The Relative Operational Efficiencies of Large United States Airlines: A Data Envelopment. Analysis

Transcription

1 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Relative Operational Efficiencies of Large United States Airlines: A Data Envelopment Analysis Work in Progress: Please do not quote, cite or distribute without the consent of the author.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 USA greerm@dowling.edu

2 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 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

3 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.

4 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 Y i 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), Y i consists of two elements: Y i = (y Carg i, y Pass i ), where y Carg i represents cargo ton-miles flown by airline i, and y Pass i represents revenue passenger miles flown by airline i. We will allow the vector X i to

5 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): X i = (x Lab i, x Fuel i, x SeatCap i, x CargCap i ), where x Lab i represents the labor input of airline i, x Fuel i represents the fuel inputs of airline i, x SeatCap i represents passenger seating capacity, and x CargCap i 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, (X i, Y i ), are also feasible inputoutput bundles. (X i, Y i ) is a feasible input-output bundle if input bundle X i can produce output bundle Y i. 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, (X A, Y A ) and (X B, Y B ), are feasible, then (X W, Y W ) = α(x A, Y A ) + (1- α)(x B, Y B ), where 0 α 1, is also a feasible input-output bundle. 3. Inputs can be freely disposed of. If (X A, Y A ) = (x Lab A,, x CargCap A, y Carg A, y Pass A ) is feasible, then so is (X O, Y O ) = (x Lab O,, x CargCap O, y Carg A, y Pass A ), where x j O >x j A for at least one j, and j x O x j A for all j s. If a certain set of outputs can be produced with a certain set of inputs, the

6 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 (X A, Y A ) = (x Lab A,, x CargCap A, y Carg A, y Pass A ) is feasible, then so is (X O, Y O ) = (x Lab A,, x CargCap A, y Carg O, y Pass O ), where y j O <y j A for at least one j j and y O y j A 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 inputoutput combination of an efficient DMU is a point on one of the outer facets of the production

7 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 inputoutput 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

8 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 inputoutput 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

9 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:

10 9 Linear Programming Problem #1 Minimize V=θ θ, λ Subject to: 1. λ i y y n i=1 n Pass i 2. λ i y y i= 1 n C arg i Pass l C arg l Labor 3. λi xi θx i=1 n Fuel 4. λi xi θx i=1 n Labor l Fuel l SeatCap 5. λi xi θx i=1 n C arg Cap 6. λi xi θx i= 1 7. λ i 0 for all i 8. θ 0 SeatCap l C arg Cap l 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 λ i s are the weights attached to the airlines inputs and n Pass outputs to construct a virtual airline. λ i y represents the passenger-miles flown by the i= 1 i 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

11 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 Labor whose efficiency score is being determined. λ i xi is the labor input used by the virtual n i= 1 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 The results derived from EMS were cross-checked for accuracy using the Solver linear programming add-in for Microsoft Excel. In those few

12 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 superefficiency criterion been applied to break the tie among the efficient airlines. These adjustments will come later.

13 12 Table 1 Airline Efficiency Score (θ ) Non-zero λ ιs at Solution Continental - 100% ML λ Continental-ML=1 JetBlue 100% λ Jetblue=1 Northwest - 100% ML λ Northwest-ML=1 United 100% λ United =1 Northwest 99.08% λ Continental-ML=0.1290, λ Jetblue= λ Northwest-ML=0.9060, λ United= America West 97.25% λ Continental-ML=0.0002, λ Jetblue=2.004, λ Northwest-ML=0.0045, λ United= Continental 94.81% λ Continental-ML=0.9987, λ Jetblue= Frontier 93.15% λ Continental-ML=0.0117, λ Jetblue= 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= Delta 88.62% λ Jetblue=2.3305, λ Northwest-ML=0.1382, λ United= Southwest 88.34% λ Continental-ML=0.1223, λ Jetblue= USAir 87.06% λ Jetblue=2.5724, λ Continental-ML=0.1052, λ United= American 84.98% λ Continental-ML=0.2241, λ Jetblue=3.4089, λ Northwest-ML=0.5922, λ United= ATA 83.59% λ Jetblue=1.1786, λ Northwest-ML= USAir-ML 81.09% λ Continental-ML=0.1877, λ Jetblue=1.6190, λ United= Alaska-ML 77.71% λ Continental-ML=0.0734, λ Jetblue= Alaska 71.19% λ Continental-ML=0.0141, λ Jetblue=1.1643, λ United= Airtran 67.69% λ Jetblue=0.6746, λ United= Spirit 62.29% λ Jetblue=0.3371, λ Northwest-ML= 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 and each of the inputs used in United s operation by , then sums the products. 6 One will generate a virtual airline using

14 13 full-time equivalent employees, million gallons of jet fuel, 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 , each of the outputs of United s operation by , 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 passengermiles. 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

15 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 inputaugmented 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 inputoutput combination moves inward toward the boundary of the shrunken production possibilities set. The minimum uniformly proportional increase in inputs required to move the inputaugmented 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:

16 15 Linear Programming Problem #2 Minimize V=θ θ, λ Subject to: 1. λ i y y n i=1 i l n Pass i 2. λ i y y i= 1 i l n C arg i Pass l C arg l Labor 3. λi xi θx i=1 i l n Fuel 4. λi xi θx i=1 i l n Labor l Fuel l SeatCap 5. λi xi θx i=1 i l n C arg Cap 6. λi xi θx i= 1 i l 7. λ i 0 for all i 8. θ 0 SeatCap l C arg Cap l 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

