- Email: [email protected]
Slacks-based measure of efficiency of airports with airplanes delays as undesirable outputs
Computers & Operations Research 38 (2011) 131–139
Contents lists available at ScienceDirect
Computers & Operations Research journal homepage: www.elsevier.com/locate/caor
Slacks-based measure of efficiency of airports with airplanes delays as undesirable outputs Sebastia´n Lozano , Ester Gutie´rrez University of Seville, Department of Industrial Management ESI, Camino de los Descubrimientos, s/n 41092 Sevilla, Spain
a r t i c l e in fo
abstract
Available online 18 April 2010
This paper reports the slacks-based measure (SBM) of efficiency of 39 Spanish airports for years 2006 and 2007. In addition to the conventional outputs (namely aircraft traffic movements, passenger movements and cargo handled), two undesirable outputs have been considered: percentage of delayed flights and average conditional delay of delayed flights. The inputs considered quantify the physical infrastructure of the airports and are considered non-discretionary. The proposed Data Envelopment Analysis (DEA) approach assumes variable returns to scale and joint weak disposability of the desirable and undesirable outputs. The SBM model used has been found to have more discriminatory power than the common directional distance function approach. Also, the inclusion in the analysis of the undesirable effects of airport operations leads to more valid results. The results show that in both years more than half of the airports are technical efficient with the rest showing in general large inefficiencies due to slacks in the different outputs, slacks that the proposed SBM approach is able to identify and quantify. Overall, the system has significant improvement potential in cargo and to a less extent in passengers and percentage of delayed flights. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Airports Data envelopment analysis Slacks-based measure of efficiency Flights delays Undesirable outputs
1. Introduction Airport efficiency has been the subject of a number of research studies, some of which will be reviewed in the next section. Normally, the inputs considered represent either the production factors (labor and capital) or the physical infrastructure of the airports while the outputs consist of the volumes of aircraft operations, passengers and cargo. Efficient airports are those that maximize their outputs with their given inputs. The pursuit of efficiency, therefore, aims at increasing the number of aircraft movements as well as the number of passengers transported and cargo handled. In other words, in most efficiency studies in the literature, these outputs are increased as much as possible within the production possibility set (PPS) derived from the existing data. There are some studies, however, that take into account that an increase in aircraft traffic also has undesirable effects. Thus, Yu [1] and Yu et al. [2] consider aircraft noise as an undesirable output while Pathomsiri et al. [3] consider airplanes delays and number of delayed flights as undesirable outputs. The rationale for considering these undesirable outputs is that, otherwise, the efficiency logic would lead to congested airports with dense aircraft traffic and the accompanying disturbances to both the passengers suffering the delays and the local population suffering the noise. This can hardly be deemed a most desirable situation.
Corresponding author. Tel.: + 34 954487208; fax: + 34 954487329.
E-mail address: [email protected] (S. Lozano). 0305-0548/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2010.04.007
These stakeholders would rather live with less efficient airports. Fortunately, the problem is not with the concept of efficiency but with the misspecification error of not including undesirable outcomes in the analysis. In this paper, in addition to the conventional outputs (namely air traffic movements, passenger movements and cargo handled), two undesirable outputs are been considered: Percentage of delayed flights and average conditional delay of delayed flights. The inputs considered quantify the physical infrastructure of the airports and are considered non-discretionary. The mathematical tool used is Data Envelopment Analysis (DEA; [4–7]), a wellknown non-parametric production frontier approach aimed at assessing the relative performance of a set of comparable units. An innovative feature of the proposed approach is the use of the slacks-based measure (SBM) of efficiency, a technical efficiency measure with many desirable properties [8]. To the best of our knowledge, no previous study has used SBM in the context of undesirable outputs. The reason is that SBM DEA models are, in principle, non-linear and their linearization in the presence of weakly disposable undesirable outputs is not easy. We have been, however, able to linearize the SBM model in our case because the inputs considered are assumed to be non-discretionary. The structure of this paper is as follows. A review of previous airport efficiency studies is presented in Section 2. In Section 3, the proposed SBM DEA model is formulated. Section 4 reports the results of the proposed approach and compares them with those of the directional distance function. Finally, Section 5 summarizes and concludes.
132
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
2. DEA and airport efficiency There are a good number of DEA applications to airports efficiency assessment and productivity change estimations. Lozano and Gutie´rrez [9] present a recent review of the literature. There is a remarkable coincidence in the outputs considered in almost all studies and these are basically aircraft traffic movement, passenger movement and cargo handled [10]. These three outputs represent the main transportation services supported by airport operations. Some researchers have considered other outputs such as suitability to airlines, convenience or quality of service [11]. On the input side there is more variety and generally more data-availability constraints. The most common inputs considered are capital stock (or fixed assets) and operating costs, the latter sometimes disaggregated into labor costs and other operating expenditures. The capital stock input is often substituted by other more specific, surrogate inputs such as terminal area, number of runways, total runway length, aircraft parking positions, boarding gates, baggage belts, etc. About the DEA model used, the most common is radial input- or output-oriented with either variable returns to scale (VRS) [12–23] or constant returns to scale (CRS) [24–29]. Barros and Peypoch [30] use a non-oriented directional distance function (DDF) approach. Special mention must be made to Gillen and Lall [31,32] and Pels et al. [33,34] who analyze the airside and the terminal services separately. However, the papers that are more relevant and directly related to this one are those that consider undesirable outputs. Thus, Yu [1] uses a DDF CRS DEA approach that considered aircraft traffic movement as desirable output and aircraft noise as undesirable output. The data used corresponded to 14 Taiwanese airports and considered the following inputs: runway area, terminal area, apron area, number of routes connections with other domestic airports and city population (non-discretionary). Yu et al. [2] use a DDF CRS DEA approach to compute Malmquist– Luenberger Productivity Indexes of panel data from 4 Taiwanese airports. Airport revenue was a desirable output and aircraft noise an undesirable output. Passengers and aircraft movements were considered non-discretionary inputs. Other inputs considered were labor costs, capital stock and operating expenditures. Pathomsiri et al. [3] also used DDF to compute Malmquist– Luenberger Productivity Indexes for a panel of 56 US airports considering passenger movements, cargo and non-delayed flights as desirable outputs and time delays and number of delayed flights as undesirable outputs. Inputs considered were land area, number of runways and total runway area. Summarizing, to the best of our knowledge, only three papers have considered undesirable outputs in airport efficiency analysis, two of them taking into account aircraft noise and another one taking into account airplanes delays. In all three cases, a DDF approach has been used. In the next section we present a novel DEA approach that considers airplanes delays as undesirable outputs (unfortunately aircraft noise data were not available) and uses SBM for computing efficiency scores. Apart from the fact that no previous airports efficiency study has used SBM, an innovative feature of the proposed approach is that all previous SBM applications, including the original SBM model in Tone [8], have only considered inputs and outputs but no undesirable outputs.
Minimizing that ratio implies the simultaneous pursuit of improvements in both inputs and outputs. It is, therefore, a non-oriented model. It is also non-radial, i.e., it does not force the input and outputs to be improved uniformly or equi-proportionally, letting the maximum possible improvement in each dimension be computed by the model. In addition, the SBM efficiency score leaves no input or output slack unaccounted, i.e. all possible improvements are exhausted and properly taken into account in the objective function. In our case, since the inputs are non-discretionary and there are both desirable and undesirable outputs. This means that the normal SBM model needs to be adjusted accordingly. Our proposal is to handle the improvements in the undesirable outputs similarly to the way the inputs improvement are handled in the conventional SBM DEA model. Therefore, the proposed SBM DEA model minimizes the ratio of the average undesirable output reduction to the average desirable output increase. VRS have been assumed since given the limited competition among the airports it cannot be expected that they operate at the ¨ et al. most productive scale size (MPSS; [35]). Also, following Fare [36] (and numerous other DEA studies that deal with undesirable outputs) the desirable and undesirable outputs have been considered jointly weakly disposable, i.e. it is assumed that the undesirable outputs can always be decreased in the same proportion in which desirable outputs are decreased. Let Data i index of inputs g number of good (i.e., desirable) outputs k¼1, 2, y, g index of desirable outputs b number of bad (i.e., undesirable) outputs r¼ 1,2, y, b index of undesirable outputs N number of airports j¼1,2, y, N index of airports 0 index of specific airport whose efficiency is being assessed xij observed amount of input i of airport j ykj observed amount of desirable output k of airport j uij observed amount of undesirable output r of airport j Variables (l1, l2, y, lN) non-negative multipliers used for computing a linear combination of the airports in the data sample þ sk0 slack (i.e., potential increase) of desirable output k of airport 0 s slack (i.e., potential reduction) of undesirable output r of r0 airport 0 a auxiliary variable due to joint weak disposability of desirable and undesirable outputs The proposed SBM model (1) can be formulated as P 1ð1=bÞ br ¼ 1 ðs r0 =ur0 Þ Min r0 ¼ P þ =yk0 Þ 1 þ ð1=gÞ gk ¼ 1 ðsk0 s.t. N X
3. Proposed SBM DEA model The SBM DEA model projects each unit onto the efficient frontier and has many attractive features, among them, units-invariance. The original SBM DEA model computes the ratio of the average inputs reduction to the average output increase.
lj xij r xi0 8i
j¼1
a
N X
þ lj ykj ¼ yk0 þ sk0 8k
j¼1
a
N X j¼1
lj urj ¼ ur0 s 8r r0
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139 N X
N X
lj ¼ 1
j¼1
s r0 Z08r
ð1Þ
Although the above model is a fractional non-linear program it can be transformed into an easy-to-solve linear program in two steps. First, the non linearity in the constraints can be removed 0 defining the new variables lj ¼ a lj 8 j. The corresponding fractional linear program (2) is Min
r0 ¼
P 1ð1=bÞ br ¼ 1 ðs r0 =ur0 Þ P þ 1 þð1=gÞ gk ¼ 1 ðsk0 =yk0 Þ
0rar1 þ l0 j Z08j sk0 Z08k
ð2Þ
r0 ¼ t
b 1X s^ r0 b r ¼ 1 ur0
s.t.
l0 j xij r a xi0 8i
tþ
j¼1
þ l0 j ykj ¼ yk0 þ sk0
þ g 1 X s^ k0 ¼1 g k ¼ 1 yk0
N X
8k
j¼1 N X
s r0 Z08r
In the second step, the model can be transformed into a common linear program using the Charnes–Cooper transformation in a similar way as in the conventional SBM 0 model [8], i.e. introducing new variables t40 l^ j ¼ t l j 8j a^ ¼ t þ þ as^ k0 ¼ t sk0 8k s^ r0 ¼ t sr0 8r. The resulting model (3) is Min
s.t.
