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The Relative Operational Efficiencies of Large United States Airlines: A Data Envelopment
Analysis
Work in Progress: Please do not quote, cite or distribute without the consent of the author.
Mark R. Greer
Associate Professor of Economics
Dowling College
Oakdale, NY 11769-1999 USA
1
I. Introduction
Using data envelopment analysis (DEA), this paper ranks fourteen major U.S. air carriers
in terms of their operational efficiencies at transforming inputs into outputs in 2003. The inputs
incorporated into this analysis are labor, aircraft fuels, fleet-wide aircraft seating capacity, and
fleet-wide aircraft cargo capacity. The outputs are revenue passenger-miles flown and cargo
(freight and mail) ton-miles flown. All inputs and outputs are measured in their physical
quantities, not in their market values. Seven of the carriers included in the study are older legacy
airlines: Alaska Airways, American Airlines, Continental Airlines, Delta Airlines, Northwest
Airlines, United Airlines and US Airways. The remaining seven carriers are discount airlines:
Airtran Airways, America West Airlines, American Trans Airlines, Frontier Airlines, JetBlue
Airways, Southwest Airlines and Spirit Airlines.
The motivation for this analysis stems in part from the ongoing shakeout in the U.S.
aviation industry as discount carriers gain market share at the expense of retrenching legacy
carriers. The lower cost structures of the discount carriers appear to count for much of their
competitive advantage vis-à-vis the legacy carriers. The lower cost structures of the discount
carriers, in turn, could be attributable to their being more efficient than the legacy carriers, their
paying lower prices for certain inputs, especially labor, than the legacy carriers, or a combination
of the two. Thus, one should not jump to the conclusion that the discount carriers are more
efficient than the legacy carriers because they have lower costs. This study should cast some
light on whether the discount carriers actually are more efficient than the legacy carriers.
The concept of efficiency employed in this paper is a physical one, not a financial or
monetary one. Inputs are measured in their physical quantities, as are outputs. Nowhere in this
2
study are price data used. The reason for this is that different airlines pay different prices for the
same inputs and receive different prices for the same outputs. These price differences originate
in differences in the competitive conditions the different airlines face in their input and output
markets. An airline whose pilots do not belong to a union will most likely pay a lower salary and
benefit package to its pilots than an airline with unionized pilots. An airline with monopoly and
near-monopoly positions on a relatively large portion of its city-pairs served will receive a higher
average fare per passenger-mile flown than an airline flying more competitive routes. Measuring
inputs in their market prices would thus entail that essentially the same input would be quantified
differently, depending on which airline uses the input. Measuring outputs in terms of their
market prices would also lead to different units of measure being used to quantify the same unit
of output, depending on which airline produced it.1 By contrast, when inputs and outputs are
measured in their physical quantities, the same set of units of measure are applied to the inputs
and outputs of all the airlines studied. Therefore, this study completely disregards price data in
its assessment of the airlines’ relative efficiencies at transforming inputs into outputs.
This study is not the first to apply DEA to the airline industry. Previous work in this area
includes Schefczyk (1993), Banker and Johnston (1994), Fethi, Jackson and Weyman-Jones
(2002), and Scheraga (2004). However, this study is the first to use exclusively physical
measures of inputs and outputs. It is also the first to include a substantial number of discount
carriers in the dataset, to adjust the airlines’ DEA scores for economies of distance, and to use
DEA weight restrictions to reflect the greater importance of airlines’ passenger hauling operation
over their cargo hauling function.
A number of complex issues arose in the collection and compilation of the data used in
this analysis. The data appendix to this paper elaborates on these issues.
3
II. Analysis
Overview of Data Envelopment Analysis (This subsection may be skipped by readers already
familiar with data envelopment analysis.)
The works of Farrell (1957), Charnes, Cooper and Rhodes (1978), and Charnes, Cooper,
Golany, Seiford and Stutz (1985) form the underpinning of DEA. Comprehensive,
contemporary surveys of DEA can be found in Charnes, Cooper, Lewin and Seiford (1994), and
Ray (2004). DEA analyzes the technical efficiency of decision-making units (DMUs) at
transforming inputs into outputs.2 DMUs are organizations that have control over the inputs they
use and the outputs they produce. A firm is a DMU, but so are not-for-profit private entities and
governmental agencies, as long as they have considerable discretion about the inputs they use,
the outputs they produce, and the ways they go about transforming their inputs into outputs.
One way of conceptualizing technical efficiency is minimizing the set of inputs used to
produce a given set of outputs. Another is to conceptualize it as maximizing the set of outputs
produced with a given quantity of inputs. In the input-oriented DEA model used in this paper,
the first sense of technical efficiency will be used.
In this overview of DEA and its application to the airline industry, some formal notation
will be used. The vector Yi represents the output set of DMU i. Since we are dealing with two
outputs in this study (cargo ton-miles flown and revenue passenger miles flown), Yi consists of
two elements: Yi = (yiCarg, yi
Pass), where yiCarg represents cargo ton-miles flown by airline i, and
yiPass represents revenue passenger miles flown by airline i. We will allow the vector Xi to
4
denote the input set of the airline in question. In this study, the input vector possesses four
elements (labor, fuel, passenger seating capacity, and cargo volume capacity): Xi = (xiLab, xi
Fuel,
xiSeatCap, xi
CargCap), where xiLab represents the labor input of airline i, xi
Fuel represents the fuel
inputs of airline i, xiSeatCap represents passenger seating capacity, and xi
CargCap represents freight
and mail cargo capacity.
Part of the appeal of DEA is that it is predicated on a minimal number of assumptions.
One does not have to make any assumption about the mathematical form of the production
technology in order to employ DEA. Since it is a non-parametric, non-stochastic technique, one
does not have to make any assumptions about underlying error or disturbance terms in the model.
Borrowing from Ray (2004, p. 27), we note that the underlying assumptions of DEA models are
the following:
1. All input-output bundles that are observed in the data, (Xi, Yi), are also feasible input-
output bundles. (Xi, Yi) is a feasible input-output bundle if input bundle Xi can produce
output bundle Yi. This assumption is simply stating that if we observe a DMU producing a
certain set of outputs from a certain set of inputs, then that input-output combination is
feasible. This hardly seems to be a contentious assumption.
2. The set of feasible input-output bundles, or the production possibilities set, is convex. If
two feasible input-output combinations, (XA, YA) and (XB, YB), are feasible, then (XW, YW) =
α(XA, YA) + (1- α)(XB, YB), where 1≤≤ α0 , is also a feasible input-output bundle.
