MEASURING AND RANKING EFFICIENCY OF MAJOR AIRPORTS

IN THE UNITED STATES USING DATA ENVELOPMENT ANALYSIS

Myunghyun Lee

Project report submitted to the faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

in

Civil Engineering

Antonio A. Trani, Chairman

Hesham Rakha

Hojong Baik

July 8, 2004

Blacksburg, Virginia

Keywords: Data Envelopment Analysis (DEA), Ranking DEA, GoDEA, TOPSIS

Efficiency of Airports

MEASURING AND RANKING EFFICIENCY OF MAJOR IRPORTS

IN THE UNITED STATES USING DATA ENVELOPMENTANALYSIS

Myunghyun Lee

Abstract

An airport is an important piece of infrastructure in air transportation system. This

project focuses on measuring and ranking the efficiency of airports in the United States

using the basic DEA, Ranking DEA, Goal programming and DEA and TOPSIS.

. In general, airport authorities of relatively inefficient airports are trying to benchmark

the operational strategies of efficient airports. This project focuses on evaluating hub

airports in the United States.

ATL, LAX, and MEM airports are relatively efficient among forty four hub

airports in the United States based on the performances and airport facilities of the 2000

year when the results of all applied methods in this project, the basic DEA ranking, the

Cross Efficiency ranking, the Andersen-Petersen ranking and TOPSIS ranking method,

are compared. The implication of this project is that airport authorities in the United

States would benchmark these three airports to maximize operation and management

efficiency for their airports. In general, most of the airports are handling passengers and

freight. Therefore, ATL and LAX would be the most efficient hub airports in the United

States. The capacities of airport facilities and more appropriate input data like financial

data should be considered in the follow up research.

TABLES OF CONTENTS

LIST OF FIGURE AND TABLES ………………………………..…………..ⅳ

1. PURPOSE ………………………………………………………..….………1

2. DEA ………………………………………………………………………….1

3. DATA COLLECTION AND PROCEDURE OF ANALYSIS ………....……3

4. DEA MODELS …………………………………………………….…..……6

4.1. Inequality Case …………………………………………………………..6

4.2. Equality Case …………………………………………………..….…….6

5. GoDEA ……………………………………………………………..………..9

6. RANKING DEA MODELS ………………………………………...……...12

6.1. Andersen-Petersen DEA …………………………………….…..…..….12

6.2. Cross Efficiency Ranking Method ……………………………...…..….13

6.3. TOPSIS ……………………………………………………………..…..17

7. LIMITATIONS AND CONCLUSIONS …………………………….….…. 19

BIBLIOGRAPHY …………………………………………………….....….....20

APPENDIX .…………………………………………………………...…....…21

iii

LIST OF FIGURE AND TABLES

Figure 1. Efficiency Score in Equality Case….………………………………..7

Table 1. Basic DEA Results …………………….……………………………..8

Table 2. Results of GoDEA ……………………….………………………….11

Table 3. Results of Andersen-Petersen DEA …………………………………13

Table 4. Cross Efficient Ranking of 12 Airports ……….…………………….15

Table 5. Results of Cross Efficiency Ranking ………………….…………….16

Table 6. Results of TOPSIS …………………………………….…………….18

Appendix 1: Airport Code ………………………………………….…………21

Appendix 2: Airport Data ……………………………………………….…….23

Appendix 3: The Example of GoDEA Preemptive Case in Excel Solver ….....24

iv

1. PURPOSE

An airport is an important piece of infrastructure in air transportation system.

This project focuses on measuring and ranking the efficiency of airports in the United

States. The rankings evaluated by different ways such as a Cross Efficiency Matrix and

Andersen-Petersen’s DEA are compared in this project. This project also provides the

ranking of TOPSIS (Technique for Order Preference by Similarity to Ideal Solution)

which is one technique of Multiple Criteria Decision Making (MCDM). The efficiency

ranking would be helpful for decision makers i.e. airport authorities and air transportation

policy makers to determinate airport strategies and air transportation policy.

In general, airport authorities of relatively inefficient airports are trying to

benchmark the operational strategies of efficient airports. This project focuses on

evaluating hub airports in the United States. In this project, GoDEA (Goal programming

and DEA) is applied to see the shortfalls or excesses of inputs and outputs under the

specific condition by minimizing the slacks associated with inputs and outputs. GoDEA

results can explain the shortfalls or excesses of inputs and outputs of airports in reaching

the target set of inputs and outputs.

2. DEA

Data Envelopment Analysis (DEA) is a non-parametric method for evaluating the

relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and

outputs. DEA is based on productivity theory of microeconomics. Productivity models

have traditionally been used to measure the efficiency of systems. DEA productivity

models for given DMU use the ratio that is based on the amount of outputs per given set

of inputs. DEA is a multi-factor productivity approach, which can consider multiple

inputs and outputs. The advantages of DEA are that no assumptions are made about the

production function and multiple inputs and outputs are aggregated without any prior

specification of weights.