N X
l0 j ¼ a
j¼1
0 r a r1 þ lj Z08j sk0 Z08k
N X
133
l^ j xij r a^ xi0 8i
j¼1
l0 j urj ¼ ur0 s r0
N X
8r
j¼1
þ l^ j ykj ¼ t yk0 þ s^ k0
8k
j¼1
Table 1 Input and output data for the year 2006. Airport
RUNAREA (m2)
APRON (stands)
BAGB (belts)
CHECKIN (counters)
BOARDG (gates)
APM (103 pax)
ATM (103 oper.)
CARGO (tonnes)
PDF (%)
ACD (min.)
˜a A Corun Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
87,300 162,000 135,000 144,000 99,000 171,000 475,020 207,000 62,100 37,500 153,000 108,000 139,500 134,550 126,000 103,500 45,000 99,000 108,000 94,500 927,000 144,000 64,260 138,000 295,650 99,315 110,475 150,000 78,930 104,400 144,000 302,310 151,200 153,000 144,000 144,000 180,000 108,000 157,500
5 2 31 15 7 1 121 21 23 3 34 17 55 11 25 9 3 5 24 5 263 43 5 5 86 7 5 6 6 8 16 12 23 16 44 35 7 8 18
3 1 9 4 3 1 19 7 0 1 8 3 19 3 8 3 1 2 8 1 53 16 1 4 16 1 3 2 2 2 5 2 6 5 14 8 2 3 2
10 4 42 17 11 4 143 36 1 5 34 18 86 12 48 13 5 13 49 3 484 85 4 18 204 4 8 4 6 8 19 6 42 37 87 42 8 12 7
4 2 16 5 9 2 65 12 1 2 10 7 38 3 12 5 2 5 16 2 230 30 2 5 68 2 5 2 3 5 12 3 10 16 22 18 5 6 3
1014.780 17.520 8893.749 1055.545 1353.030 80.464 30,008.152 3876.062 19.568 171.444 4424.880 3614.223 10,286.635 1086.221 4460.141 1381.560 38.846 1175.328 5626.337 126.648 45,530.010 13,076.252 308.313 1645.886 22,408.302 375.309 1385.157 29.308 368.009 649.447 1994.519 435.887 3870.600 4025.601 8845.668 4969.113 457.618 1187.730 173.607
17.406 1.347 76.816 18.452 17.987 4.434 327.636 58.573 9.212 4.55 44.044 33.436 114.938 17.583 54.146 46.534 3.384 21.362 50.174 6.296 435.018 127.769 10.696 18.136 190.28 11.419 24.894 8.656 12.076 15.195 24.712 11.405 58.565 65.295 65.774 87.906 11.582 19.655 12.348
554.039 0 4930.928 35.55 199.497 0 93397.869 3417.746 0 164.079 3197.021 502.407 38,360.982 69.554 4423.566 309.873 4.593 1382.556 6113.887 0 315,808.744 5125.898 430.375 6.921 22,442.448 59.217 5.931 0 280.999 3.119 2587.799 5930.191 11530.23 23,180.961 9414.806 13,067.72 120.963 1252.411 30,343.616
14.18 3.71 15.35 12.33 13.72 6.43 13.20 12.60 3.51 0.63 8.70 7.68 5.05 10.82 11.16 10.08 0.37 3.35 11.65 12.26 18.93 12.86 3.22 14.01 13.30 12.90 10.83 2.00 13.65 12.53 9.35 6.16 7.72 4.46 8.94 10.18 11.56 12.69 6.09
17.50 26.68 19.50 19.64 18.35 17.79 19.20 18.82 40.75 14.39 18.55 20.62 18.26 20.62 21.60 19.04 15.39 19.16 23.34 15.98 18.36 20.41 17.85 19.40 18.58 17.48 19.88 25.95 17.35 18.01 18.66 21.24 19.43 18.33 19.59 19.16 16.72 18.59 20.80
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
134 N X
4. Numerical results and discussion
l^ j urj ¼ t ur0 s^ 8r r0
j¼1 N X
l^ j ¼ a^
j¼1
0 r a^ r t þ l^ j Z 08j s^ k0 Z 08k
s^ r0 Z08r
ð3Þ
In addition to the SBM efficiency score r0, the optimal solution þ to model (3) given by t , l^ j , a^ ,ðs^ k0 Þ ,ðs^ r0 Þ allows the computation of the target outputs for airport 0 as y k0 ¼ a
N X
lj ykj ¼
j¼1
N X j¼1
N 1 X l^ y
l0 j ykj ¼ t
j
kj
j¼1
þ 1 ðs^ Þ þ ¼ ½t yk0 þ ðs^ k0 Þ ¼ yk0 þ k0 8k t t N N N X X 1 X lj urj ¼ l0 j urj ¼ l^ j urj u r0 ¼ a t j¼1 j¼1 j¼1 1 ðs^ r0 Þ ¼ ½t ur0 ðs^ r0 Þ ¼ ur0 8r t t
In this section, we present and discuss the results of the application of the proposed SBM DEA model to 39 Spanish airports for years 2006 and 2007. All the airports are managed by the Spanish Airport and Air Navigation Agency (AENA, Aeropuertos ˜oles y Navegacio´n Ae´rea). The inputs considered are related to Espan the existing infrastructure at the airports, namely total runway area (RUNAREA), apron capacity (APRON), number of baggage belts (BAGB), number of check-in counters (CHECKIN) and number of boarding gates (BOARDG). These inputs are considered nondiscretionary (i.e., fixed) and have been extracted from AENA [37]. The desirable outputs considered include annual passenger movements (APM) and aircraft traffic movements (ATM) as well as cargo handled (CARGO) and the corresponding data are available on AENA website at http://www.aena.es/csee/Satellite?pagename=Estadisti cas/Home (last accessed 18 December, 2009). In addition, data on the percentage of delayed flights (PDF) and average conditional delay of delayed flights (ACD) at each airport were obtained from the Central Office for Delay Analysis (CODA) service of Eurocontrol (http://www.eurocontrol.int/eatm/public/standard_page/coda.html, last accessed 18 December, 2009). Tables 1 and 2 show the input and output data used.
Table 2 Input and output data for the year 2007. Airport
RUNAREA (m2)
APRON (stands)
BAGB (belts)
CHECKIN (counters)
BOARDG (gates)
APM (103 pax)
ATM (103 oper.)
CARGO (tonnes)
PDF (%)
ACD (min)
˜a A Corun Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
87,300 162,000 135,000 144,000 99,000 171,000 475,020 207,000 62,100 37,500 153,000 108,000 139,500 134,550 126,000 103,500 45,000 99,000 108,000 94,500 927,000 144,000 64,260 138,000 295,650 99,315 110,475 150,000 78,930 104,400 144,000 302,310 151,200 153,000 144,000 144,000 180,000 108,000 157,500
5 2 31 15 7 1 121 21 23 3 34 17 55 11 25 9 3 5 24 5 263 43 5 5 86 7 5 6 6 8 16 12 23 16 44 35 7 8 18
3 1 9 4 3 1 19 7 0 1 8 3 19 3 8 3 1 2 8 1 53 16 1 4 16 1 3 2 2 2 5 2 6 5 14 8 2 3 2
10 4 42 17 11 4 143 36 1 5 34 18 86 12 48 13 5 13 49 3 484 85 4 18 204 4 8 4 6 8 19 6 42 37 87 42 8 12 7
4 2 16 5 9 2 65 12 1 2 10 7 38 3 12 5 2 5 16 2 230 30 2 5 68 2 5 2 3 5 12 3 10 16 22 18 5 6 3
1266.804 19.888 9120.819 1206.634 1560.830 91.789 32,800.570 4277.610 22.429 184.762 4630.056 4848.619 10,354.858 1467.590 4765.121 1607.834 40.569 1207.572 5625.580 161.705 52,143.275 13,590.537 338.650 1995.162 23,227.983 498.473 1305.894 65.215 466.494 761.783 2050.121 512.184 4507.142 4125.034 8639.341 5929.916 512.929 1405.968 173.877
18.73 1.856 79.75 20.139 19.148 4.181 352.489 63.079 10.886 4.79 44.871 45.282 114.351 21.82 57.853 50.364 3.466 20.426 52.968 7.328 483.284 129.693 11.146 20.099 197.354 13.439 25.699 10.352 12.736 16.998 24.637 14.755 65.087 65.836 65.036 96.591 14.093 19.999 12.266
291.307 0.01 4531.829 19.89 196.741 0.08 96,769.571 3229.774 0 171.379 3133.231 234.18 37,231.907 72.443 4308.513 89.927 0.638 1398.325 5784.899 0.341 322,244.276 5814.847 434.097 1.728 22,833.556 47.455 11.213 0 245.436 1.473 2749.964 20,151.235 7389.789 25,166.142 9168.073 13,367.069 31.012 1952.616 31,359.305
15.24 3.33 11.54 13.91 16.20 7.90 13.17 13.60 4.13 0.29 10.44 10.49 6.61 12.65 11.28 11.20 0.26 3.19 12.12 14.91 19.53 15.24 2.98 9.07 14.18 13.73 11.64 5.15 14.50 13.10 11.97 7.20 7.39 4.32 8.48 9.46 12.15 14.64 8.46
18.60 19.60 18.94 18.54 17.68 18.53 18.63 18.15 22.52 15.77 17.68 18.19 16.88 18.54 22.70 17.10 18.32 16.50 19.63 17.83 18.05 18.67 15.47 18.76 19.16 18.03 19.16 18.77 16.35 17.43 18.28 19.65 19.40 17.64 17.06 19.63 17.62 18.00 20.05
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
135
Table 3 SBM efficiency score and output slacks for the year 2006. Airport
q0
+ sAPM (103 pax)
+ sAPM (103 oper.)
