables have large differences between their maximum and minimum values. This suggests that LCCs operate in non-fully-competitive markets. According to the data presented in Fig. 1 to Fig. 4, a number of points can be made. Firstly, the sample data have great variability in company sizes. For example, the largest LCC, Southwest, is 20 times larger in terms of staff members compared with small US LCCs such as Allegiant Air. Secondly, it appears that US companies are larger than European companies with the exception of Allegiant Air. This can be partly explained by the airline deregulation which started in the US from 1978 and in the EU from 1987. Figs. 1 to 4 also illustrate a wide range of variation in factor prices. Southwest has the highest labor price, followed by JetBlue. It is thus interesting to measure LCCs’ capacity utilization due to the variability in company sizes. Another point worth mentioning is that Southwest has the highest number of seats, but its fleet price is not the lowest, which is most likely caused by it having the highest maintenance cost among LCCs. Moreover, US Airways has recorded the highest unit in fuel, because they have not entered into any new transactions to hedge their fuel consumptions. Finally, although Southwest only has 69 destinations, it has reported $807 million in related airport charges, hence it has the largest network price. This variability in LCC factor prices is not commonly referred to as the law of one price, so it is also necessary to account for the conditions of real-life markets, which often are not fully competitive.

Table 1 Data descriptions of variables. Variables Variable inputs Staff Quantity Unit Price Fuel Quantity Unit Price Fixed inputs Fleet Quantity Unit Price Network

Output Traffic

Quantity Unit Price

Definitions

Units

The The The The

Persons USD thousands Thousands of gallons USD

number of full-time employees on the payroll. total salary of the full-time employees divided by the number of full-time employees. fuel consumption, which is the total fuel used on the total block times. total fuel cost divided by the fuel consumption.

The total number of seats of owned and leased aircraft. The sum of the maintenance, depreciation and leasing costs divided by the total number of seats. The number of destinations The sum of airport charges and other costs divided by the number of destinations. The airport charges include aircraft landing charges, charges for the processing of passengers and freight and other charges related to the use of airport infrastructure, and the other costs include ground handling charges, advertising fees, commission fees and so on.

Seats USD thousands

Available seat-kilometers, which is measured by seats available for passengers multiplied by the number of kilometers flown.

Million seat-km

Destinations USD thousands

Data source

The annual reports of 13 LCCs

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191

Table 2 Descriptive statistics of LCCs in 2010. Input

Output

Staff

Fuel

Number of employee Price (000$ USD) Gallons

Fleet

Network

Traffic

Price (USD) Number of seats Price (000$ USD) Number of destinations Price (000$ USD) ASK (million)

(000) Mean Std. dev. Maximum Minimum

10,567 102,887 349,017 16,147

73 16 106 54

474,738 462,968 1,459,677 18,547

2.4 0.9 4 0.4

26,913 20,551 74,701 6820

21 7 31 7

121 67 250 52

12,356 8118 33,362 2341

56,526 45,248 157,512 9170

Fig. 1. Input data– Number of employees.

Fig. 2. Input data– Fuel consumption.

4.2. Empirical results and discussion The estimated values of physical capacity utilization, technical efficiency, cost efficiency and market efficiency for each LCC are shown in Table 3. Cost efficiency is further divided into short-run and long-run cost efficiencies, while market efficiency is separated into short-run local market, short-run global market, longrun local market and long-run global market efficiencies. However, in order to understand the effect of price adjustments and the

effect of levels and the mix of inputs, we apply the conventional €re et al. (1985) to assess the cost efficiency, approach proposed by Fa which means that the short-run and long-run cost efficiencies are the respective measures of the potential short-run and long-run cost reductions achievable given the current input prices at each LCC. In Table 3, the average score of capacity utilization is 0.848, indicating that 15.2% of the capacities of LCCs are not utilized. For the individual carriers, US Airways, Southwest, JetBlue, WestJet, ExpressJet and Allegiant Air have the best capacity utilization

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Fig. 3. Input data– Number of seats.