3. Inputs can be freely disposed of. If (XA, YA) = (xALab, …, xA
CargCap, yACarg, yA
Pass) is feasible,
then so is (XO, YO) = (xOLab, …, xO
CargCap, yACarg, yA
Pass), where xOj>xA
j for at least one j, and
xOj ≥ xA
j for all j’s. If a certain set of outputs can be produced with a certain set of inputs, the
5
same bundle of outputs can be produced using a greater quantity of at least one input and no
less of any input. If necessary, any extraneous inputs can be thrown away.
4. Outputs can be freely disposed of. If (XA, YA) = (xALab, …, xA
CargCap, yACarg, yA
Pass) is
feasible, then so is (XO, YO) = (xALab, …, xA
CargCap, yOCarg, yO
Pass), where yOj<yA
j for at least one
j and yOj ≤ yA
j for all j’s. If a certain set of outputs can be produced with a certain set of inputs,
then it is possible to use the same set of inputs to produce a set of outputs where at least one
output is produced in a lower quantity and no output is produced in a greater quantity. A
DMU could do this, for example, by throwing away some of its units of output.
DEA can be performed under a variety of assumptions about returns to scale (constant,
variable, non-increasing, and non-decreasing.) A number of empirical studies indicates that the
airline industry exhibits constant returns to scale (White 1979; Caves et al. 1984, 1985). In
addition, Schefczyk (1993, p. 307) provides a theoretical reason why a constant returns to scale
version of DEA is the most appropriate form to apply to the airline industry. Therefore, the
analysis undertaken here uses a constant returns to scale DEA model. Again following Ray
(2004, p. 27), this assumption may be formally expressed as:
5. If (X, Y) is a feasible input-output bundle, then so is (βX, βY) for any β>0.
One critical step in DEA is the empirical specification of the production possibilities set.
In order to accomplish this, one must identify the technically efficient DMUs. These best
practices DMUs provide empirical evidence pertaining to the outer boundary of the production
possibilities set. This boundary is called the “efficiency frontier.” More specifically, the input-
output combination of an efficient DMU is a point on one of the outer facets of the production
6
possibilities set. In the input-oriented DEA model used here, a technically efficient DMU is one
whose observed set of outputs cannot be produced while using less of each input.3
One way it may be possible to produce a DMU’s outputs in the same quantities while
using less of each input would be by taking a linear combination of the input-output bundles of
one or more other DMUs in the industry. If this can be done, then the DMU is not efficient. If
this cannot be done, then it is efficient. For example, suppose that summing together 30% of the
input-output combination of Airline A and 110% of the input-output combination of Airline B
created a virtual composite airline that produced the same number of passenger-miles flown and
10% more freight and mail ton-miles flown as Airline C but used 15% less fuel, 10% less labor,
5% less passenger seating capacity and 10% less cargo capacity than Airline C. In this case,
Airline C would not be efficient, for it is possible to combine the production processes of two
other airlines in the industry and produce the same quantity of each output using 5% less of each
input. (Recall that under assumptions three and four enumerated above, any excess outputs and
inputs of the combination virtual airline are disposable). If one were to implement Airline A’s
production process on a smaller scale and combine this scaled down production process with
Airline B’s production process scaled-up slightly, one would come up with an airline that is more
technically efficient than Airline C. This imagined combination of input-output bundles of other
DMUs scaled up or down is called a “virtual DMU.” Another virtual DMU could be the input-
output set of just one actual DMU scaled-up or down by a certain factor. If it is possible to
construct a virtual DMU that produces the same set of outputs as the DMU in question while
using less of each input by either (1) scaling up or down the input-output set of another DMU, or
(2) taking a linear combination of the input-output sets of two or more other DMUs, then the
DMU in question is inefficient, and its input-output combination lies inside the efficiency
7
frontier. If it is not possible to do this, then the DMU is efficient, and its input-output
combination lies on the outer boundary of the production possibilities set.
The basic dichotomy between an efficient and an inefficient DMU now noted, we move
on to the second integral step of DEA, which is to come up with a measure of the relative
efficiency of a DMU. This measure of efficiency is the minimum possible uniform proportion of
the DMU’s inputs that could be used to produce the same set of outputs that the DMU is
producing. In the case of an efficient DMU, as defined above, this minimum possible proportion
is 100%; it is not possible, by scaling up or down the input-output combination of any other
DMU, or by creating a virtual DMU based on the observed input-output combinations of other
DMUs, to produce the same quantities of outputs using less of each input. Therefore, 100% of
each quantity of input the efficient DMU is using is needed to produce its output bundle. One
might say that this DMU is 100% efficient in its utilization of inputs.
The case of an inefficient DMU is different, though. In this instance, the efficiency score
will fall somewhere below 100%, for it is possible, by creating a virtual DMU, to use a
uniformly smaller portion of each input and still produce the same output set. The minimum
possible fraction of the DMU’s inputs that could still produce its outputs in the same quantities
would be its efficiency score, which would fall below 100% in the case of an inefficient DMU.
(In the hypothetical three airline case portrayed previously, the efficiency score of airline C
would be 95% or less, depending on whether one could construct another virtual airline that was
more efficient than 30%-110% mix of Airlines A and B at producing Airline C’s output set.) In
order to find this minimum possible proportion, one compares the inefficient DMU’s input-
output set with the input-output sets of virtual DMUs created by combining the input-output sets
of the efficient DMUs.4 The virtual DMU that produces the same quantities of outputs using the
8
smallest possible percentage of inputs then becomes the benchmark for the inefficient DMU in
question. Also, this smallest possible percentage of inputs is the efficiency score for the DMU.
Application of DEA to the US Airline Industry
Linear programming is used to identify the efficient and inefficient DMUs, along with
calculating the DMUs’ efficiency scores. The linear programming problem for the constant
returns to scale, input-oriented, four-input, two-output scenario analyzed here is:
9
Linear Programming Problem #1
Minimize V=θ θ, λ
Subject to: 1. yyPass
l
n
i
Pass
ii ≥∑
=1λ
2. yyC
l
n
i
C
ii
arg
1
arg≥∑
=
λ
3. xxLabor
l
n
i
Laborii θλ ≤∑
=1
4. xxFuel
l
n
i
Fuelii θλ ≤∑
=1
5. xxSeatCap
l
n
i
SeatCapii θλ ≤∑
=1
6. xxCapC
l
n
i
CapCii θλ arg
1
arg ≤∑=
7. ii allfor 0≥λ
8. 0≥θ
This linear programming problem must be solved for each carrier. n represents the number of
airlines in the data set. l is the subscript for the airline whose efficiency is being evaluated. θ is
the airline’s efficiency score. The λi’s are the weights attached to the airlines’ inputs and
outputs to construct a virtual airline. ∑=
n
i
Pass
ii y
1
λ represents the passenger-miles flown by the
virtual airline. Note that it is a linear combination of the passenger mile outputs of all airlines.