+ sCARGO (Tonnes)
sPCF (%)
+ sACD (min)
˜a A Corun Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
0.535 0.178 1.000 0.003 0.069 1.000 1.000 0.261 1.000 1.000 0.375 1.000 1.000 1.000 0.242 1.000 1.000 1.000 0.323 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.106 0.001 0.199 0.563 0.892 1.000 0.473 0.632 0.026 0.190 1.000
0.000 73.080 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 367.841 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 156.055 0.000 0.000 0.000 0.000 0.000 0.000 2431.305 34.576 0.000 0.000
0.000 2.608 0.000 1.990 0.824 0.000 0.000 0.000 0.000 0.000 2.653 0.000 0.000 0.000 2.137 0.000 0.000 0.000 11.934 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 9.272 1.846 0.000 0.000 29.635 0.000 0.000 0.000 0.000
506.363 70.933 0.000 21,470.871 4190.162 0.000 0.000 18,644.272 0.000 0.000 14,452.112 0.000 0.000 0.000 15,376.070 0.000 0.000 0.000 8045.089 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4312.517 9223.207 20,062.547 6622.005 2543.005 0.000 11,784.809 3621.304 7597.734 6191.287 0.000
8.32 0.00 0.00 7.95 10.52 0.00 0.00 6.48 0.00 0.00 0.92 0.00 0.00 0.00 7.65 0.00 0.00 0.00 8.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 9.06 7.40 4.84 1.77 0.41 0.00 3.34 3.21 9.39 10.64 0.00
0.29 14.94 0.00 1.07 2.46 0.00 0.00 0.25 0.00 0.00 0.00 0.00 0.00 0.00 5.38 0.00 0.00 0.00 7.62 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.07 0.18 0.08 2.24 0.60 0.00 2.81 1.88 0.70 2.90 0.00
Tables 3 and 4 show the SBM efficiency score r0 as well as the þ desirable and undesirable outputs slacks (sk0 and s r0 , respectively) for each airport in 2 years, 2006 and 2007. Although a good a number of airports (22 in year 2006 and 24 in 2007) are found efficient, the efficiency scores of the inefficient airports are rather low. The desirable output that can be increased by a larger amount is cargo handled. In some smaller airports (like Almerı´a or Santander) the potential output increase is much larger (more than 1000 times) the amount of cargo actually handled. In general, the other two desirable outputs can also often be increased but by smaller amounts (13.4% and 28.0% in average for APM in years 2006 and 2007 respectively, and 8.8% and 6.4% in average for ATM in years 2006 and 2007, respectively). As for the undesirable outputs, the potential reduction of PDF is generally larger (21.7% and 21.0% in average in years 2006 and 2007, respectively) than for ACD (5.0% and 4.1% in average years 2006 and 2007, respectively). The results are interesting because on the one hand it is surprising that so many airports are technical efficient. Of course, they are so in relative terms. Should the sample include also airports from other countries it is likely that fewer airports would be labeled efficient. Note that an efficient airport is one that, with its current infrastructure, carries out as many aircraft, passenger and freight movements as possible at the same time that delays are minimized. Airport inefficiencies can, thus, come from two main sources: low utilization (much less traffic than the nominal
capacity) or congestion (high throughput but excess delays). On the other hand, it is rather remarkable, and more noticeable in year 2007, the absence of airports with intermediate efficiency scores; either an airport is efficient or it is rather inefficient. Fig. 1 shows the change of the SBM efficiency score between both years. It can be noted that the efficiency of most airports does not change much from one year to the next. There are however a few exceptions that may require an inquiry for the possible reasons why their efficiency has increased significantly (as in the case of A ˜ a, Saragossa and Valencia) or has decreased significantly (as Corun in the case of La Gomera and Salamanca). To aid in this inquiry for the causes of inefficiency the SBM model provides the potential improvements for each output (desirable and undesirable) thus indicating in which dimensions are the airports underperforming (with respect to their benchmarks). As an argument for the consideration of the undesirable effects of activities in general and airport operations in particular we would like to check something that has been noted by other authors [38]: that not taking into account the undesirable outputs (when these exist) can give misleading efficiency assessments. Thus, Fig. 2 shows the SBM efficiency scores with and without taking into account the two undesirable outputs PDF and ACD. Note that disregarding the undesirable outputs generally improves the efficiency assessment except for a few cases (like La Gomera and Salamanca in year 2006 and, to a lesser extent, Seville in year 2007).
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
136
Table 4 SBM efficiency score and output slacks for the year 2007. Airport
q0
+ sAPM (103 pax)
+ sATM (103 oper.)
+ sCARGO (tonnes)
sPDF (%)
sACD (min)
˜a A Corun Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
1.000 0.267 1.000 0.002 0.091 1.000 1.000 0.256 1.000 1.000 0.292 1.000 1.000 1.000 0.233 1.000 0.333 1.000 0.305 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.215 0.100 0.000 0.197 1.000 1.000 1.000 0.404 1.000 0.007 0.270 1.000
0.000 56.749 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 507.673 0.000 125.080 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 302.149 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 120.412 0.000 0.000
0.000 1.101 0.000 1.141 4.207 0.000 0.000 0.000 0.000 0.000 7.299 0.000 0.000 0.000 2.457 0.000 0.828 0.000 9.810 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.116 0.000 0.000 9.780 0.000 0.000 0.000 29.992 0.000 0.000 0.740 0.000
0.000 54.181 0.000 21,552.113 3688.054 0.000 0.000 18,677.479 0.000 0.000 15,281.887 0.000 0.000 0.000 16,193.392 0.000 153.012 0.000 11,288.987 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 410.858 3808.789 7744.461 21,187.960 0.000 0.000 0.000 17,800.516 0.000 8259.743 5248.110 0.000
0.00 0.00 0.00 8.48 10.59 0.00 0.00 6.60 0.00 0.00 4.54 0.00 0.00 0.00 7.60 0.00 0.00 0.00 9.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.04 11.18 9.29 6.51 0.00 0.00 0.00 4.37 0.00 9.02 12.93 0.00
0.00 10.73 0.00 0.18 0.23 0.00 0.00 0.34 0.00 0.00 0.00 0.00 0.00 0.00 5.76 0.00 4.18 0.00 3.37 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.93 0.00 0.88 0.00 0.00 0.00 0.00 0.51 0.00 0.45 1.57 0.00
Finally, we will compare the proposed SBM efficiency score with the DDF efficiency measure that is commonly used when undesirable outputs are considered [39,40]. In particular, the proportional distance function corresponding to the direction vector g ¼(0,y, u) has been computed for years 2006 and 2007 and they are shown in Table 5. Note the lower discriminatory power of this efficiency measure, which can only project onto weakly efficient operation points. Thus, although the zero DDF value computed for most airports indicates that not all the desirable outputs can be improved and the undesirable outputs be reduced at the same time, the DDF efficiency measure does not tell us anything about the existing slacks along these output dimensions. There must exist, however, consistency between the SBM and DDF efficiency measures since whenever r0 is equal to unity (i.e., an airport is labeled as efficient by SBM) then DDF must ˜ a, Albacete, Lanzarote and San be zero. As the cases of A Corun Sebastian in year 2006 and Albacete, La Gomera and San Sebastian in year 2007 attest, the opposite does not necessarily hold, i.e. a zero DDF value of a weakly efficient airport does not imply true efficiency and therefore its SBM efficiency score r0 may be smaller than unity.