Fig. 4. Input data– Number of destinations.

values of 100%, implying that the actual levels of the total number of seats and the number of destinations of those carriers are the same as their long-run optimal levels of these two fixed inputs. In other words, they fully utilize their fixed inputs with an appropriate amount of inputs to produce the current output levels. On the other hand, SkyWest exhibits lower capacity utilization, and only utilizes 35.3% of its capacity, indicating that SkyWest should reduce its total number of seats and the number of destinations at the current level of ASK. In addition, although Allegiant Air has the lowest ASK, it has full capacity utilization. This result implies that a carrier having higher ASK does not mean that it can achieve better capacity utilization, because capacity utilization is used to describe the concept in terms of reduction of fixed inputs to produce a given level of output. Since technical efficiency is one component of physical capacity utilization (Coelli et al., 2002), we also compute the technical efficiency scores for individual carriers. From Table 3, it can be seen that if Alaska Air, AirTran and Aer Lingus want to enhance their capacity utilization, they must improve their technical inefficiency. However, full capacity utilization does not always represent cost

minimizing behavior. It is necessary to further investigate the short-run cost efficiencies for individual carriers. In addition, in order to understand the level of cost savings when fixed and variable costs can be adjusted, the long-run cost efficiency is also assessed. Table 3 shows that 8 out of 13 LCCs achieve 100% shortrun cost efficiency, and 4 achieve 100% long-run cost efficiency. US Airways, Southwest, JetBlue, WestJet, ExpressJet, Allegiant Air, EasyJet and Ryanair are the efficient carriers in terms of short-run cost, in which the capacity utilization of EasyJet and Ryanair is less than one, implying that these carriers can achieve short-run cost minimizing behaviors even though they have some idle capacity. This result4 echoes the argument of Coelli et al. (2002) and indicates that it is unlikely that the point of maximum physical

4 Based on the principle of short-run profit maximization, Coelli et al. (2002) have argued that it was unlikely that the point of maximum physical output capacity and the short-run profit maximizing point would ever coincide. Hence, if an increase in capacity utilization reduced short-run profit, the optimal behavior of the specific firm was to have some idle capacity.

M.-M. Yu et al. / Journal of Air Transport Management 53 (2016) 186e198

193

Table 3 Capacity utilization and efficiency. Airlines

Capacity utilization

Technical efficiency

Short-run cost efficiency

Long-run cost efficiency

Short-run local market efficiency

Short-run global market efficiency

Long-run local market efficiency

Long-run global market efficiency

US Airways Group Southwest Alaska Air Group SkyWest JetBlue AirTran WestJet ExpressJet Allegiant Air EasyJet Ryanair Aer Lingus Norwegian Mean

1.000

1.000

1.000

0.820

0.537

0.265

0.585

0.282

1.000 0.840

1.000 0.784

1.000 0.834

1.000 0.740

0.579 0.480

0.281 0.257

0.579 0.458

0.281 0.257

0.353 1.000 0.904 1.000 1.000 1.000

1.000 1.000 0.874 1.000 1.000 1.000

0.858 1.000 0.883 1.000 1.000 1.000

0.599 1.000 0.875 0.935 0.765 1.000

0.708 0.556 0.632 0.617 0.372 0.921

0.482 0.272 0.322 0.348 0.277 0.498

0.774 0.429 0.533 0.539 0.477 0.921

0.433 0.242 0.299 0.300 0.267 0.498

0.628 0.643 0.784 0.877 0.848

1.000 1.000 0.820 1.000 0.960

1.000 1.000 0.874 0.873 0.948

1.000 0.962 0.760 0.686 0.857

0.411 0.548 0.698 0.703 0.597

0.268 0.361 0.361 0.371 0.336

0.387 0.569 0.568 0.679 0.577

0.263 0.375 0.350 0.417 0.328

Note: (1) Short-run cost efficiency is defined as the ratio of the short-run minimum cost to the actual cost; (2) long-run cost efficiency is defined as the ratio of the long-run minimum cost to the actual cost.