17 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 Super-efficiency Score Airline (θ ) JetBlue % United % Northwest - ML % Continental-ML % 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-

18 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. Superefficiency 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: lny i = α + βlnx i + u i, where Y i represents the i th airline s DEA percentage efficiency score expressed as a whole number, and X i 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:

19 18 Table 3 Ln DEA Score Predicted Score Residual JetBlue Northwest- ML Northwest United Southwest USAir Continental America West Continental- ML Frontier Delta Delta-ML American USAir-ML American-ML Alaska-ML Alaska ATA Airtran Spirit 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 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

20 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

21 20 Consequently, it would be advisable to place more weight on each airline s revenue passengermiles 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 twooutput, four-input, input-oriented, constant returns to scale DEA, the dual linear programming model is: Linear Programming Problem #3 Maximize μ ν Pass Pass C μ y + μ l arg y C arg l Labor Labor Fuel Fuel SeatCap SeatCap C arg Cap C arg Cap Subject to 1. ν xl + ν xl + ν x + ν x = 1 l Pass Pass C arg C arg Labor Labor Fuel Fuel SeatCap SeatCap C arg Cap C arg Cap 2. μ y + μ y ν x j + ν x j + ν x j + ν x j, μ Pass C, μ j j=1,,n arg, ν Labor, ν j Fuel, ν SeatCap C, ν arg Cap μ r represents the weight given to output r, ν s 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 ε l

22 21 output and input has a non-zero weight in the solution to the linear program. By duality, Pass* Pass C arg* C arg μ y + μ y = θ *. l l 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 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: Pass = 10 C arg 3. μ μ Labor C 4. ν = 10ν Fuel C 5. ν = 10ν arg Cap arg Cap SeatCap C 6. ν = 10ν arg Cap 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.

23 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 Solution Non-zero λ i s at Jet Blue % λ Jetblue=1 America West 82.72% λ Jetblue = Frontier 74.87% λ Jetblue = Southwest 70.68% λ Jetblue = Airtran 62.50% λ Jetblue = American Trans Air 61.90% λ Jetblue = Alaska Airways - ML 60.26% λ Jetblue = USAir 57.47% λ Jetblue = Spirit 57.41% λ Jetblue = Alaska Airways 53.90% λ Jetblue = USAir - ML 50.62% λ Jetblue = Continental - ML 50.08% λ Jetblue = Continental 49.02% λ Jetblue = Delta 48.17% λ Jetblue = Delta - ML 48.15% λ Jetblue = United 47.49% λ Jetblue = American - ML 46.74% λ Jetblue = American 44.91% λ Jetblue = Northwest 42.36% λ Jetblue = Northwest - ML 39.58% λ Jetblue = 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

24 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 The rational for including input and output data on closely controlled regional affiliates in the data for the parent legacy carrier is that

25 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 fulltime 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 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

26 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 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 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.

27 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 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

28 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 Labor (FTE Employees) Fuel (Millions Gallons) Seating Capacity (# Seats) Cargo Capacity (Cu. Ft.) Freight and Mail Ton- Miles Flown (Millions) Revenue Passenger Miles Flown (Millions) Airline Airtran 5, ,044 65, ,806.2 Alaska 13, , , ,529.9 America West 11, , , ,553.3 American 97,172 3, ,475 1,745,205 2, ,444.8 ATA 6, , , ,294.4 Continental 41,724 1,494 64, , ,676.0 Delta 72,212 2, ,528 1,357,906 1, ,419.4 Frontier 3, ,909 37, ,166.7 JetBlue 4, ,131 59, ,990.9 Northwest 45,917 1,893 74,126 1,101,692 1, Southwest 33,276 1,143 51, , ,455.2 Spirit 2, ,415 35, ,811.7 United 67,825 1,955 95,501 1,297,879 1, ,829.8 US Air 34, , , ,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

29 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: Airline (Mainline Operation Only) Labor (FTE Employees) Fuel (Millions Gallons) Table 6 Seating Capacity (# Seats) Cargo Capacity (Cu. Ft.) Freight and Mail Ton- Miles Flown (Millions) Revenue Passenger Miles Flown (Millions) Alaska 10, , , ,180.7 American 87,424 2, ,540 1,650,034 2, ,383.1 Continental 23 36,174 1,232 54, , ,264.0 Delta 61,528 2,019 92,549 1,259,488 1, ,471.0 Northwest 40,882 1,752 66,636 1,047,809 1, ,945.8 United 24 67,825 1,955 95,501 1,297,879 1, ,829.8 US Air 28, , , ,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:

30 29 Table 7 Average Stage Airline 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: Airline (Mainline Operation Only) Table 8 Alaska 800 American 1,332 Continental 1,252 Delta 1,045 Northwest 897 United 1,289 US Air 859 Average Stage Length (Miles)

31 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.

32 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 with a standard error of The R- squared and adjusted R-squared for the regression equation were and 0.155, respectively. The Durbin-Watson statistic was Nineteen percent of Northwest s total payload was freight and mail in 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