5. Summary and conclusion In this paper, SBM approach for airport efficiency assessment considering undesirable outputs has been proposed. Using
information on flight delays resulting from airport traffic congestion, the approach has been applied to the efficiency assessment of 39 Spanish airports in years 2006 and 2007. For each airport, the model computes an efficiency score and an improving slack (and therefore a target) for each output dimension. The application of SBM model for airports efficiency is novel and more so because our approach considers undesirable outputs, something which has not been considered in any previous application of SBM. The results show that the efficiency assessment of the airports when their undesirable outputs are ignored is generally different and can therefore be misleading. It has also been shown that the DDF approach commonly used when measuring efficiency in the presence of undesirable outputs has a lower discriminatory power than the proposed SBM approach. Specifically, the results indicate that a large proportion (more than a half) of airports are technical efficient with the rest having significant inefficiencies. Comparing the efficiency in each of the 2 years studied, the performance assessment of most of the airports is stable although a few airports have improved and others worsened their scores for reason that would have to be investigated by management case by case. Overall, the system has significant improvement potential in cargo and to a less extent in passengers and percentage of delayed flights. As for the managerial implications of the study, there are many not only at the level of each airport management, which can get feedback about its performance in each output dimension
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
A Coruña Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
1.00
SBM efficiency score
0.75
0.50
0.25
0.00 2007
2006
137
Fig. 1. Change in efficiency between years 2006 and 2007.
SBM efficiency score
0.75
0.50
0.25
0.00
with PDF & ACD
w/o PDF & ACD
Year 2007 1.00
0.75 SBM efficiency score
Year 2006 1.00
A Coruña Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
0.50
0.25
0.00 with PDF & ACD
w/o PDF & ACD
Fig. 2. SBM efficiency scores with and without undesirable outputs.
compared with its peers but also at the organizational level. This is so because all Spanish airports are under the responsibility of AENA which can take a system view when assigning priorities of new investments and deploying resources based on the observed utilization levels of the current infrastructure provided by the computed efficiency scores. Also the identification of airports with congestion problems may lead to strategic decisions of promoting the use of alternative nearby airports with slack capacity.
The information about which airport is in which situation can be extracted from the results of the DEA assessment. About possible continuations of this research, one is, of course, enlarging the dataset with observations from other airports outside Spain so that a more ambitious benchmarking be carried out. Another is studying productivity changes along time. And finally, another venue of research would be to explore the two subsystems (airside and terminal) that some authors have
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
138
Table 5 Proportional Distance Function efficiency assessment for years 2006 and 2007. Airport
DDF (2006)
DDF (2007)
Airport
DDF (2006)
DDF (2007)
˜a A Corun Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon
0.000 0.000 0.000 0.190 0.066 0.000 0.000 0.064 0.000 0.000 0.084 0.000 0.000 0.000 0.187 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.124 0.000 0.000 0.000 0.071 0.000 0.000 0.049 0.000 0.000 0.000 0.226 0.000 0.000 0.000 0.133 0.000
Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.105 0.167 0.166 0.018 0.000 0.095 0.006 0.051 0.103 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.146 0.000 0.062 0.118 0.000 0.000 0.000 0.013 0.000 0.086 0.055 0.000
identified and apply a network DEA model that would analyze the efficiency of each stage separately.
Acknowledgments The authors would like to thank Eurocontrol for providing the data on flights delays without which the analysis carried out in this paper would have not been possible. We also thank the reviewers for their constructive comments and suggestions.
References [1] Yu MM. Measuring physical efficiency of domestic airports in Taiwan with undesirable outputs and environmental factors. Journal of Air Transport Management 2004;10:295–303. [2] Yu MM, Hsu SH, Chang CC, Lee DH. Productivity growth of Taiwan’s major domestic airports in the presence of aircraft noise. Transportation Research Part E 2008;44(3):543–54. [3] Pathomsiri S, Haghani A, Dresner M, Windle RJ. Impact of undesirable outputs on the productivity of US airports. Transportation Research Part E 2008;44:235–59. [4] Thanassoulis E. Introduction to the theory and application of data envelopment analysis: a foundation text with integrated software. Norwell, MA: Kluwer Academic Publishers; 2001. [5] Cooper WW, Seiford LM, Tone K. Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software. 2nd ed. New York: Springer; 2006. [6] Cooper WW, Seiford LM, Zhu J. Handbook on data envelopment analysis. Springer; 2004. [7] Zhu J. Quantitative models for performance evaluation and benchmarking: data envelopment analysis with spreadsheets and DEA excel solver. Heidelberg: Springer; 2002. [8] Tone K. A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research 2001;130:498–509. [9] Lozano, S., Gutie´rrez, E., Efficiency analysis and target setting of Spanish airports. Networks and Spatial Economics (in press) doi:10.1007/ s11067-008-9096-1. [10] Barros CP, Weber WL. Productivity growth and biased technological change in UK airports. Transportation Research Part E 2009;45(4):642–53. [11] Adler N, Berechman J. Measuring airport quality from the airlines’ viewpoint: an application of data envelopment analysis. Transport Policy 2001;8: 171–81. [12] Parker D. The performance of BAA before and after privatisation: a DEA study. International Journal of Transport Economics 1999;33(2):133–46. [13] Sarkis J. An analysis of the operational efficiency of major airports in the United States. Journal of Operations Management 2000;18:335–51. [14] Fernandes E, Pacheco RR. Efficient use of airport capacity. Transportation Research Part A 2002;36:225–38. [15] Barros CP, Sampaio A. Technical and allocative efficiency in airports. International Journal of Transport Economics 2004;31(3):355–77.
[16] Yoshida Y, Fujimoto H. Japanese-airport benchmarking with the DEA and endogenous-weight TFP methods: testing the criticism of overinvestment in Japanese regional airports. Transportation Research Part E 2004;40:533–46. [17] Pacheco RR, Fernandes E, Santos MPS. Management style and airport performance in Brazil. Journal of Air Transportation Management 2006;12:324–30. [18] Lin LC, Hong CH. Operational performance evaluation of international major airports: an application of data envelopment analysis. Journal of Air Transport Management 2006;12:342–51. [19] Martı´n JC, Roma´n C. An application of DEA to measure the efficiency of Spanish airports prior to privatization. Journal of Air Transport Management 2001;7:149–57. [20] Martı´n JC, Roma´n C. A benchmarking analysis of Spanish commercial airports. A comparison between SMOP and DEA ranking methods. Network Spatial Economics 2006;6:111–34. [21] Martı´n JC, Roma´n C. Political opportunists and mavericks? A typology of Spanish airports International Journal of Transport Economics, XXXIV 2007(2):247–71. [22] Barros CP, Dieke PUC. Performance evaluation of Italian airports: a data envelopment analysis. Journal of Air Transport Management 2007;13: 184–91. [23] Barros CP, Dieke PUC. Measuring the economic efficiency of airports: a Simar–Wilson methodology analysis. Transportation Research Part E 2008;44(6):1039–51. [24] Murillo-Melchor C. An analysis of technical efficiency and productivity changes in Spanish airports using a Malmquist Index. International Journal of Transport Economics XXVI 1999(2):271–92. [25] Abbot M, Wu S. Total factor productivity and efficiency of Australian airports. Australian Economic Review 2002;35(3):244–60. [26] Bazargan M, Vasigh B. Size versus efficiency: a case study of US commercial airports. Journal of Air Transportation Management 2003;9:187–93. [27] Sarkis J, Talluri S. Performance based clustering for benchmarking US airports. Transportation Research Part A 2004;38:329–46. [28] Fung MKY, Wan KKH, Hui YV, Law JS. Productivity changes in Chinese airports 1995–2004. Transportation Research Part E 2008;44:521–42. [29] Tapiador FJ, Mateos A, Martı´-Henneberg J. The geographical efficiency of Spain’s regional airports. A quantitative analysis. Journal of Air Transport Management 2008;14(4):205–12. [30] Barros CP, Peypoch N. A comparative analysis of productivity change in Italian and Portuguese airports. International Journal of Transport Economics 2008;35(2):205–16. [31] Gillen D, Lall A. Developing measures of airport productivity and performance: an application of data envelopment analysis. Transportation Research E 1997;33(4):261–73. [32] Gillen D, Lall A. Non-parametric measures of efficiency of US airports. International Journal of Transport Economics 2001;28:283–306. [33] Pels E, Nijkamp P, Rietveld P. Relative efficiency of European airports. Transport Policy 2001;8:183–92. [34] Pels E, Nijkamp P, Rietveld P. Inefficiencies and scale economics of European airport operations. Transportation Research Part E 2003;39:341–61. [35] Banker RD. Estimating most productive scale size using data envelopment analysis. European Journal of Operational Research 1984;17:35–44. ¨ [36] Fare R, Grosskopf S, Lovell CAK, Pasurka C. Multilateral productivity comparisons when some outputs are undesirable: a non parametric approach. The Review of Economics and Statistics 1989;71:90–8.
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
˜ oles y [37] AENA. Spanish airports and tourism. Madrid: Aeropuertos Espan Navegacio´n Aerea; 2007. [38] Yu MM, Fan CK. Measuring the cost effectiveness of multimode bus transit in the presence of accident risks. Transportation Planning and Technology 2006;29(5):383–407.
139
¨ [39] Chung YR, Fare R, Grosskopf S. Productivity and undesirable outputs: a directional distance function approach. Journal of Environmental Management 1997;51:229–40. ¨ [40] Fare R, Grosskopf S. New directions: efficiency and productivity. Boston: Kluwer Academic Publishers; 2004.