capacity and the short-run cost minimizing point will ever coincide. This suggests that the maximum scale measure is not very meaningful. It is not sensible to suggest that a firm operates at full capacity, because any decrease in fixed inputs might result in an increase in cost. In other words, when a decrease in capacity utilization will reduce the short-run cost, it is better for carriers to bear some idle capacity. In terms of the long-run cost efficiency, Southwest, JetBlue, Allegiant Air and EasyJet achieve long-run cost efficiency. The result indicates that the current levels of resources of those carriers are correct in the long run, but other carriers use an inappropriate level of resources and should adjust their costs to the corresponding long-run levels. Since LCCs operate in markets which are not fully competitive, such as Southwest, Alaska Air, Ryanair and Aer Lingus,5 the shortrun and long-run market efficiency should be explored to capture the levels of deviations from fully competitive settings leading to price differences across LCCs. In addition, LCCs may operate in different local markets. Hence, the local market and global market efficiencies are also investigated. Based on our data set, there are two local markets: the American market and the European market. US Airways, Southwest, Alaska Air, SkyWest, JetBlue, AirTran, WestJet, ExpressJet and Allegiant Air mainly operate in the American market, while EasyJet, Ryanair, Aer Lingus and Norwegian mainly operate in the European market. In Table 3, the results indicate that, whether in the short run or long run, no LCCs can achieve 100% local and global market efficiencies. In the short run, Allegiant Air has better market efficiency in the American market, while Aer Lingus and Norwegian achieve better market efficiency in the European market. In terms of short-run global market efficiency, all LCCs should strive to search for ways to reduce variable input prices if they want to lower their costs. With regard to the long-run local market efficiency, the set of input prices for Allegiant Air is closer to the set of minimum input prices in the American market, while that for Norwegian is closer to the set of minimum

5 Although both Southwest and Alaska Air operate in the American market, Southwest is a traditional LCC, but Alaska Air belongs to the hybrid LCC category, which adopts features of full service airlines. The traditional and hybrid LCCs adopt different business models, in terms of fleet composition, airport and route choice, carrier's service and pricing policy. Hence, the American market is not fully competitive. Similarly, Ryanair is a traditional LCC, while Aer Lingus is a hybrid LCC, so the European market is not fully competitive. Another 9 LCCs also are either traditional LCCs or hybrid LCCs.

input prices in the European market. Finally, all LCCs should make more effort to control their input prices, because if they could pay for their inputs at the global minimum prices, on average, the cost could be only 32.8% of the long-run cost and 28.1% of the actual cost. Furthermore, we compute the cost gap between actual and global long-run minimum costs and its components. The results are presented in Table 4. In terms of the cost gap between actual and global long-run minimum costs, all carriers should improve their resource utilization in order to narrow the cost gap. Moreover, the cost gap between actual and global long-run minimum costs can be decomposed into six components: the cost gaps between actual and technically efficient costs, between technically efficient and shortrun minimum costs, between short-run minimum and local shortrun minimum costs, between local and global short-run minimum costs, between global short-run minimum and local long-run minimum costs, and between local and global long-run minimum costs. In Table 4, the results of the cost gap between actual and technically efficient costs show that there is no cost gap for US Airways, Southwest, SkyWest, JetBlue, WestJet, ExpressJet, Allegiant Air, EasyJet, Ryanair and Norwegian, indicating that these carriers operate with technical efficiency. The remaining carriers should improve their technical inefficiency. The result of the cost gap between technically efficient and short-run minimum costs indicates that, given the current input price levels, US Airways, Southwest, JetBlue, WestJet, ExpressJet, Allegiant Air, EasyJet, Ryanair and Aer Lingus operate at a cost minimizing point in the short run. Other carriers should improve their resource allocation in the short run. In terms of the cost gap between the short-run minimum cost given the current variable input price levels at each LCC and local short-run minimum cost, the results show that no carriers pay for all their variable inputs at the local minimum cost in the individual local markets. In the American market, it is easier for Allegiant Air to attain the local short-run minimum cost than for other carriers, while Aer Lingus and Norwegian find it easier to achieve the local short-run minimum cost than other carriers in the European market, indicating that these carriers operate in favorable cost conditions compared to the other carriers in the respective markets. From Figs. 1e2, we can find that Allegiant Air and Norwegian respectively pay the minimum price for fuel consumption and hire the minimum number of full-time employees in the American and European markets, and their sizes are smaller than to other