Constraint #1 posits that the revenue passenger-miles output of the virtual airline must be at least
10
as large as the revenue passenger-miles output of the airline whose efficiency score is being
calculated. Constraint #2 imposes the condition that the freight and mail ton-miles output of the
virtual airline must be at least as large as the freight and mail ton-miles output of the airline
whose efficiency score is being determined. ∑=
n
i
Laborii x
1λ is the labor input used by the virtual
airline. Constraint #3 is stating that the labor input used by the virtual airline must be no greater
than the labor input used by the airline whose efficiency score is being calculated, weighted by
its efficiency score. Constraints #4, #5 and #6 are imposing similar restrictions on the three other
inputs. Constraints #7 and #8 preclude negative values for the weights attached to the airlines
used in creating virtual airlines, and for the efficiency score.
Solving program #1 entails finding the lowest possible efficiency score such that the
benchmark virtual airline produces at least as much of the two outputs as the carrier while using
no more of any input than the carrier uses, weighted by θ. If the smallest θ that will meet all
eight constraints is 1, then the smallest percentage of the carrier’s inputs that can produce its
outputs is 100%, which means that the airline is efficient. (Also, all the λi’s, except the λi for
the carrier itself, in the solution to the linear programming problem will have values of zero in
this case. In effect, the virtual benchmark for the efficient airline is itself.) In the case of an
inefficient airline, θ will fall below 1.
Results of Analysis
The software used to undertake the linear programming in this project was Efficiency
Measurement System (EMS), version 1.3.0.5 The results derived from EMS were cross-checked
for accuracy using the Solver linear programming add-in for Microsoft Excel. In those few
11
instances where minor discrepancies arose, the results obtained from Solver are reported since
Solver has a lower tolerance level than EMS. Table 1 reports the results. “-ML” signifies
mainline operation only. An asterisk is used to denote the value of a variable at the solution to
the linear programming problem. One should bear in mind two very important caveats: the
numbers displayed in Table 1 are not adjusted for economies of distance, nor has the super-
efficiency criterion been applied to break the tie among the efficient airlines. These adjustments
will come later.
12
Table 1
Airline
Efficiency Score (θ∗)
Non-zero λ∗ιs at Solution Continental -
ML 100% λ∗
Continental-ML=1
JetBlue 100% λ∗Jetblue=1
Northwest - ML
100% λ∗Northwest-ML=1
United 100% λUnited=1 Northwest 99.08% λ∗
Continental-ML=0.1290, λ∗Jetblue=0.4380 λ∗
Northwest-ML=0.9060, λ∗
United=0.0274 America West 97.25% λ∗
Continental-ML=0.0002, λ∗Jetblue=2.004, λ∗
Northwest-ML=0.0045, λ∗
United=0.0289 Continental 94.81% λ∗
Continental-ML=0.9987, λ∗Jetblue=0.5354
Frontier 93.15% λ∗Continental-ML=0.0117, λ∗
Jetblue=0.4611 Delta - ML 90.26% λ∗
Jetblue=2.4589, λ∗Northwest-ML=0.1982, λ∗
United=0.5450, American - ML 89.55% λ∗
Jetblue=3.7733, λ∗Northwest-ML=0.8175, λ∗
United=0.2875 Delta 88.62% λ∗
Jetblue=2.3305, λ∗Northwest-ML=0.1382, λ∗
United=0.7089 Southwest 88.34% λ∗
Continental-ML=0.1223, λ ∗Jetblue=4.4290
USAir 87.06% λ∗Jetblue=2.5724, λ∗
Continental-ML=0.1052, λ ∗United=0.1402
American 84.98% λ∗Continental-ML=0.2241, λ∗
Jetblue=3.4089, λ ∗Northwest-ML=0.5922,
λ∗United=0.4004
ATA 83.59% λ∗Jetblue=1.1786, λ∗
Northwest-ML=0.0120 USAir-ML 81.09% λ∗
Continental-ML=0.1877, λ∗Jetblue=1.6190, λ∗
United=0.1005 Alaska-ML 77.71% λ∗
Continental-ML=0.0734, λ∗Jetblue=0.9781
Alaska 71.19% λ∗Continental-ML=0.0141, λ∗
Jetblue=1.1643, λ∗United=0.0305
Airtran 67.69% λ∗Jetblue=0.6746, λ∗
United=0.0033 Spirit 62.29% λ∗
Jetblue=0.3371, λ∗Northwest-ML=0.0014
The λ*i’s in the last column are the weights given to each efficient airline’s inputs and outputs in
constructing the virtual airline that ended-up as the benchmark for the airline in the first column.
These λ*i’s achieve the lowest possible efficiency score for that airline. To take an example of
how the λ*i’s are used, examine the row for Airtran and consider what happens if one multiplies
each of the inputs of Jetblue’s operation by 0.6746 and each of the inputs used in United’s
operation by 0.0033, then sums the products.6 One will generate a virtual airline using 3198.0
13
full-time equivalent employees, 123.2 million gallons of jet fuel, 5127.7 seats of fleet-wide
seating capacity, and 44,441.7 cubic feet of fleet-wide cargo volume capacity. Each of these
input quantities is 67.69% or less than the corresponding input quantity for Airtran.7 If one
multiplies each of the outputs of Jetblue’s operation by 0.6746, each of the outputs of United’s
operation by 0.0033, then sums the resulting products, one will find that the virtual airline
produces 8.1 million more cargo ton-miles than Airtran and just as many revenue passenger-
miles.8 Hence, the virtual airline produces at least as much of each output as Airtran produces
while using 67.69% or less of each input.
Casual eyeballing of the stage length data in Tables 7 and 8 in the data appendix,
considered in conjunction with the DEA efficiency scores in Table 1, provides some indication
that economies of distance may be impacting the airlines’ efficiency scores. The airlines with
the 100% efficiency scores also happen to be airlines with relatively large average stage lengths,
for example. Later, we will adjust the efficiency rankings for economies of distance. First,
however, it is necessary to break the tie between the four efficient airlines.