Contents lists available at ScienceDirect
Computers & Operations Research journal homepage: www.elsevier.com/locate/caor
Slacks-based measure of efficiency of airports with airplanes delays as undesirable outputs Sebastia´n Lozano , Ester Gutie´rrez University of Seville, Department of Industrial Management ESI, Camino de los Descubrimientos, s/n 41092 Sevilla, Spain
a r t i c l e in fo
abstract
Available online 18 April 2010
This paper reports the slacks-based measure (SBM) of efficiency of 39 Spanish airports for years 2006 and 2007. In addition to the conventional outputs (namely aircraft traffic movements, passenger movements and cargo handled), two undesirable outputs have been considered: percentage of delayed flights and average conditional delay of delayed flights. The inputs considered quantify the physical infrastructure of the airports and are considered non-discretionary. The proposed Data Envelopment Analysis (DEA) approach assumes variable returns to scale and joint weak disposability of the desirable and undesirable outputs. The SBM model used has been found to have more discriminatory power than the common directional distance function approach. Also, the inclusion in the analysis of the undesirable effects of airport operations leads to more valid results. The results show that in both years more than half of the airports are technical efficient with the rest showing in general large inefficiencies due to slacks in the different outputs, slacks that the proposed SBM approach is able to identify and quantify. Overall, the system has significant improvement potential in cargo and to a less extent in passengers and percentage of delayed flights. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Airports Data envelopment analysis Slacks-based measure of efficiency Flights delays Undesirable outputs
1. Introduction Airport efficiency has been the subject of a number of research studies, some of which will be reviewed in the next section. Normally, the inputs considered represent either the production factors (labor and capital) or the physical infrastructure of the airports while the outputs consist of the volumes of aircraft operations, passengers and cargo. Efficient airports are those that maximize their outputs with their given inputs. The pursuit of efficiency, therefore, aims at increasing the number of aircraft movements as well as the number of passengers transported and cargo handled. In other words, in most efficiency studies in the literature, these outputs are increased as much as possible within the production possibility set (PPS) derived from the existing data. There are some studies, however, that take into account that an increase in aircraft traffic also has undesirable effects. Thus, Yu [1] and Yu et al. [2] consider aircraft noise as an undesirable output while Pathomsiri et al. [3] consider airplanes delays and number of delayed flights as undesirable outputs. The rationale for considering these undesirable outputs is that, otherwise, the efficiency logic would lead to congested airports with dense aircraft traffic and the accompanying disturbances to both the passengers suffering the delays and the local population suffering the noise. This can hardly be deemed a most desirable situation.
Corresponding author. Tel.: + 34 954487208; fax: + 34 954487329.
E-mail address: [email protected] (S. Lozano). 0305-0548/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2010.04.007
These stakeholders would rather live with less efficient airports. Fortunately, the problem is not with the concept of efficiency but with the misspecification error of not including undesirable outcomes in the analysis. In this paper, in addition to the conventional outputs (namely air traffic movements, passenger movements and cargo handled), two undesirable outputs are been considered: Percentage of delayed flights and average conditional delay of delayed flights. The inputs considered quantify the physical infrastructure of the airports and are considered non-discretionary. The mathematical tool used is Data Envelopment Analysis (DEA; [4–7]), a wellknown non-parametric production frontier approach aimed at assessing the relative performance of a set of comparable units. An innovative feature of the proposed approach is the use of the slacks-based measure (SBM) of efficiency, a technical efficiency measure with many desirable properties [8]. To the best of our knowledge, no previous study has used SBM in the context of undesirable outputs. The reason is that SBM DEA models are, in principle, non-linear and their linearization in the presence of weakly disposable undesirable outputs is not easy. We have been, however, able to linearize the SBM model in our case because the inputs considered are assumed to be non-discretionary. The structure of this paper is as follows. A review of previous airport efficiency studies is presented in Section 2. In Section 3, the proposed SBM DEA model is formulated. Section 4 reports the results of the proposed approach and compares them with those of the directional distance function. Finally, Section 5 summarizes and concludes.
132
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
2. DEA and airport efficiency There are a good number of DEA applications to airports efficiency assessment and productivity change estimations. Lozano and Gutie´rrez [9] present a recent review of the literature. There is a remarkable coincidence in the outputs considered in almost all studies and these are basically aircraft traffic movement, passenger movement and cargo handled [10]. These three outputs represent the main transportation services supported by airport operations. Some researchers have considered other outputs such as suitability to airlines, convenience or quality of service [11]. On the input side there is more variety and generally more data-availability constraints. The most common inputs considered are capital stock (or fixed assets) and operating costs, the latter sometimes disaggregated into labor costs and other operating expenditures. The capital stock input is often substituted by other more specific, surrogate inputs such as terminal area, number of runways, total runway length, aircraft parking positions, boarding gates, baggage belts, etc. About the DEA model used, the most common is radial input- or output-oriented with either variable returns to scale (VRS) [12–23] or constant returns to scale (CRS) [24–29]. Barros and Peypoch [30] use a non-oriented directional distance function (DDF) approach. Special mention must be made to Gillen and Lall [31,32] and Pels et al. [33,34] who analyze the airside and the terminal services separately. However, the papers that are more relevant and directly related to this one are those that consider undesirable outputs. Thus, Yu [1] uses a DDF CRS DEA approach that considered aircraft traffic movement as desirable output and aircraft noise as undesirable output. The data used corresponded to 14 Taiwanese airports and considered the following inputs: runway area, terminal area, apron area, number of routes connections with other domestic airports and city population (non-discretionary). Yu et al. [2] use a DDF CRS DEA approach to compute Malmquist– Luenberger Productivity Indexes of panel data from 4 Taiwanese airports. Airport revenue was a desirable output and aircraft noise an undesirable output. Passengers and aircraft movements were considered non-discretionary inputs. Other inputs considered were labor costs, capital stock and operating expenditures. Pathomsiri et al. [3] also used DDF to compute Malmquist– Luenberger Productivity Indexes for a panel of 56 US airports considering passenger movements, cargo and non-delayed flights as desirable outputs and time delays and number of delayed flights as undesirable outputs. Inputs considered were land area, number of runways and total runway area. Summarizing, to the best of our knowledge, only three papers have considered undesirable outputs in airport efficiency analysis, two of them taking into account aircraft noise and another one taking into account airplanes delays. In all three cases, a DDF approach has been used. In the next section we present a novel DEA approach that considers airplanes delays as undesirable outputs (unfortunately aircraft noise data were not available) and uses SBM for computing efficiency scores. Apart from the fact that no previous airports efficiency study has used SBM, an innovative feature of the proposed approach is that all previous SBM applications, including the original SBM model in Tone [8], have only considered inputs and outputs but no undesirable outputs.
Minimizing that ratio implies the simultaneous pursuit of improvements in both inputs and outputs. It is, therefore, a non-oriented model. It is also non-radial, i.e., it does not force the input and outputs to be improved uniformly or equi-proportionally, letting the maximum possible improvement in each dimension be computed by the model. In addition, the SBM efficiency score leaves no input or output slack unaccounted, i.e. all possible improvements are exhausted and properly taken into account in the objective function. In our case, since the inputs are non-discretionary and there are both desirable and undesirable outputs. This means that the normal SBM model needs to be adjusted accordingly. Our proposal is to handle the improvements in the undesirable outputs similarly to the way the inputs improvement are handled in the conventional SBM DEA model. Therefore, the proposed SBM DEA model minimizes the ratio of the average undesirable output reduction to the average desirable output increase. VRS have been assumed since given the limited competition among the airports it cannot be expected that they operate at the ¨ et al. most productive scale size (MPSS; [35]). Also, following Fare [36] (and numerous other DEA studies that deal with undesirable outputs) the desirable and undesirable outputs have been considered jointly weakly disposable, i.e. it is assumed that the undesirable outputs can always be decreased in the same proportion in which desirable outputs are decreased. Let Data i index of inputs g number of good (i.e., desirable) outputs k¼1, 2, y, g index of desirable outputs b number of bad (i.e., undesirable) outputs r¼ 1,2, y, b index of undesirable outputs N number of airports j¼1,2, y, N index of airports 0 index of specific airport whose efficiency is being assessed xij observed amount of input i of airport j ykj observed amount of desirable output k of airport j uij observed amount of undesirable output r of airport j Variables (l1, l2, y, lN) non-negative multipliers used for computing a linear combination of the airports in the data sample þ sk0 slack (i.e., potential increase) of desirable output k of airport 0 s slack (i.e., potential reduction) of undesirable output r of r0 airport 0 a auxiliary variable due to joint weak disposability of desirable and undesirable outputs The proposed SBM model (1) can be formulated as P 1ð1=bÞ br ¼ 1 ðs r0 =ur0 Þ Min r0 ¼ P þ =yk0 Þ 1 þ ð1=gÞ gk ¼ 1 ðsk0 s.t. N X
3. Proposed SBM DEA model The SBM DEA model projects each unit onto the efficient frontier and has many attractive features, among them, units-invariance. The original SBM DEA model computes the ratio of the average inputs reduction to the average output increase.
lj xij r xi0 8i
j¼1
a
N X
þ lj ykj ¼ yk0 þ sk0 8k
j¼1
a
N X j¼1
lj urj ¼ ur0 s 8r r0
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139 N X
N X
lj ¼ 1
j¼1
s r0 Z08r
ð1Þ
Although the above model is a fractional non-linear program it can be transformed into an easy-to-solve linear program in two steps. First, the non linearity in the constraints can be removed 0 defining the new variables lj ¼ a lj 8 j. The corresponding fractional linear program (2) is Min
r0 ¼
P 1ð1=bÞ br ¼ 1 ðs r0 =ur0 Þ P þ 1 þð1=gÞ gk ¼ 1 ðsk0 =yk0 Þ
0rar1 þ l0 j Z08j sk0 Z08k
ð2Þ
r0 ¼ t
b 1X s^ r0 b r ¼ 1 ur0
s.t.
l0 j xij r a xi0 8i
tþ
j¼1
þ l0 j ykj ¼ yk0 þ sk0
þ g 1 X s^ k0 ¼1 g k ¼ 1 yk0
N X
8k
j¼1 N X
s r0 Z08r
In the second step, the model can be transformed into a common linear program using the Charnes–Cooper transformation in a similar way as in the conventional SBM 0 model [8], i.e. introducing new variables t40 l^ j ¼ t l j 8j a^ ¼ t þ þ as^ k0 ¼ t sk0 8k s^ r0 ¼ t sr0 8r. The resulting model (3) is Min
s.t.