194

M.-M. Yu et al. / Journal of Air Transport Management 53 (2016) 186e198

Table 4 Cost gap between actual and global long-run minimum costs and its components. Airlines

CðyÞ  C GLR ðyÞ

CðyÞ  C TE ðyÞ

C TE ðyÞ  C SR ðyÞ

C SR ðyÞ  C LSR ðyÞ

C LSR ðyÞ  C GSR ðyÞ

C GSR ðyÞ  C LLR ðyÞ

C LLR ðyÞ  C GLR ðyÞ

US Airways Group Southwest Alaska Air Group SkyWest JetBlue AirTran WestJet ExpressJet Allegiant Air EasyJet Ryanair Aer Lingus Norwegian Mean

8,693,484 8,044,301 2,905,337 2,001,418 2,795,129 1,904,416 1,485,314 2,743,838 300,088 2,768,670 2,259,469 1,142,980 1,017,750 2,927,861

0 0 436,705 0 0 203,842 0 0 0 0 0 196,629 0 64,398

0 0 157,955 385,094 0 98,697 0 0 0 0 0 0 181,018 63,290

5,240,978 4,703,531 1,555,699 677,193 1,636,538 837,811 790,393 2,165,742 46,982 2,210,959 1,598,833 411,311 370,100 1,711,236

3,076,323 3,340,770 665,705 523,114 1,046,143 704,812 557,007 327,299 253,106 538,805 660,636 458,661 412,479 966,528

2,434,151 3,340,770 445,914 135,308 578,239 470,333 323,387 302,780 253,106 448,595 660,636 181,554 201,987 ¡752,059

2,810,334 3,340,770 535,187 551,325 690,687 529,587 461,301 553,577 253,106 467,501 660,636 257,932 256,140 974,468

carriers’. Hence, they more easily adjust the quantity of fuel consumption and the salary of the full-time employees to achieve the minimum costs in respective markets. In addition, although Aer Lingus does not pay the minimum prices for fuel consumption and the minimum salary for full-time employees, it uses relatively low quantities of full-time employees and fuel consumption. This result lets Aer Lingus have a smaller gap between the short-run minimum and local short-run minimum variable costs. With regard to the cost gap between local and global short-run minimum costs, the results indicate that no carriers use the optimal global variable cost to produce outputs. However, compared to other carriers, US Airways and Southwest find it more difficult to achieve the global short-run minimum costs. As can been seen in Figs. 1e2, US Airways pays the highest price for fuel consumption, and Southwest pays the highest salary for the full-time employees among 13 LCCs. In addition, they have larger operational sizes. Hence, they have more excess costs in both the American market and the global market. The results of the cost gap between global short-run minimum cost and local long-run minimum cost show that all carriers will increase their total costs if they use the local minimum prices to buy their inputs. These carriers should make more effort to reduce the costs of their staff and fuel, so as to achieve the global minimum variable costs. This means that if these carriers can pay the global minimum prices for fuel consumption and salary, they will obtain more cost savings compared to paying the local minimum prices for all inputs. In addition, it is noteworthy that the local short-run minimum costs of Southwest, Allegiant Air and Ryanair are equal to their local long-run minimum costs, respectively,6 indicating that Southwest, Allegiant Air and Ryanair operate at their optimal local capacity levels, respectively, if they can pay the local minimum price for fuel consumption and the local minimum salary for full-time employees. In other words, the local short-run and long-run average cost curves of Southwest, Allegiant Air and Ryanair are tangent at the current output levels. Finally, the cost gap between local and global long-run minimum costs is analyzed. From Table 4, it can be seen that, from a global perspective, all carriers should modify the problem of overpayment for inputs. However, the global short-run minimum costs of Southwest, Allegiant Air and Ryanair are equal to their global long-run minimum costs, respectively,7 implying that Southwest, Allegiant Air and