Application of Tiebreaker
As a tiebreaker, we use the “super-efficiency” construct devised by Andersen and
Petersen (1993). To understand how this tiebreaker works, recall that the input-output
combination of an efficient DMU specifies one of the the outer boundaries of the feasible
production possibilities set for the industry. If one of the efficient DMUs is removed from the
set of DMUs used to construct the production possibilities set, one of the outer facets of the
production possibilities set disappears, and the new efficiency frontier is situated inside the old
14
one. Andersen and Petersen’s tiebreaking criterion works by calculating how far the efficient
DMU’s input-output combination lies outside the efficiency frontier of the new, now shrunken,
production possibilities set that is generated when the input-output set of that efficient DMU is
disregarded in the construction of the production possibilities set. More specifically, the
tiebreaker calculation ascertains the minimum uniformly proportional increase in the efficient
DMU’s inputs, holding each of its outputs unchanged, that would place the now input-
augmented efficient DMU on the frontier of the now shrunken production possibilities set.
Before boosting its inputs, the efficient DMU’s input-output combination lies outside the
boundary of the shrunken production possibilities set. As its inputs are increased while holding
its outputs constant, the input-augmented efficient DMU becomes less efficient, and its input-
output combination moves inward toward the boundary of the shrunken production possibilities
set. The minimum uniformly proportional increase in inputs required to move the input-
augmented efficient DMU to the efficiency frontier of the shrunken production possibilities set
serves as a measure of how efficient the efficient DMU is, compared to other efficient DMU’s.
An efficient DMU for which at least a 40% proportional increase in inputs is necessary to move
it inward to the frontier of the production possibilities set that ignores its input-output
combination can be viewed as more efficient than an efficient DMU that requires only a 5%
proportional increase in inputs to accomplish the same.
Following Andersen and Petersen (1993, p. 1262), we note that the linear programming
problem for this super-efficiency tiebreaker is the following:
15
Linear Programming Problem #2
Minimize V=θ θ, λ
Subject to: 1. yyiPass
l
n
lii
Pass
i≥∑
≠=1
λ
2. yyC
l
n
lii
C
ii
arg
1
arg≥∑
≠=
λ
3. xxLabor
l
n
lii
Laborii θλ ≤∑
≠=1
4. xxFuel
l
n
lii
Fuelii θλ ≤∑
≠=1
5. xxSeatCap
l
n
lii
SeatCapii θλ ≤∑
≠=1
6. xxCapC
l
n
lii
CapCii θλ arg
1
arg ≤∑≠=
7. ii allfor 0≥λ
8. 0≥θ
The subtle difference between linear programming problems #1 and #2 is that, in problem #2, the
summations on the left hand sides of the first six constraints exclude the data point for the
efficient DMU being evaluated. In effect, this omission entails that the calculated production
possibilities set and efficiency frontier exclude the data from the DMU being analyzed. In the
case of an efficient DMU, this exclusion effectively removes the facet of the old efficiency
frontier specified by its input-output combination, which in turn leaves the efficient DMU’s
input-output combination situated outside the boundary of the new, now shrunken production
16
possibilities set. In the case of an efficient DMU, the solution for θ will have to be greater than
one, because the efficient DMU’s inputs must be proportionally increased for constraints 3-6 to
hold. (The efficiency score for an inefficient DMU will be the same as in linear programming
problem #1.)
EMS was used to solve linear programming problem #2 for each of the four efficient
airlines. The results from EMS were cross-checked using the Solver plug-in to Microsoft Excel.
The results are reported in Table 2:
Table 2
Airline
Super-efficiencyScore (θ∗)
JetBlue 123.79% United 116.81%
Northwest - ML 112.32% Continental-ML 103.10%
Under the super-efficiency tie-breaking criterion, JetBlue is the most efficient of the efficient
carriers, followed by United, etc. The next step in the analysis is to adjust for economies of
distance.
Adjustment for Economies of Distance
Airlines with higher average stage lengths will inherently tend to have higher DEA
efficiency (and super-efficiency) scores than those with shorter average stage lengths. The
reason for this is that certain resources must be used as part of the terminal function. Examples
include gate attendants and baggage loading personnel. In addition, an aircraft must burn a non-
17
negligible quantity of fuel to take it from the gate, to the runway, and then on the ascent to its
cruising altitude, which is another resource used-up as part of the terminal function. The
quantities of resources associated with the terminal function vary little, if at all, with the distance
of the flight. However, the terminal resources consumed per flight mile decrease as on-flight
distance increases because the fixed terminal resources are spread over more miles. As a result,
an airline’s DEA efficiency score should be expected to increase as its average stage length goes
up. Since airlines vary in their average stage lengths, this phenomenon distorts the relative
measure of an airline’s technical efficiency.
In order to adjust the efficiency scores for differences in average stage length, we first
estimate what the relationship between average stage length and efficiency score is. Super-
efficiency scores for the efficient airlines are used in lieu of their 100% regular efficiency scores
in estimating this relationship. A log-linear regression model is applied to the efficiency scores
and average stage lengths to estimate this relationship.9 More specifically, the model used is the
following:
lnYi = α + βlnXi + ui,
where Yi represents the ith airline’s DEA percentage efficiency score expressed as a whole
number, and Xi represents its average stage length. The estimated slope coefficient, β, turns out
to be 0.272, with a standard error of 0.128, which is significant at 5%.10
We next employ the estimated log-linear regression equation to predict what the natural
logarithm of each airline’s DEA efficiency score would be based on the estimated relationship
between efficiency score and average stage length. The residuals of the regression equation are
used to determine the ranking of the airlines. The final ranking appears in Table 3:
18
Table 3
Ln DEA Score
Predicted Score Residual
JetBlue 4.8186 4.5854 0.2332Northwest-ML 4.7214 4.4903 0.2310Northwest 4.5959 4.4065 0.1895United 4.7605 4.5890 0.1716Southwest 4.4812 4.3612 0.1200USAir 4.4666 4.3955 0.0711Continental 4.5519 4.4888 0.0631America West 4.5773 4.5213 0.0560Continental-ML 4.6357 4.5810 0.0547Frontier 4.5342 4.4842 0.0500Delta 4.4844 4.4492 0.0352Delta-ML 4.5027 4.5319 -0.0292American 4.4424 4.5164 -0.0739USAir-ML 4.3956 4.4786 -0.0830American-ML 4.4948 4.5979 -0.1031Alaska-ML 4.3530 4.4592 -0.1062Alaska 4.2654 4.3750 -0.1097ATA 4.4259 4.5909 -0.1649Airtran 4.2149 4.3805 -0.1656Spirit 4.1318 4.5164 -0.3845
It is noteworthy that JetBlue remains the most technically efficient airline, even after adjusting
its DEA super-efficiency score for its relatively long average stage length. Northwest may not
be as technically efficient as the adjusted scores for its overall and mainline operations indicate.
