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Journal of Air Transport Management 16 (2010) 334e336

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Journal of Air Transport Management

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Measuring the influence of congestion on efficiency in worldwide airports

Rui Cunha Marques*, Pedro SimõesCenter of Urban and Regional Systems, Technical University of Lisbon, Avenida Rovisco Pais, Lisbon, Portugal

Keywords:AirportsCongestionEfficiency

* Corresponding author. Tel.: þ351 218418305; fax:E-mail address: rcmar@civil.ist.utl.pt (R.C. Marque

0969-6997/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.jairtraman.2010.03.002

a b s t r a c t

This short communication evaluates the influence of congestion on the technical efficiency of airportsusing three different approaches. To accomplish this aim a sample of 141 worldwide airports is used. Theresults show considerable signs of congestion inefficiency in some airports, highlighting the importanceof studying this phenomenon.

� 2010 Elsevier Ltd. All rights reserved.

1. The problem of congestion

Congestion is an issue in the airport industry; for example, dueto the number of movements, particularly in the peak hours.Congestion is characterized by the decrease of outputs produced asa consequence of a large increase of inputs used or the decrease ofone or more outputs by the increase of other. In this communica-tion we compare three different approaches available to computethe congestion effect on efficiency. The first was introduced by Färeet al. (1985). It was the first study to define congestion algebraicallyusing a radial measure. Later, other two alternatives to measurecongestion efficiency were proposed respectively by Cooper et al.(2001) and Tone and Sahoo (2004) using non-radial measures.Cooper et al. argue that input congestion occurs whenever morethan one input is employed while all other inputs are held constant,and this leads to a fall in the outputs. This approach is based on thehypothesis of diminishing marginal returns. Congestion requiresa negative marginal product to take place. Tone and Sahoo usesa unified approach to measure congestion efficiency rooted in theslacks-based measure (SBM).

2. Different approaches to measure congestion

2.1. Färe et al. approach

The Färe et al. method to measure congestion comprises twostages whereby each one distinguishes the “strong disposal” from“weak disposal” properties given by the inequality and equality inthe traditional Charnes, Cooper and Rhodes (CCR) model (Charneset al., 1978), respectively. Therefore, it is possible to compute twomeasures of technical efficiency (q* e b*). With more restrictive

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constraints in the ‘weak disposal’model, we will obtain 0 � q* � b*.This property allows for measuring the congestion by means of 0 �Cðq*; b*Þ¼ q

*

b* � 1. The computation of the two models in a two-

stage procedure provides the Färe et al. estimation of congestion. Inthis case, an airport shows signs of congestion if and only ifCðq*; b*Þ < 1. In contrast, congestion is not present if Cðq*; b*Þ ¼ 1.

2.2. Cooper et al. approach

The Cooper et al. approach also proceeds in a two-stage methodto compute the congestion. The comparison with the Färe et al.approach reveals some differences between them, inter alia, theaddition of the convexity condition and consequently it includesthe Banker, Charnes and Cooper (BCC) model (Banker et al., 1984)and also the incorporation of slacks into the objective function,beingmultiplied by the non-Archimedean value (3> 0). The latter isa relevant difference when compared with the Färe et al. approach.Under a general perspective, in the Cooper et al. approach the non-zero slacks have more weight. Furthermore, the second stage usedas Brockett et al. (1998) increases even more the differences for thetreatment of slacks adopted by Färe et al.

2.3. Tone and Sahoo’s approach

Tone and Sahoo have proposed a new unified approach tomeasure congestion efficiency. This method allows us to evaluatecongestion of inputs via an output oriented approach and it issimilar to Cooper et al. output oriented method in so far as a BCCoutput-oriented model is used in the first stage. However, this isdistinguished by the SBM procedure used in the second stage (Tone,2001). The main interpretation of this ratio is that the correlationbetween an average reduction in inputs corresponds to a certainincrease of outputs produced.

Tone and Sahoo developed two definitions distinguishing strongfrom weak congestion. In practical terms, strong congestion

Fig. 1. Technical inefficiency of worldwide airports according to CRS and VRS models.

Fig. 2. Levels of congestion inefficiency of airports according to Färe et al. approach.

Fig. 3. Levels of congestion inefficiency of airports according to Cooper et al. approach.

R.C. Marques, P. Simões / Journal of Air Transport Management 16 (2010) 334e336 335

corresponds to the congestion of all inputs while in the weakcongestion not all inputs are congested. Strong congestion impliesweak congestion but not vice-versa. This approach has severalappealing features, such as the fact that negative marginalproductivity is linked to the existence of congestion (unlike Färeet al. method), the analysis can easily be carried out using friendlysoftware and, finally, the result is comprehensive and easilyunderstood.

3. Are the worldwide airports congested?

3.1. Data, model specification and data envelopment analysisresults

We considered a model with four inputs and three outputs. Theoutputs adopted were the number of movements, the number ofpassengers and the cargo transported whereas the inputs were thenumber of runways, the number of gates, the terminal area and the

number of employees. The orientation of the model is nota consensual aspect of the efficiency models in airports. An inputminimization orientation, which favors the public service view, isusually adopted but nowadays airport industry is much more thanjust this and although the public services component isunchangeable, we privileged here an output orientation.