6 The gap between the local short-run and long-run minimum costs can be calculated by using the value in the sixth column in Table 4 minus the value in the seventh column in Table 4. 7 Similarly, the gap between the global short-run and long-run minimum costs can be calculated by using the value in the seventh column in Table 4 minus the value in the eighth column in Table 4.

Ryanair operate at their global capacity level if they can achieve the global short-run minimum costs. Similarly, this means that the global short-run and long-run average cost curves of Southwest, Allegiant Air and Ryanair are tangent at the current output levels. This result also indicates that their costs based on the local minimum input prices are higher than those based on the global minimum variable input prices. Although all carriers should make more efforts to pay lower prices for all of their variable inputs, they also have different directions for improvement. US Airways, JetBlue, WestJet and ExpressJet should focus on improving resource utilization in the long run. Alaska Air, AirTran and Aer Lingus should increase their technical efficiency. SkyWest should re-distribute the mix of variable inputs, and at the same time improve its resource utilization in the long run. Norwegian should enhance its resource utilization in the long run.

5. Conclusions Although many studies have employed DEA models to measure the technical efficiency of airlines at the company level, no study has paid attention to the issue of the capacity utilization of LCCs using DEA models. In order to fill this void, this paper uses an inputoriented DEA model to assess the capacity utilization, market efficiency and cost gap between the actual and global long-run minimum costs. The cost gap between the actual and global long-run minimum costs can be further decomposed into six components. The first component is the cost gap between actual and technically efficient costs, which is used to capture the excess cost due to technical inefficiency. The second component is the cost gap between technically efficient and short-run minimum costs, which indicates the excess cost due to allocative inefficiency. The third and fifth components are the cost gaps between short-run minimum and local short-run minimum costs, and between global short-run minimum and local long-run minimum costs, respectively, which represent the excess cost due to local market inefficiency. The fourth and sixth components are the cost gaps between local and global short-run minimum costs, and between local and global long-run minimum costs, respectively, which refer to the excess cost due to global market inefficiency. By decomposing the cost gap between actual and global long-run minimum costs, we can provide the directions of cost reduction. The main difference between our paper and other studies is that we take the situation that firms operate in markets which are not fully competitive into consideration; this more closely matches real life. We illustrate our method on a real case study of 13 LCCs around the world for the year 2010. Our empirical results indicate that, first, more than half of the

M.-M. Yu et al. / Journal of Air Transport Management 53 (2016) 186e198

LCCs should improve their capacity utilization, in which Alaska Air, AirTran and Aer Lingus can increase their capacity utilization by improving the technical inefficiency. Second, the relationship between output and capacity utilization may be not positive, such as for Allegiant Air, because capacity utilization is measured in terms of inputs. Third, more than half of the LCCs achieve the full shortrun cost efficiency, but only Southwest, JetBlue, Allegiant Air and EasyJet achieve the full long-run cost efficiency. Although EasyJet and Ryanair do not have full capacity utilization, they achieve the short-run cost efficiency, indicating that it is better for them to bear some idle capacity, which echoes the argument of Coelli et al. (2002). Fourth, in the markets which are not fully competitive, none of the LCCs achieves market efficiency, because they don't pay the minimum input prices. Fifth, all LCCs should improve their resource utilization to narrow the cost gap. Sixth, Allegiant Air, Aer Lingus and Norwegian more easily achieve the minimum costs in respective markets due to the favorable cost conditions, such as paying the minimum price or quantity for variable inputs, and smaller operational size, whereas US Airways and Southwest have more excess costs in both the American market and the global market because they pay higher prices for variable inputs and have larger operational sizes. Seventh, compared to paying the local minimum prices for all inputs, these 13 LCCs can obtain more cost savings by paying the global minimum prices for variable inputs. Eighth, Southwest, Allegiant Air and Ryanair can operate at the optimal local and global capacity levels, respectively, by paying the local and global minimum prices for variable inputs, respectively. Finally, since the sources of excess costs among LCCs are different, LCCs should have different directions for improvement to reduce their costs. However, one of the limitations of this paper is that the application does not take environmental factors into account. Those inefficiencies and excess costs are somewhat influenced by the operational environment, so investigation of these empirical environmental effects is warranted in the future.