One shortcoming of DEA is that a DMU with an extreme point within its input-output set tends
to end-up on the efficiency frontier. During 2003, Northwest operated a fleet of twelve Boeing
747-200 dedicated freighters whose sole function was to haul freight. No other carrier in the
sample operated a dedicated fleet of cargo carriers, and Northwest’s freight and mail ton-miles
flown was a larger percentage of total payload by weight than any other carrier.11 Northwest’s
19
being an outlier in terms of the freight and mail output may account, at least in part, for its
relatively high efficiency score.
Perhaps the most striking characteristic of Table 3 is that there is no evident association
between whether an airline is a discount carrier and its position in the ranking. While the most
efficient carrier is a discount carrier, the next three carriers in the ranking are legacy carriers. In
addition, the three airlines at the bottom of the ranking are discount carriers.
We should not yet jump to the conclusion that the discount carriers, considered as a
whole, are no more efficient than the legacy carriers. In its basic form, DEA places equal
emphasis on all inputs and all outputs and does not assume that one or more outputs is more
important than the others, or that one or more inputs is more important than the others. In the
case of the airline industry, though, the passenger hauling function is far more prominent and
central than the cargo hauling function; moreover, the discount carriers haul even less cargo as a
percentage of total payload than the legacy carriers. It is possible that the basic DEA model, by
ignoring the greater importance of the passenger hauling function, carries with it a systematic
bias toward the legacy carriers. The imposition of weights restrictions, which is done in the next
section, is intended to rectify this.
III. Imposition of Weights Restrictions
One important limitation of DEA in its basic form is that it treats all outputs and all
inputs as being equally important. In the case of the airline industry, this is not a trivial
limitation of the analysis, for the primary function of all the major air carriers is to carry
passengers, with the cargo function serving as an adjunct to the passenger hauling function.12
20
Consequently, it would be advisable to place more weight on each airline’s revenue passenger-
miles flown output than its cargo ton-miles flown output, and on each airline’s labor, fuel, and
seating capacity inputs than its cargo volume capacity input. The author has undertaken some
preliminary work using weights restrictions within DEA.13 The guiding principle behind the
weights restrictions is that the passenger hauling function is more central to an airline’s
operations than the cargo hauling function. The reader is advised that the analysis and results
reported in this section are preliminary, highly tentative and incomplete.
In order to understand how weights restrictions work in DEA, it is helpful to refer to the
dual of the linear programming model used in the body of the paper. In the context of our two-
output, four-input, input-oriented, constant returns to scale DEA, the dual linear programming
model is:
Linear Programming Problem #3
Maximize yy Cl
CPassl
Pass argargμμ + μ ν
Subject to 1. 1argarg =+++ xxxx CapCl
CapCSeatCapl
SeatCapFuell
FuelLaborl
Labor νννν
2. ≤+ yy Cj
CPassj
Pass argargμμ xxxx CapCj
CapCSeatCapj
SeatCapFuelj
FuelLaborj
Labor argargνννν +++ ,
j=1,…,n
εννννμμ ≥CapCSeatCapFuelLaborCPass argarg ,,,,,
μr represents the weight given to output r, νs refers to the weight given to input s, and ε is a non-
Archimedean infinitesimal. Each of the weights is set greater than ε in order to assure that each
21
output and input has a non-zero weight in the solution to the linear program. By duality,
.*argarg** θμμ =+ yy Cl
CPassl
Pass
We next restrict the weights in such a way that more emphasis is placed on the passenger
hauling function than cargo hauling. The weights are not arbitrary; instead, they are based on the
ton-miles of passengers and cargo that the airlines in the data set hauled in 2003.14 During that
year, the ton-miles of revenue passengers, their carry-on bags, and their checked bags were
estimated by the author to be approximately ten times the ton-miles of cargo carried.15 In light of
these relative physical weights, the following weights restrictions are added to the constraints of
linear programming problem #3:
3. μμ arg10 CPass =
4. νν CapCLabor arg10=
5. νν CapCFuel arg10=
6. νν CapCSeatCap arg10=
These four weight restrictions entail that, at the solution to linear programming problem #3, the
weight attached to revenue passengers will be ten times as large as the weight attached to cargo
ton-miles in the objective function. Similarly, the weight attached to the input singularly
associated with the cargo hauling function will be one-tenth the weight attached to each other
input. While imposing these weights restrictions has the virtue of placing more emphasis on the
more important of the two functions of an airline’s operations, θ* no longer represents the
smallest possible proportion of all inputs that can produce at least as much of each output (Allen
et al 1997, p. 27). That is, with weights restrictions, θ* can be taken as a measure of the relative
efficiency of the airline only in an ordinal sense.
22
EMS was used to solve linear programming problem #3, with weights restrictions 3-6.
(The results have not been cross-checked with the Solver add-in to Microsoft Excel.) The results
are reported in Table 4:
Table 4
Airline θ∗ Non-zero λ∗
i’s at Solution
Jet Blue 100.00% λ∗Jetblue=1
America West 82.72% λ∗Jetblue =2.2557
Frontier 74.87% λ∗Jetblue =0.5123
Southwest 70.68% λ∗Jetblue =4.9651
Airtran 62.50% λ∗Jetblue =0.7009
American Trans Air 61.90% λ∗Jetblue =1.2363
Alaska Airways - ML 60.26% λ∗Jetblue =1.2999
USAir 57.47% λ∗Jetblue =4.1465
Spirit 57.41% λ∗Jetblue =0.3439
Alaska Airways 53.90% λ∗Jetblue =1.4678
USAir - ML 50.62% λ∗Jetblue =3.2400
Continental - ML 50.08% λ∗Jetblue =4.3852
Continental 49.02% λ∗Jetblue =4.9150
Delta 48.17% λ∗Jetblue =8.6166
Delta - ML 48.15% λ∗Jetblue =7.6907
United 47.49% λ∗Jetblue =7.9341
American - ML 46.74% λ∗Jetblue =9.9764
American 44.91% λ∗Jetblue =10.4097
Northwest 42.36% λ∗Jetblue =5.5676
Northwest - ML 39.58% λ∗Jetblue =4.7977
Table 4 provides far stronger evidence than Table 1 that the discount carriers are more efficient
than the legacy carriers. All but one of the top ten airlines in the ranking is a discount carrier,
and none of the airlines in the lower half of the ranking are discount carriers. However, the
results in Table 4 still need to be adjusted for economies of distance. Considering that θ* now
has a far more convoluted interpretation than it did in the absence of weights restrictions, it is not
23
self-evident what functional form should be used in the regression to adjust for economies of
distance. This is part of the future work that remains to be undertaken in this project.