N X
l0 j ¼ a
j¼1
0 r a r1 þ lj Z08j sk0 Z08k
N X
133
l^ j xij r a^ xi0 8i
j¼1
l0 j urj ¼ ur0 s r0
N X
8r
j¼1
þ l^ j ykj ¼ t yk0 þ s^ k0
8k
j¼1
Table 1 Input and output data for the year 2006. Airport
RUNAREA (m2)
APRON (stands)
BAGB (belts)
CHECKIN (counters)
BOARDG (gates)
APM (103 pax)
ATM (103 oper.)
CARGO (tonnes)
PDF (%)
ACD (min.)
˜a A Corun Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
87,300 162,000 135,000 144,000 99,000 171,000 475,020 207,000 62,100 37,500 153,000 108,000 139,500 134,550 126,000 103,500 45,000 99,000 108,000 94,500 927,000 144,000 64,260 138,000 295,650 99,315 110,475 150,000 78,930 104,400 144,000 302,310 151,200 153,000 144,000 144,000 180,000 108,000 157,500
5 2 31 15 7 1 121 21 23 3 34 17 55 11 25 9 3 5 24 5 263 43 5 5 86 7 5 6 6 8 16 12 23 16 44 35 7 8 18
3 1 9 4 3 1 19 7 0 1 8 3 19 3 8 3 1 2 8 1 53 16 1 4 16 1 3 2 2 2 5 2 6 5 14 8 2 3 2
10 4 42 17 11 4 143 36 1 5 34 18 86 12 48 13 5 13 49 3 484 85 4 18 204 4 8 4 6 8 19 6 42 37 87 42 8 12 7
4 2 16 5 9 2 65 12 1 2 10 7 38 3 12 5 2 5 16 2 230 30 2 5 68 2 5 2 3 5 12 3 10 16 22 18 5 6 3
1014.780 17.520 8893.749 1055.545 1353.030 80.464 30,008.152 3876.062 19.568 171.444 4424.880 3614.223 10,286.635 1086.221 4460.141 1381.560 38.846 1175.328 5626.337 126.648 45,530.010 13,076.252 308.313 1645.886 22,408.302 375.309 1385.157 29.308 368.009 649.447 1994.519 435.887 3870.600 4025.601 8845.668 4969.113 457.618 1187.730 173.607
17.406 1.347 76.816 18.452 17.987 4.434 327.636 58.573 9.212 4.55 44.044 33.436 114.938 17.583 54.146 46.534 3.384 21.362 50.174 6.296 435.018 127.769 10.696 18.136 190.28 11.419 24.894 8.656 12.076 15.195 24.712 11.405 58.565 65.295 65.774 87.906 11.582 19.655 12.348
554.039 0 4930.928 35.55 199.497 0 93397.869 3417.746 0 164.079 3197.021 502.407 38,360.982 69.554 4423.566 309.873 4.593 1382.556 6113.887 0 315,808.744 5125.898 430.375 6.921 22,442.448 59.217 5.931 0 280.999 3.119 2587.799 5930.191 11530.23 23,180.961 9414.806 13,067.72 120.963 1252.411 30,343.616
14.18 3.71 15.35 12.33 13.72 6.43 13.20 12.60 3.51 0.63 8.70 7.68 5.05 10.82 11.16 10.08 0.37 3.35 11.65 12.26 18.93 12.86 3.22 14.01 13.30 12.90 10.83 2.00 13.65 12.53 9.35 6.16 7.72 4.46 8.94 10.18 11.56 12.69 6.09
17.50 26.68 19.50 19.64 18.35 17.79 19.20 18.82 40.75 14.39 18.55 20.62 18.26 20.62 21.60 19.04 15.39 19.16 23.34 15.98 18.36 20.41 17.85 19.40 18.58 17.48 19.88 25.95 17.35 18.01 18.66 21.24 19.43 18.33 19.59 19.16 16.72 18.59 20.80
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
134 N X
4. Numerical results and discussion
l^ j urj ¼ t ur0 s^ 8r r0
j¼1 N X
l^ j ¼ a^
j¼1
0 r a^ r t þ l^ j Z 08j s^ k0 Z 08k
s^ r0 Z08r
ð3Þ
In addition to the SBM efficiency score r0, the optimal solution þ to model (3) given by t , l^ j , a^ ,ðs^ k0 Þ ,ðs^ r0 Þ allows the computation of the target outputs for airport 0 as y k0 ¼ a
N X
lj ykj ¼
j¼1
N X j¼1
N 1 X l^ y
l0 j ykj ¼ t
j
kj
j¼1
þ 1 ðs^ Þ þ ¼ ½t yk0 þ ðs^ k0 Þ ¼ yk0 þ k0 8k t t N N N X X 1 X lj urj ¼ l0 j urj ¼ l^ j urj u r0 ¼ a t j¼1 j¼1 j¼1 1 ðs^ r0 Þ ¼ ½t ur0 ðs^ r0 Þ ¼ ur0 8r t t
In this section, we present and discuss the results of the application of the proposed SBM DEA model to 39 Spanish airports for years 2006 and 2007. All the airports are managed by the Spanish Airport and Air Navigation Agency (AENA, Aeropuertos ˜oles y Navegacio´n Ae´rea). The inputs considered are related to Espan the existing infrastructure at the airports, namely total runway area (RUNAREA), apron capacity (APRON), number of baggage belts (BAGB), number of check-in counters (CHECKIN) and number of boarding gates (BOARDG). These inputs are considered nondiscretionary (i.e., fixed) and have been extracted from AENA [37]. The desirable outputs considered include annual passenger movements (APM) and aircraft traffic movements (ATM) as well as cargo handled (CARGO) and the corresponding data are available on AENA website at http://www.aena.es/csee/Satellite?pagename=Estadisti cas/Home (last accessed 18 December, 2009). In addition, data on the percentage of delayed flights (PDF) and average conditional delay of delayed flights (ACD) at each airport were obtained from the Central Office for Delay Analysis (CODA) service of Eurocontrol (http://www.eurocontrol.int/eatm/public/standard_page/coda.html, last accessed 18 December, 2009). Tables 1 and 2 show the input and output data used.
Table 2 Input and output data for the year 2007. Airport
RUNAREA (m2)
APRON (stands)
BAGB (belts)
CHECKIN (counters)
BOARDG (gates)
APM (103 pax)
ATM (103 oper.)
CARGO (tonnes)
PDF (%)
ACD (min)
˜a A Corun Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
87,300 162,000 135,000 144,000 99,000 171,000 475,020 207,000 62,100 37,500 153,000 108,000 139,500 134,550 126,000 103,500 45,000 99,000 108,000 94,500 927,000 144,000 64,260 138,000 295,650 99,315 110,475 150,000 78,930 104,400 144,000 302,310 151,200 153,000 144,000 144,000 180,000 108,000 157,500
5 2 31 15 7 1 121 21 23 3 34 17 55 11 25 9 3 5 24 5 263 43 5 5 86 7 5 6 6 8 16 12 23 16 44 35 7 8 18
3 1 9 4 3 1 19 7 0 1 8 3 19 3 8 3 1 2 8 1 53 16 1 4 16 1 3 2 2 2 5 2 6 5 14 8 2 3 2
10 4 42 17 11 4 143 36 1 5 34 18 86 12 48 13 5 13 49 3 484 85 4 18 204 4 8 4 6 8 19 6 42 37 87 42 8 12 7
4 2 16 5 9 2 65 12 1 2 10 7 38 3 12 5 2 5 16 2 230 30 2 5 68 2 5 2 3 5 12 3 10 16 22 18 5 6 3
1266.804 19.888 9120.819 1206.634 1560.830 91.789 32,800.570 4277.610 22.429 184.762 4630.056 4848.619 10,354.858 1467.590 4765.121 1607.834 40.569 1207.572 5625.580 161.705 52,143.275 13,590.537 338.650 1995.162 23,227.983 498.473 1305.894 65.215 466.494 761.783 2050.121 512.184 4507.142 4125.034 8639.341 5929.916 512.929 1405.968 173.877
18.73 1.856 79.75 20.139 19.148 4.181 352.489 63.079 10.886 4.79 44.871 45.282 114.351 21.82 57.853 50.364 3.466 20.426 52.968 7.328 483.284 129.693 11.146 20.099 197.354 13.439 25.699 10.352 12.736 16.998 24.637 14.755 65.087 65.836 65.036 96.591 14.093 19.999 12.266
291.307 0.01 4531.829 19.89 196.741 0.08 96,769.571 3229.774 0 171.379 3133.231 234.18 37,231.907 72.443 4308.513 89.927 0.638 1398.325 5784.899 0.341 322,244.276 5814.847 434.097 1.728 22,833.556 47.455 11.213 0 245.436 1.473 2749.964 20,151.235 7389.789 25,166.142 9168.073 13,367.069 31.012 1952.616 31,359.305
15.24 3.33 11.54 13.91 16.20 7.90 13.17 13.60 4.13 0.29 10.44 10.49 6.61 12.65 11.28 11.20 0.26 3.19 12.12 14.91 19.53 15.24 2.98 9.07 14.18 13.73 11.64 5.15 14.50 13.10 11.97 7.20 7.39 4.32 8.48 9.46 12.15 14.64 8.46
18.60 19.60 18.94 18.54 17.68 18.53 18.63 18.15 22.52 15.77 17.68 18.19 16.88 18.54 22.70 17.10 18.32 16.50 19.63 17.83 18.05 18.67 15.47 18.76 19.16 18.03 19.16 18.77 16.35 17.43 18.28 19.65 19.40 17.64 17.06 19.63 17.62 18.00 20.05
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
135
Table 3 SBM efficiency score and output slacks for the year 2006. Airport
q0
+ sAPM (103 pax)
+ sAPM (103 oper.)