Appendix A Given the current variable input prices, the short-run minimum variable cost of LCC o can be determined by solving the following input-oriented model:

C v ðyÞ ¼ min

I X

wvio xvi

i¼1

lk  0; k ¼ 1; …; K;

Given the current fixed and variable input prices, the long-run minimum cost of LCC o can be calculated by the following inputoriented model:

C LR ðyÞ ¼ min

¼

f xjo ;

K X

lk xvik  xvi  0; i ¼ 1; …; I;

lk ysk  yso ; s ¼ 1; …; S;

K X

lk xfjk  xfj  0; j ¼ 1; …; J;

k¼1 K X

lk xvik  xvi  0; i ¼ 1; …; I;

k¼1 K X

lk ysk  yso ; s ¼ 1; …; S;

k¼1 K X

lk ¼ 1;

k¼1

lk  0; k ¼ 1; …; K;

k¼1

(A.2)

where C LR ðyÞ is the measure of the long-run minimum cost achievable with the current input prices for LCC o. In order to reflect the cost penalties due to paying higher prices than other LCCs, a potential minimum price for each input is identified. Following Camanho and Dyson (2008), we assume that the potential local minimum price is equal to the minimum price observed in these LCCs in the same local market, and the potential global minimum price is equal to the minimum price observed in all LCCs in the data set. Assuming that there are N local markets, and that LCC o operates in the local market n, n ¼ 1; …; N, the local short-run minimum variable cost of LCC o can be obtained by solving the following input-oriented model: I X

~ vin xvi w

i¼1

K X

lk xfjk ¼ xfjo ; j ¼ 1; …; J;

K X

lk xvik  xvi  0; i ¼ 1; …; I;

k¼1

lk ¼ 1;

wfjo xfj

j¼1

k¼1

k¼1 K X

J X

s.t.

k¼1 K X

wvio xvi þ

s.t.

j ¼ 1; …; J;

k¼1

I X i¼1

C lv ðyÞ ¼ min f lk xjk

(A.1)

where C v ðyÞ is the measure of the minimum variable cost achievable with the current prices for LCC o. Then, the short-run minimum cost of LCC o can be computed as: PJ f f C SR ðyÞ ¼ C v ðyÞ þ j¼1 wjo xjo .

s.t. K X

195

K X k¼1

lk ysk  yso ; s ¼ 1; …; S;

196

M.-M. Yu et al. / Journal of Air Transport Management 53 (2016) 186e198

K X

K X

lk ¼ 1;

lk  0; k ¼ 1; …; K;

(A.3)

where C lv ðyÞ is the measure of the local minimum variable cost achievable with the local minimum variable input prices for LCC o; ~ vin is the local minimum price of the ith variable input among and w all LCCs in the local market n. Then, the local short-run minimum PJ f f cost of LCC o can be computed as: C LSR ðyÞ ¼ C lv ðyÞ þ j¼1 wjo xjo . Furthermore, the global short-run minimum variable cost of LCC o can be calculated by solving the following input-oriented model: I X

C gv ðyÞ ¼ min

lk  0; k ¼ 1; …; K;

where C LLR ðyÞ is the measure of the local long-run minimum cost ~ fjn achievable with the local minimum input prices for LCC o; and w is the local minimum price of the jth fixed input among all LCCs in the local market n. Finally, the global long-run minimum cost of LCC o can be obtained by solving the following input-oriented model:

C GLR ðyÞ ¼ min

K X

v

e ~ i xvi þ w

J X

f

e ~ j xfj w

j¼1

f

f

lk xjk  xj  0; j ¼ 1; …; J;

k¼1 f

f

lk xjk ¼ xjo ; j ¼ 1; …; J;

K X

k¼1

lk xvik  xvi  0; i ¼ 1; …; I;

k¼1

lk xvik



xvi

 0; i ¼ 1; …; I;

K X

k¼1 K X

I X

s.t.

s.t.

K X

(A.5)

i¼1

v e ~ i xvi w

i¼1

K X

lk ¼ 1;

k¼1

k¼1

lk ysk  yso ; s ¼ 1; …; S;

k¼1

lk ysk  yso ; s ¼ 1; …; S;

K X

k¼1

lk ¼ 1;

k¼1 K X

lk ¼ 1;

lk  0; k ¼ 1; …; K;

k¼1

lk  0; k ¼ 1; …; K;

(A.4)

where C gv ðyÞ is the measure of the global minimum variable cost achievable with the global minimum variable input prices for LCC o; v e ~ is the global minimum price of the ith variable input among and w i

all LCCs in the data set. Then, the global short-run minimum cost of PJ f f LCC o can be computed as: C GSR ðyÞ ¼ C gv ðyÞ þ j¼1 wjo xjo . In the long run, the local long-run minimum cost of LCC o can be determined by solving the following input-oriented model:

C LLR ðyÞ ¼ min

I X

~ vin xvi þ w

i¼1

J X j¼1

s.t. K X

f

f

lk xjk  xj  0; j ¼ 1; …; J;

k¼1

In order to obtain the technically efficient cost, the technical efficiency of LCC o needs to be calculated by the following inputoriented SBM-DEA model:

b q ¼ min

@1  1 J

J sf  X jo j¼1

xfjo

1 I sv 1X io A  I i¼1 xvio

K X

lk xfjk þ sfjo ¼ xfjo ; j ¼ 1; …; J;

k¼1

lk xvik  xvi  0; i ¼ 1; …; I;

k¼1 K X

Appendix B

s.t.

k¼1 K X

where C GLR ðyÞ is the measure of the global long-run minimum cost f e ~j achievable with the global minimum input prices for LCC o; and w is the global minimum price of the jth fixed input among all LCCs in the data set.

0 ~ fjn xfj w

(A.6)

K X

v lk xvik þ sv io ¼ xio ; i ¼ 1; …; I;

k¼1

lk ysk  yso ; s ¼ 1; …; S;

K X k¼1

lk ysk  yso ; s ¼ 1; …; S;

M.-M. Yu et al. / Journal of Air Transport Management 53 (2016) 186e198

K X

lk ¼ 1;

k¼1

lk  0; k ¼ 1; …; K; f

sjo  0; j ¼ 1; …; J; sv io  0; i ¼ 1; …; I:

(B.1) f *

where b q is the measure of the technical efficiency of LCC o. l* , sjo

and sv* io denote the optimal solutions to Eq. (B.1). The optimal input P P f v x o Þ ¼ ð Kk¼1 l*k xfjk ðcjÞ; Kk¼1 l*k xvik ðciÞÞ. Then, vector for LCC o is ðb xo ; b the technically efficient cost of LCC o can be computed as: P P v C TE ðyÞ ¼ Jj¼1 wfj xfjo þ Ii¼1 wvi b x io . Appendix C

Table C List of sample LCCs Airlines

Country

US Airways Group Southwest Alaska Air Group SkyWest JetBlue AirTran WestJet ExpressJet Allegiant Air EasyJet Ryanair Aer Lingus Norwegian

United States United States United States United States United States United States Canada United States United States United Kingdom Ireland Ireland Norway

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