Data Appendix
The collection and compilation of the data for this study raised complex issues about
which data should be used and how they should be grouped and compiled. Therefore, an
appendix is devoted to explaining the sources and compilation of the data.
All of the legacy airlines farm out all or part of their commuter operations to regional
affiliates who operate turboprop and regional jets on behalf of the mainline carrier. The regional
affiliates generally fly short feeder routes from small markets to a hub of the legacy carrier. In
instances where the legacy airline exerts little or no operational control, other than scheduling
and aircraft appearance, over the affiliate, data on the affiliate’s inputs and outputs are not
included in the data for the legacy carrier. In these instances, the legacy carrier has little
influence over the production process used by the regional affiliate and how efficiently the
affiliate transforms its inputs into outputs. On the other hand, in cases where the legacy carrier
exerts significant operational control over the production process of the regional affiliate, data
for the regional affiliate are included in the data for the legacy carrier. The ownership of a
substantial equity position in the regional affiliate by the legacy carrier is taken as evidence of
the latter’s exerting substantial operational control over the former. This includes one instance
of a regional affiliate, Pinnacle Airlines, where the legacy carrier, Northwest Airlines, divested
most of its stake in the regional affiliate during 2003.16 The rational for including input and
output data on closely controlled regional affiliates in the data for the parent legacy carrier is that
24
the legacy carrier exercises considerable influence on the operational procedures and efficiency
of the regional affiliates.17
With the exception of US Airways and its subsidiaries, data pertaining to each carrier’s
full-time equivalent employees at the end of 2002 and 2003 were obtained from the Air Carrier
Employees database, which is available on the Website of the United States Department of
Transportation’s Bureau of Transportation Statistics (BTS).18 The BTS reports the number of
full-time and the number of part-time employees at the end of each calendar year. The author
calculated the number of full-time equivalent employees at the end of each year by weighing the
number of part-time employees by .5, then adding the resulting product to the number of full-
time employees. An airline’s year-round average number of full-time equivalent employees for
2003 was calculated as the mean of its full-time equivalent employees at calendar yearends 2002
and 2003. This is the labor input in the DEA analysis. Due to the omission by the BTS of
certain employee data on the wholly owned regional affiliates of US Airways, the December
2002 and 2003 annual reports of US Airways were used to obtain data on the labor input for this
airline.
Aircraft fuel consumption data were obtained from the Schedule T-2 of the Air Carrier
Summary Data database found on the BTS’s website.19 The BTS data were cross-referenced
with data reported in the companies’ annual reports and United States Securities and Exchange
Commission Form 10-K filings. In cases where discrepancies existed, the data disclosed in the
annual reports and 10-Ks were used.20
With the exception of Spirit Airlines, a privately held company whose seating capacity
data were supplied to the author by SH&E Aviation Consultants, data on fleet-wide aircraft
seating capacity were obtained from the airlines’ annual reports and 10-K filings, along with
25
their company Websites. Each airline’s total fleet-wide seating capacity at yearend was
calculated by multiplying its reported seats per plane for each model of airplane in its fleet at
yearend by the number of aircraft of that model owned or leased at yearend, then summing the
products. The estimated daily average fleet-wide seating capacity during 2003 was the mean of
the numbers for yearends 2002 and 2003.
Each airline’s estimated daily average cargo volume capacity during 2003 was derived
from the airline’s annual reports, its 10-K filings, its company Website, and Jane’s All the
World’s Aircraft, various editions.21 Total fleet-wide cargo capacity at yearend was estimated by
first multiplying the number of aircraft of a given model owned or leased at yearend by the cubic
feet of cargo capacity for that model of aircraft. This provided an estimate of cargo volume
capacity by each model of aircraft in the carrier’s fleet. The fleet-wide cargo volume capacity at
yearend was derived by summing the volumes for the model categories. The airline’s daily
average cargo volume capacity during 2003 was arrived at by averaging the data for yearends
2002 and 2003.
Turning now to data on outputs, it is desirable to measure both revenue passenger-miles
flown and cargo ton-miles flown by market distance, that is, the great circle distance from origin
to final destination. From the standpoint of the user, the service rendered the airline is taking
him, her, or his/her cargo from point of origin to final destination, not from point of origin to an
intermediate stop, then to the final destination. Any additional miles incurred in the trip beyond
the great circle distance between the origin and final destination due to an intermediate stop are
extraneous miles from the standpoint of the user. No rational user, except perhaps one who
enjoys airplane rides, would regard the additional miles flown beyond the distance between
origin and final destination because of an intermediate stop as an additional service rendered.
26
Using output data based on flight segment distance would lead to an overstatement of the
airline’s true output because flight segment data include a substantial number of such extraneous
miles in the case of most airlines, especially those using extensive hub-and-spoke networks.
Revenue passenger-miles were obtained by multiplying the airline’s revenue passengers
by the average market distance flown by its passengers in 2003.22 With the exception of Spirit
Airlines, each airline’s revenue passengers number was acquired from its 2003 annual report or
10-K filing. Spirit Airline’s revenue passengers number was obtained from Schedule T-1 of the
BTS’s on-line databases. The average market distance flown data were obtained from Schedule
DB1B of the BTS’s on-line database. The data contained in Schedule DB1B are derived from a
ten percent sample of all tickets sold.
Freight and mail ton-miles flow by market distance were obtained from Schedule T-100
Market of the BTS’s on-line database. The author has doubts about the quality of these data, but
there are no other sources for this data available.