+ sCARGO (Tonnes)
sPCF (%)
+ sACD (min)
˜a A Corun Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
0.535 0.178 1.000 0.003 0.069 1.000 1.000 0.261 1.000 1.000 0.375 1.000 1.000 1.000 0.242 1.000 1.000 1.000 0.323 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.106 0.001 0.199 0.563 0.892 1.000 0.473 0.632 0.026 0.190 1.000
0.000 73.080 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 367.841 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 156.055 0.000 0.000 0.000 0.000 0.000 0.000 2431.305 34.576 0.000 0.000
0.000 2.608 0.000 1.990 0.824 0.000 0.000 0.000 0.000 0.000 2.653 0.000 0.000 0.000 2.137 0.000 0.000 0.000 11.934 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 9.272 1.846 0.000 0.000 29.635 0.000 0.000 0.000 0.000
506.363 70.933 0.000 21,470.871 4190.162 0.000 0.000 18,644.272 0.000 0.000 14,452.112 0.000 0.000 0.000 15,376.070 0.000 0.000 0.000 8045.089 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4312.517 9223.207 20,062.547 6622.005 2543.005 0.000 11,784.809 3621.304 7597.734 6191.287 0.000
8.32 0.00 0.00 7.95 10.52 0.00 0.00 6.48 0.00 0.00 0.92 0.00 0.00 0.00 7.65 0.00 0.00 0.00 8.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 9.06 7.40 4.84 1.77 0.41 0.00 3.34 3.21 9.39 10.64 0.00
0.29 14.94 0.00 1.07 2.46 0.00 0.00 0.25 0.00 0.00 0.00 0.00 0.00 0.00 5.38 0.00 0.00 0.00 7.62 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.07 0.18 0.08 2.24 0.60 0.00 2.81 1.88 0.70 2.90 0.00
Tables 3 and 4 show the SBM efficiency score r0 as well as the þ desirable and undesirable outputs slacks (sk0 and s r0 , respectively) for each airport in 2 years, 2006 and 2007. Although a good a number of airports (22 in year 2006 and 24 in 2007) are found efficient, the efficiency scores of the inefficient airports are rather low. The desirable output that can be increased by a larger amount is cargo handled. In some smaller airports (like Almerı´a or Santander) the potential output increase is much larger (more than 1000 times) the amount of cargo actually handled. In general, the other two desirable outputs can also often be increased but by smaller amounts (13.4% and 28.0% in average for APM in years 2006 and 2007 respectively, and 8.8% and 6.4% in average for ATM in years 2006 and 2007, respectively). As for the undesirable outputs, the potential reduction of PDF is generally larger (21.7% and 21.0% in average in years 2006 and 2007, respectively) than for ACD (5.0% and 4.1% in average years 2006 and 2007, respectively). The results are interesting because on the one hand it is surprising that so many airports are technical efficient. Of course, they are so in relative terms. Should the sample include also airports from other countries it is likely that fewer airports would be labeled efficient. Note that an efficient airport is one that, with its current infrastructure, carries out as many aircraft, passenger and freight movements as possible at the same time that delays are minimized. Airport inefficiencies can, thus, come from two main sources: low utilization (much less traffic than the nominal
capacity) or congestion (high throughput but excess delays). On the other hand, it is rather remarkable, and more noticeable in year 2007, the absence of airports with intermediate efficiency scores; either an airport is efficient or it is rather inefficient. Fig. 1 shows the change of the SBM efficiency score between both years. It can be noted that the efficiency of most airports does not change much from one year to the next. There are however a few exceptions that may require an inquiry for the possible reasons why their efficiency has increased significantly (as in the case of A ˜ a, Saragossa and Valencia) or has decreased significantly (as Corun in the case of La Gomera and Salamanca). To aid in this inquiry for the causes of inefficiency the SBM model provides the potential improvements for each output (desirable and undesirable) thus indicating in which dimensions are the airports underperforming (with respect to their benchmarks). As an argument for the consideration of the undesirable effects of activities in general and airport operations in particular we would like to check something that has been noted by other authors [38]: that not taking into account the undesirable outputs (when these exist) can give misleading efficiency assessments. Thus, Fig. 2 shows the SBM efficiency scores with and without taking into account the two undesirable outputs PDF and ACD. Note that disregarding the undesirable outputs generally improves the efficiency assessment except for a few cases (like La Gomera and Salamanca in year 2006 and, to a lesser extent, Seville in year 2007).
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
136
Table 4 SBM efficiency score and output slacks for the year 2007. Airport
q0
+ sAPM (103 pax)
+ sATM (103 oper.)
+ sCARGO (tonnes)
sPDF (%)
sACD (min)
˜a A Corun Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
1.000 0.267 1.000 0.002 0.091 1.000 1.000 0.256 1.000 1.000 0.292 1.000 1.000 1.000 0.233 1.000 0.333 1.000 0.305 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.215 0.100 0.000 0.197 1.000 1.000 1.000 0.404 1.000 0.007 0.270 1.000
0.000 56.749 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 507.673 0.000 125.080 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 302.149 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 120.412 0.000 0.000
0.000 1.101 0.000 1.141 4.207 0.000 0.000 0.000 0.000 0.000 7.299 0.000 0.000 0.000 2.457 0.000 0.828 0.000 9.810 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.116 0.000 0.000 9.780 0.000 0.000 0.000 29.992 0.000 0.000 0.740 0.000
0.000 54.181 0.000 21,552.113 3688.054 0.000 0.000 18,677.479 0.000 0.000 15,281.887 0.000 0.000 0.000 16,193.392 0.000 153.012 0.000 11,288.987 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 410.858 3808.789 7744.461 21,187.960 0.000 0.000 0.000 17,800.516 0.000 8259.743 5248.110 0.000
0.00 0.00 0.00 8.48 10.59 0.00 0.00 6.60 0.00 0.00 4.54 0.00 0.00 0.00 7.60 0.00 0.00 0.00 9.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.04 11.18 9.29 6.51 0.00 0.00 0.00 4.37 0.00 9.02 12.93 0.00
0.00 10.73 0.00 0.18 0.23 0.00 0.00 0.34 0.00 0.00 0.00 0.00 0.00 0.00 5.76 0.00 4.18 0.00 3.37 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.93 0.00 0.88 0.00 0.00 0.00 0.00 0.51 0.00 0.45 1.57 0.00
Finally, we will compare the proposed SBM efficiency score with the DDF efficiency measure that is commonly used when undesirable outputs are considered [39,40]. In particular, the proportional distance function corresponding to the direction vector g ¼(0,y, u) has been computed for years 2006 and 2007 and they are shown in Table 5. Note the lower discriminatory power of this efficiency measure, which can only project onto weakly efficient operation points. Thus, although the zero DDF value computed for most airports indicates that not all the desirable outputs can be improved and the undesirable outputs be reduced at the same time, the DDF efficiency measure does not tell us anything about the existing slacks along these output dimensions. There must exist, however, consistency between the SBM and DDF efficiency measures since whenever r0 is equal to unity (i.e., an airport is labeled as efficient by SBM) then DDF must ˜ a, Albacete, Lanzarote and San be zero. As the cases of A Corun Sebastian in year 2006 and Albacete, La Gomera and San Sebastian in year 2007 attest, the opposite does not necessarily hold, i.e. a zero DDF value of a weakly efficient airport does not imply true efficiency and therefore its SBM efficiency score r0 may be smaller than unity.
5. Summary and conclusion In this paper, SBM approach for airport efficiency assessment considering undesirable outputs has been proposed. Using
information on flight delays resulting from airport traffic congestion, the approach has been applied to the efficiency assessment of 39 Spanish airports in years 2006 and 2007. For each airport, the model computes an efficiency score and an improving slack (and therefore a target) for each output dimension. The application of SBM model for airports efficiency is novel and more so because our approach considers undesirable outputs, something which has not been considered in any previous application of SBM. The results show that the efficiency assessment of the airports when their undesirable outputs are ignored is generally different and can therefore be misleading. It has also been shown that the DDF approach commonly used when measuring efficiency in the presence of undesirable outputs has a lower discriminatory power than the proposed SBM approach. Specifically, the results indicate that a large proportion (more than a half) of airports are technical efficient with the rest having significant inefficiencies. Comparing the efficiency in each of the 2 years studied, the performance assessment of most of the airports is stable although a few airports have improved and others worsened their scores for reason that would have to be investigated by management case by case. Overall, the system has significant improvement potential in cargo and to a less extent in passengers and percentage of delayed flights. As for the managerial implications of the study, there are many not only at the level of each airport management, which can get feedback about its performance in each output dimension
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
A Coruña Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
1.00
SBM efficiency score
0.75
0.50
0.25
0.00 2007
2006
137
Fig. 1. Change in efficiency between years 2006 and 2007.