Thiswork uses airports data relative to the year 2006.Weused thedatabase of Air Transport Research Society (ATRS), although in somecases we collected data from airport websites and from their annualaccount reports to complement it. The sample includes 141 airports.With the exception of Tone and Sahoo’s approach, all the computa-tions are carried out with Matlab codes developed by the authors.

The performance of worldwide airports was measured by theapplication of data envelopment analysis (DEA) with an outputorientation (see, about DEA technique, Fried et al., 2008). Therefore,two models were computed, namely DEA-CCR (consideringconstant returns to scalee CRS) and DEA-BCC (considering variablereturns to scale e VRS).

Table 1Comparison of congestion results between the three approaches.

Färe et al. Cooper et al. Tone and Sahoo

Congestion average (whole sample) 0.057 0.077 0.063Maximum 0.58 0.65 0.67Congested airports (no.) 73 77 80Average of congested airports 11.0 13.8 11.1

Fig. 4. Levels of congestion inefficiency of airports according to Tone and Sahoo’s approach.

R.C. Marques, P. Simões / Journal of Air Transport Management 16 (2010) 334e336336

Fig. 1 provides the inefficiency estimates using the DEA-CCR andDEA-BCC models. The computation of scale inefficiency from thefigure is immediate. The results show that 28 airports out of 141 areefficient under the DEA-CCR model and 53 under the DEA-BCCmodel. As expected, the DEA-BCC model shows higher efficiencythan the DEA-CCR model. The DEA-BCC model presents an averagevalue of inefficiency of 0.19 while DEA-CCR model gives a value of0.3.

3.2. Färe et al. approach

Färe et al. approach, assuming VRS (with the CRS the results arecomparable), measures the congestion through the ratio betweenstrong efficiency and weak efficiency. The results show that 73 outof the 141 airports are congested. On average, the worldwideairports are 5.7% inefficiently congested. However, congestioninefficiency increases to 11.0% in airports whenwe consider just thecongested ones. Fig. 2 presents the congestion inefficiency resultsof the 141 airports analyzed. Richmond, Dubai, Munich, LondonStansted, Albany, Paris Orly, Christchurch, Winnipeg, Orlando andBirmingham are the airports which display the greatest congestioninefficiency.

3.3. Cooper et al. approach

Regarding Cooper et al. approach, the results show that 77airports are inefficiently congested. The average value obtained forall the sample was 7.7% and 13.8% for inefficiently congestedairports. Fig. 3 shows the congestion inefficiency results of eachairport. We found that the airports of Munich, Dubai, Detroit, Bir-mingham, Richmond, Vienna, Christchurch, Jakarta, Paris-Orly andPortland have the highest congestion inefficiencies. In general theresults are quite similar to the Färe et al. approach.

3.4. Tone and Sahoo’s approach

At last we applied the Tone and Sahoo’s approach and we foundthat 80 airports are inefficiently congested. The average ofcongestion inefficiency in the whole sample corresponds to 6.3% ofinefficiency. For the inefficiently congested airports this percentagerises to 11.1%. From the highest congested airports the Tone andSahoo’s approach identified Vienna, Chiang Kai-Check, Macau,Zurich, Ottawa, Albany, Portland, London Heathrow, LondonStansted and Paris Orly. Fig. 4 shows the congestion inefficiencyresults of each airport with the Tone and Sahoo’s approach.

3.5. Concluding remarks

From the comparison between different approaches we identi-fied important differences in the results, since the assumptions ofeach approach are diverse. However, there are several congestedairports in the three methodologies and with similar levels ofinefficiency. A priori there are no doubts about the existence ofcongestion in these airports. In this circumstance we found 34airports. Table 1 systematizes the results obtained with the threeapproaches adopted and available in the literature. Although thereis lack of consensus about how to measure congestion inefficiencyand what is the best technique to use, this paper highlights theimportance of this phenomenon. In our sample, we found thatmore than 50% are inefficiently congested and that they representat least about 6% of inefficiency for the whole sample and 11% onlyfor the inefficiently congested ones.

References

Banker, R., Charnes, A., Cooper, W., 1984. Some models for estimating technical andscale inefficiencies in data envelopment analysis. Management Science 30,1078e1092.

Brockett, P., Cooper, W., Shin, H., Wang, Y., 1998. Inefficiency and congestion inChinese production before and after the 1978 economic reforms. Socio-Economic Planning Sciences 32, 1e20.

Charnes, A., Cooper, W., Rhodes, E., 1978. Measuring the efficiency of decisionmaking units. European Journal of Operational Research 2, 429e444.

Cooper, W., Gu, B., Li, S., 2001. Comparisons and evaluations of alternativeapproaches to the treatment of congestion in DEA. European Journal of Oper-ational Research 132, 62e74.

Färe, R., Grosskopf, S., Lovell, C., 1985. The Measurement of Efficiency of Production.Kluwer-Nijhoff, Boston.

Fried, H., Lovell, K., Schmidt, S., 2008. The Measurement of Productive Efficiency andProductivity Change. Oxford University Press, New York.

Tone, K., 2001. A slacks-based measure of efficiency in data envelopment analysis.European Journal of Operational Research 130, 498e509.

Tone, K., Sahoo, B., 2004. Degree of scale economies and congestion: a unified DEAapproach. European Journal of Operational Research 158, 755e772.