The analysis undertaken here does not distinguish between passengers flown in different
classes of service. One revenue passenger mile flown in first class is treated the same as a
revenue passenger mile flown in business class, which is treated the same as a passenger mile
flown in economy class. To be sure, these outputs are not qualitatively the same, and one could
argue that equating them tends to understate the relative revenue passenger mile outputs of
carriers that fly a disproportionate number of passengers in the higher service classes. This could
be adjusted for by attaching weighting factors greater than one to the two higher classes of
service, which would improve the DEA efficiency measures of carriers that provide a
disproportionate quantity of service in the two higher service classes. There are two reasons,
however, why this adjustment is best not made. To begin with, there are no evident objective
27
values for the weighting factors; therefore, their values would be highly arbitrary. Secondly, and
more importantly, to the extent an airline offers the two higher classes of service, it reduces its
seating capacity input used in the DEA, given its overall fleet size, because a given area of floor
space within the passenger compartment of an aircraft can accommodate fewer seats of a higher
service class than economy class seats. This consideration already improves the DEA efficiency
measures of airlines offering higher service classes in disproportionate quantities. Consequently,
it is not advisable to adjust the outputs of these airlines by an arbitrary weighting factor attached
to the higher classes of service.
Table 5 reports the input and output data obtained. These are the data used in the DEA.
Table 5
Airline
Labor (FTE Employees)
Fuel (MillionsGallons)
Seating Capacity(# Seats)
Cargo Capacity(Cu. Ft.)
Freight and Mail Ton- Miles Flown (Millions)
Revenue Passenger Miles Flown(Millions)
Airtran 5,011 182 8,044 65,655 1.1 9,806.2 Alaska 13,408 391 17,772 165,221 73.2 20,529.9 America West 11,295 423 19,821 166,179 69.9 31,553.3 American 97,172 3,161 134,475 1,745,205 2,007.5 145,444.8 ATA 6,802 276 14,400 137,899 27.3 17,294.4 Continental 41,724 1,494 64,640 691,917 917.0 68,676.0 Delta 72,212 2,370 105,528 1,357,906 1,388.4 120,419.4 Frontier 3,342 105 4,909 37,281 12.9 7,166.7 JetBlue 4,407 173 7,131 59,490 4.8 13,990.9 Northwest 45,917 1,893 74,126 1,101,692 1,801.7 77718.5 Southwest 33,276 1,143 51,158 384,760 133.2 69,455.2 Spirit 2,479 100 4,415 35,869 4.2 4,811.7 United 67,825 1,955 95,501 1,297,879 1,795.6 110,829.8 US Air 34,400 975 46,002 460,386 360.5 57,978.6
The network of each legacy carrier consists of a mainline operation and a
commuter/feeder system whereas each discount airline runs a mainline operation only. The
economic characteristics of these two types of systems differ in important ways, e.g. average
28
stage length and size of aircraft used. In order make valid efficiency comparisons between the
legacy carriers and the discounters, the DEA analysis conducted in this paper isolates input and
output data for each legacy carrier’s mainline operation only and treats the mainline operation as
a separate carrier. Table 6 reports these data:
Table 6
Airline (Mainline Operation Only)
Labor (FTE Employees)
Fuel (MillionsGallons)
Seating Capacity(# Seats)
Cargo Capacity(Cu. Ft.)
Freight and Mail Ton- Miles Flown (Millions)
Revenue Passenger Miles Flown(Millions)
Alaska 10,048 337 14,321 133,912 71.9 18,180.7 American 87,424 2,956 121,540 1,650,034 2,007.2 139,383.1 Continental23 36,174 1,232 54,730 624,967 915.6 61,264.0 Delta 61,528 2,019 92,549 1,259,488 1,331.3 107,471.0 Northwest 40,882 1,752 66,636 1,047,809 1,801.7 66,945.8 United24 67,825 1,955 95,501 1,297,879 1,795.6 110,829.8 US Air 28,439 873 41,274 424,375 360.2 45,295.8
One of the final steps in the efficiency analysis undertaken later in this paper will be to
adjust the airlines’ efficiency scores for economies of distance. All other factors equal, an airline
having a longer average stage length will achieve lower input/output ratios than an airline having
a shorter average stage length. This economy of distance occurs because resources used at the
terminals are spread over more miles of output, the greater is the average stage length of an
airline’s operations. Economies of distance tend to boost the DEA efficiency scores of airlines
that have longer average stage lengths, even though stage length has nothing to do with how
efficiently an airline is run. Therefore, part of the forthcoming analysis will involve an
adjustment of the airlines’ efficiency scores for differences in their average stage length.
Data on average stage length were obtained from the companies’ annual reports, their 10-
K filings, and the BTS. These data are reported in Table 7:
29
Table 7
Airline
Average Stage Length (Miles)
Airtran 599 Alaska 587 America West 1005 American 987 ATA 1,298 Continental 892 Delta 771 Frontier 877 JetBlue 1,272 Northwest 659 Southwest 558 Spirit 987 United 1,289 US Air 633
Table 8 reports the average stage length data for the mainline operations of the legacy carriers:
Table 8
Airline (Mainline Operation Only)
Average StageLength (Miles)
Alaska 800 American 1,332 Continental 1,252 Delta 1,045 Northwest 897 United 1,289 US Air 859
30
Endnotes
1 Schefczyk (1993, p. 302) identifies a series of other considerations that cast doubt on the
usefulness of financial data when comparing the efficiencies of different airlines.
2 As explained by Ray (2004, p. 14), technical efficiency is not the same concept as economic
efficiency, which has to do with maximizing the profitability of the input-output bundle the
decision-making unit is using. Ray points out that technical efficiency is a necessary condition
for economic efficiency, however, in that maximizing profit requires transforming inputs into
outputs in the most technically efficient manner possible.
3 If an additive, as opposed to a radial, measure of efficiency in DEA analysis were used, then a
technically efficient DMU would be one for which it is impossible to produce the same set of
outputs using less of at least one input and no more of any input. The shortcoming of additive
DEA models is that they are not invariant to the units of measure chosen for the inputs and
outputs (Charnes et al 1994, chap. 2). By contrast, radial models are invariant to units of measure
(ibid); therefore, a radial measure of efficiency will be used here.
4 Of course, one could also try out virtual DMUs created from other inefficient DMUs in the
industry to serve as potential benchmarks for the DMU in question. There is no point in doing
this, however, since there will always be at least one virtual DMU constructed from efficient
DMUs that is more efficient than any virtual DMU constructed from inefficient DMUs.
5 EMS was written by Dr. Holger Scheel of the Department of Operations Research at the
University of Dortmund, Germany.
6 Input data can be found in Tables 5 and 6 in the data appendix.
31
7 The fuel and cargo capacity inputs of the virtual airline are equal to 67.69% of the fuel and
cargo capacity inputs of Airtran. The labor and seating capacity inputs of the virtual airline are
less than 67.69% of the labor and seating capacity inputs of Airtran. The reader may not get the
exact same results due to rounding.