SBM efficiency score
0.75
0.50
0.25
0.00
with PDF & ACD
w/o PDF & ACD
Year 2007 1.00
0.75 SBM efficiency score
Year 2006 1.00
A Coruña Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
0.50
0.25
0.00 with PDF & ACD
w/o PDF & ACD
Fig. 2. SBM efficiency scores with and without undesirable outputs.
compared with its peers but also at the organizational level. This is so because all Spanish airports are under the responsibility of AENA which can take a system view when assigning priorities of new investments and deploying resources based on the observed utilization levels of the current infrastructure provided by the computed efficiency scores. Also the identification of airports with congestion problems may lead to strategic decisions of promoting the use of alternative nearby airports with slack capacity.
The information about which airport is in which situation can be extracted from the results of the DEA assessment. About possible continuations of this research, one is, of course, enlarging the dataset with observations from other airports outside Spain so that a more ambitious benchmarking be carried out. Another is studying productivity changes along time. And finally, another venue of research would be to explore the two subsystems (airside and terminal) that some authors have
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
138
Table 5 Proportional Distance Function efficiency assessment for years 2006 and 2007. Airport
DDF (2006)
DDF (2007)
Airport
DDF (2006)
DDF (2007)
˜a A Corun Albacete Alicante Almeria Asturias Badajoz Barcelona Bilbao Cordoba El Hierro Fuerteventura Girona-Costa Brava Gran Canaria Granada-Jaen Ibiza Jerez La Gomera La Palma Lanzarote Leon
0.000 0.000 0.000 0.190 0.066 0.000 0.000 0.064 0.000 0.000 0.084 0.000 0.000 0.000 0.187 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.124 0.000 0.000 0.000 0.071 0.000 0.000 0.049 0.000 0.000 0.000 0.226 0.000 0.000 0.000 0.133 0.000
Madrid Barajas Malaga Melilla Murcia Palma de Mallorca Pamplona Reus Salamanca San Sebastian Santander Santiago Saragossa Seville Tenerife North Tenerife South Valencia Valladolid Vigo Vitoria
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.105 0.167 0.166 0.018 0.000 0.095 0.006 0.051 0.103 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.146 0.000 0.062 0.118 0.000 0.000 0.000 0.013 0.000 0.086 0.055 0.000
identified and apply a network DEA model that would analyze the efficiency of each stage separately.
Acknowledgments The authors would like to thank Eurocontrol for providing the data on flights delays without which the analysis carried out in this paper would have not been possible. We also thank the reviewers for their constructive comments and suggestions.
References [1] Yu MM. Measuring physical efficiency of domestic airports in Taiwan with undesirable outputs and environmental factors. Journal of Air Transport Management 2004;10:295–303. [2] Yu MM, Hsu SH, Chang CC, Lee DH. Productivity growth of Taiwan’s major domestic airports in the presence of aircraft noise. Transportation Research Part E 2008;44(3):543–54. [3] Pathomsiri S, Haghani A, Dresner M, Windle RJ. Impact of undesirable outputs on the productivity of US airports. Transportation Research Part E 2008;44:235–59. [4] Thanassoulis E. Introduction to the theory and application of data envelopment analysis: a foundation text with integrated software. Norwell, MA: Kluwer Academic Publishers; 2001. [5] Cooper WW, Seiford LM, Tone K. Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software. 2nd ed. New York: Springer; 2006. [6] Cooper WW, Seiford LM, Zhu J. Handbook on data envelopment analysis. Springer; 2004. [7] Zhu J. Quantitative models for performance evaluation and benchmarking: data envelopment analysis with spreadsheets and DEA excel solver. Heidelberg: Springer; 2002. [8] Tone K. A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research 2001;130:498–509. [9] Lozano, S., Gutie´rrez, E., Efficiency analysis and target setting of Spanish airports. Networks and Spatial Economics (in press) doi:10.1007/ s11067-008-9096-1. [10] Barros CP, Weber WL. Productivity growth and biased technological change in UK airports. Transportation Research Part E 2009;45(4):642–53. [11] Adler N, Berechman J. Measuring airport quality from the airlines’ viewpoint: an application of data envelopment analysis. Transport Policy 2001;8: 171–81. [12] Parker D. The performance of BAA before and after privatisation: a DEA study. International Journal of Transport Economics 1999;33(2):133–46. [13] Sarkis J. An analysis of the operational efficiency of major airports in the United States. Journal of Operations Management 2000;18:335–51. [14] Fernandes E, Pacheco RR. Efficient use of airport capacity. Transportation Research Part A 2002;36:225–38. [15] Barros CP, Sampaio A. Technical and allocative efficiency in airports. International Journal of Transport Economics 2004;31(3):355–77.
[16] Yoshida Y, Fujimoto H. Japanese-airport benchmarking with the DEA and endogenous-weight TFP methods: testing the criticism of overinvestment in Japanese regional airports. Transportation Research Part E 2004;40:533–46. [17] Pacheco RR, Fernandes E, Santos MPS. Management style and airport performance in Brazil. Journal of Air Transportation Management 2006;12:324–30. [18] Lin LC, Hong CH. Operational performance evaluation of international major airports: an application of data envelopment analysis. Journal of Air Transport Management 2006;12:342–51. [19] Martı´n JC, Roma´n C. An application of DEA to measure the efficiency of Spanish airports prior to privatization. Journal of Air Transport Management 2001;7:149–57. [20] Martı´n JC, Roma´n C. A benchmarking analysis of Spanish commercial airports. A comparison between SMOP and DEA ranking methods. Network Spatial Economics 2006;6:111–34. [21] Martı´n JC, Roma´n C. Political opportunists and mavericks? A typology of Spanish airports International Journal of Transport Economics, XXXIV 2007(2):247–71. [22] Barros CP, Dieke PUC. Performance evaluation of Italian airports: a data envelopment analysis. Journal of Air Transport Management 2007;13: 184–91. [23] Barros CP, Dieke PUC. Measuring the economic efficiency of airports: a Simar–Wilson methodology analysis. Transportation Research Part E 2008;44(6):1039–51. [24] Murillo-Melchor C. An analysis of technical efficiency and productivity changes in Spanish airports using a Malmquist Index. International Journal of Transport Economics XXVI 1999(2):271–92. [25] Abbot M, Wu S. Total factor productivity and efficiency of Australian airports. Australian Economic Review 2002;35(3):244–60. [26] Bazargan M, Vasigh B. Size versus efficiency: a case study of US commercial airports. Journal of Air Transportation Management 2003;9:187–93. [27] Sarkis J, Talluri S. Performance based clustering for benchmarking US airports. Transportation Research Part A 2004;38:329–46. [28] Fung MKY, Wan KKH, Hui YV, Law JS. Productivity changes in Chinese airports 1995–2004. Transportation Research Part E 2008;44:521–42. [29] Tapiador FJ, Mateos A, Martı´-Henneberg J. The geographical efficiency of Spain’s regional airports. A quantitative analysis. Journal of Air Transport Management 2008;14(4):205–12. [30] Barros CP, Peypoch N. A comparative analysis of productivity change in Italian and Portuguese airports. International Journal of Transport Economics 2008;35(2):205–16. [31] Gillen D, Lall A. Developing measures of airport productivity and performance: an application of data envelopment analysis. Transportation Research E 1997;33(4):261–73. [32] Gillen D, Lall A. Non-parametric measures of efficiency of US airports. International Journal of Transport Economics 2001;28:283–306. [33] Pels E, Nijkamp P, Rietveld P. Relative efficiency of European airports. Transport Policy 2001;8:183–92. [34] Pels E, Nijkamp P, Rietveld P. Inefficiencies and scale economics of European airport operations. Transportation Research Part E 2003;39:341–61. [35] Banker RD. Estimating most productive scale size using data envelopment analysis. European Journal of Operational Research 1984;17:35–44. ¨ [36] Fare R, Grosskopf S, Lovell CAK, Pasurka C. Multilateral productivity comparisons when some outputs are undesirable: a non parametric approach. The Review of Economics and Statistics 1989;71:90–8.
S. Lozano, E. Gutie´rrez / Computers & Operations Research 38 (2011) 131–139
˜ oles y [37] AENA. Spanish airports and tourism. Madrid: Aeropuertos Espan Navegacio´n Aerea; 2007. [38] Yu MM, Fan CK. Measuring the cost effectiveness of multimode bus transit in the presence of accident risks. Transportation Planning and Technology 2006;29(5):383–407.
139
¨ [39] Chung YR, Fare R, Grosskopf S. Productivity and undesirable outputs: a directional distance function approach. Journal of Environmental Management 1997;51:229–40. ¨ [40] Fare R, Grosskopf S. New directions: efficiency and productivity. Boston: Kluwer Academic Publishers; 2004.