8 Output data can be found in Tables 5 and 6 in the data appendix.
9 A log-linear model was chosen because, with fixed terminal resources spread over an
increasing average stage length, an airline’s DEA efficiency score should be expected to increase
at a decreasing rate as its average stage length increases.
10 The estimated value of the intercept term was 2.641 with a standard error of 0.874. The R-
squared and adjusted R-squared for the regression equation were 0.447 and 0.155, respectively.
The Durbin-Watson statistic was 1.682.
11 Nineteen percent of Northwest’s total payload was freight and mail in 2003. The next closest
was United, for which freight and mail accounted for 13% of total payload.
12 The obvious exceptions are the package delivery companies, such as United Parcel Service
and FedEx, that operate fleets of dedicated cargo carriers. These companies are not part of the
study undertaken here.
13 See Allen et al (1997) for a comprehensive overview of weights restrictions in DEA.
14 The author could have used the relative revenues generated by these two functions. However,
to do so would have involved introducing price data into the analysis. For reasons explained
previously, this is to be avoided.
15 This calculation was made on the assumption that the average weight of a passenger plus
his/her carry-on bags was 200 lbs. The United States Department of Transportation uses this
number in calculating revenue passenger ton-miles. The author also assumed that the average
32
number of checked bags per passenger was one, and that the average weight of a checked bag
was 30 lbs. These two assumptions are consistent with the results of a recent aircraft weight and
balance survey conducted by the United States Federal Aviation Administration (2003).
16 During 2003, Northwest transferred 89% of its Pinnacle common stock shares to the pension
plans for various employee groups at Northwest.
17 Data for Alaska Airways include data for Horizon Airways. Data for American Airlines
include data for American Eagle and Executive Airlines. Data for Continental Airlines include
data for Continental Express and Continental Micronesia. Data for Delta Airlines include data
for Comair and Atlantic Southeast Airlines. Data for Northwest Airlines include data for
Mesaba Airlines and Pinnacle Airlines. Data for US Airways include data for Piedmont Airlines,
PSA Airlines, Mid-Atlantic Airways and Allegheny Airlines. United Airlines does not hold a
substantial equity position in any of its regional affiliates.
18 The Website for all BTS data used in this study can be found at www.transtats.bts.gov.
19 Aircraft fuel data for US Airways’ regional affiliates are not publicly available. The author
estimated this number using the available data on fuels and fleet-wide seating capacity for all the
airlines in the sample.
20 The author assumes that airline companies are more careful about providing accurate data to
their shareholders and the Securities and Exchange Commission than the Department of
Transportation.
21 Cargo weight capacity data could not be obtained for certain older aircraft models still in
service. Therefore, cargo volume capacity data, which could be obtained for all aircraft using
Jane’s All the World’s Aircraft, were used instead.
33
22 Schedule T-100 Market of the BTS’s on-line database includes data on passenger-miles flown
by market distance for each airline. However, there is reason to believe that the numbers
reported here significantly understate the passenger-miles flown by market distance for each
airline. Therefore, these data were not used.
23 The data for Continental’s mainline operation include data from Continental Micronesia.
24 The data for United’s mainline operation are the same as those for its overall operation.
United does not possess substantial ownership in any of its regional affiliates. Therefore, none
of the data on its regional affiliates are included in the data for its overall operation, for reasons
explained previously.
References
Allen, R., Athanassopoulos, A., Dyson, R.G., and Thanassoulis, E. (1997). Weights Restrictions
and Value Judgements in Data Envelopment Analysis: Evolution, Development and Future
Directions. Annals of Operations Research, Vol. 73, pp. 13-34.
Andersen, P. and Petersen, N.C. (1993). A Procedure for Ranking Efficient Units in Data
Envelopment Analysis. Management Science, Vol. 39, pp. 1261-1264.
Banker, R.D. and Johnston, H. H. (1994). Evaluating the Impacts of Operating Strategies on
Efficiency in the U.S. Airline Industry, in Data Envelopment Analysis: Theory, Methodology,
and Application. Boston: Kluwer Academic Publishers.
34
Caves, D.W., Christensen, L.R. and Tretheway, M.W. (1984). Economies of Density versus
Economies of Scale: Why Trunk and Local Service Airline Costs Differ. Rand Journal of
Economics, Vol. 15, No. 4, pp. 471-489.
Caves, D.W., Christensen, L.R., Tretheway, M.W. and Windle, R.T. (1985). The Effects of New
Entry on Productivity Growth in the U.S. Airline Industry 1947-1981. Logistics and
Transportation Review, Vol. 21, No. 4, pp. 299-335.
Charnes, A., Cooper, W.W., Lewin, A.Y., and Seiford, L.M., eds. (1994). Data Envelopment
Analysis: Theory, Methodology, and Application. Boston: Kluwer Academic Publishers.
Charnes, A., Cooper, W. W, and Rhodes, E. (1978). Measuring the Efficiency of Decision
Making Units. European Journal of Operations Research, Vol. 2, pp. 429-444.
Charnes, A., Cooper, W. W., Golany, B., Seiford, L., and Stutz, J. (1985). Foundations of Data
Envelopment Analysis for Pareto-Koopmans Efficient Empirical Production Functions. Journal
of Econometrics, Vol. 30, pp. 91-107.
Farrell, M. J. (1957). The Measurement of Productive Efficiency. Journal of the Royal Statistical
Society, A, Vol. 120, pp. 253-281.
35
Fethi, M.D., Jackson, P.M., and Weyman-Jones, T.G. (2002). Measuring the Efficiency of
European Airlines: An Application of DEA and Tobit Analysis. Working Paper. University of
Leicester, Management Center, Leicester, United Kingdom.
Jane’s All the World’s Aircraft (various editions). London: Sampson Low, Marston & Co.
Ray, S.D. (2004). Data Envelopment Analysis: Theory and Techniques for Economics and
Operations Research. Cambridge, UK: Cambridge University Press.
Schefczyk, M. (1993). Operational Performance of Airlines: An Extension of Traditional
Measurement Paradigms, Strategic Management Journal, Vol. 14, pp. 301-317.
Scheraga, C.A. (2004). Operational Efficiency versus Financial Mobility in the Global Airline
Industry: A Data Envelopment and Tobit Analysis, Transportation Research Part A, Vol. 38, pp.
383-404.
United States Federal Aviation Administration (2003). Operational Factors/Human
Performance Group Chairman’s Factual Report, Attachment 21, Document #DCA03MA022.