According to Gillen and Lall (1997), methods of measuring efficiency are

summarized below:

1

- non-parametric methods: indexes of partial and total factor productivity, DEA

- parametric methods: estimation of neoclassical and stochastic cost or production

functions

Partial productivity measures are not able to handle multiple outputs, and they do

not consider the difference in factor prices nor do they take account the difference in the

other factors used in production. One solution to some of these problems is to calculate

and compare an index of total factor productivity (TFP). TFP can not solver completely

the shortcomings of partial productivity measure. It is not very informative for ranking

management strategies. Extracting and obtaining more information from measures of TFP

typically depends on reliance on estimating parametric neo-classical cost or production

functions. The data requirements are more difficult to analyze than partial measures. In

addition, data on physical inputs and outputs, this measure also needs information on

prices, which is used to aggregate inputs and outputs. DEA is another alternative when

the outputs are not easily or clearly defined; for example in measuring productivity in

schools, hospitals or government institutes. It is also useful in determining the efficiency

of firms, especially, as it is difficult to recognize their natural prices.

DEA is a linear programming-based technique. The basic model requires

information on inputs and outputs. Indeed, this is also a major weakness of DEA, as it

does not incorporate any information of factor prices of production. For this reason DEA

cannot be used to analyze cost efficiency. Firms may be technically efficient but cost

inefficient. Additionally, it is possible that firms ranked technically inefficient by DEA

may be able to produce their outputs at a lower cost than those ranked as technically

efficient. DEA can include multiple outputs and inputs. Inputs and outputs can be defined

in a very general manner without getting into problems of aggregation. All productivity

measures have the weakness that they do not directly include user-borne costs. Using

proxies can include these. If more of a measure is desirable it can be modeled as output

and if less of something is better, it can be regarded as input. This is an attractive feature

as in many service industries like a bank. DEA can also use the proxy outputs including

output combinations that would not be used with other efficiency measures. For example,

gross-ton-miles and car-miles or gross-ton-miles and revenues are able to be regarded as

alternative measures of outputs in the rail industry (Gillen and Lall, 1997).

2

3. DATA COLLECTION AND PROCEDURE OF ANALYSIS

The efficiency of forty four airports in the United States is measured using four

outputs and two inputs in this project. Forty four airports as DMUs are listed at the

Appendix 1. All thirty one large hub airports are included. The used outputs and inputs

are shown below (Appendix 2);

- Outputs: the number of enplaned passengers, the number of enplaned revenue-

tons (freight + mail), the number of aircraft departure, the number of total delays

(departure + arrival)

- Inputs: the number of runways, the number of gates

All data used in the analysis are based on the year 2000. For example, the lesser the

number of total flight delays, the better the performance of the airport is. The more

outputs except total delays are, the better the performances of airports get. Therefore, the

number of total delays needs to be modified. The approaches of considering undesirable

outputs like delay flights at an airport in DEA are summarized below:

▪ The indirect approaches: to transform the value of the undesirable output variables

(1) additive inverse method: f(Q) = - Q

(2) undesirable output Q are considered as input

(3) large scalar M is added to the undesirable outputs: M-Q

(4) multiplicative inverse method: 1/Q

▪ The direct approaches: to include the undesirable output data directly into the DEA

model, to modify the assumption of the model

The third method of the indirect approaches is applied while making the

analytical basic data in this project. The proxy, (100,000 – the number of total delays), is

used instead of the number of total delays in the analysis. Delay in airports is a very

important issue recently because of the consumer’s complaint increase and the resource

limitation for airport facility improvement. Therefore, mitigating delay of airports is one

of the key policies of FAA.

The output-oriented model is conducted because it might be almost impossible

for inputs like a runway and a gate to be changed in order to minimize the operating costs

of an airport for the short period. When an airport invests into the new runway or the new

3

gate in a terminal, it might be very difficult for airport managers to disinvest to save costs.

The construction of a runway and a gate needs a long period. Sometimes several years are

needed. The construction period would be longer if the planning step were considered in

a construction period. The CCR (Charnes, Cooper and Rhodes) model assumes constant

returns to scale and the BCC (Banker, Charnes and Cooper) model assumes variable

returns to scale while determining the efficiency score of DMUs. The CCR model is

applied in this project because the change of inputs like a runway or a gate need a long

time as I mentioned before. The input-oriented model is to minimize inputs while

satisfying at least the given output levels. The output-oriented model is to maximize

outputs without requiring more of any of the observed input values. This model explains

how much outputs can be increased without an increase in inputs. It is called as the

output increasing measure of technical efficiency. The formulations of input-oriented and

output-oriented CCR model are shown below. The BCC model has one more constraint

( ) than the CCR model in the dual formulation. 11

=∑=

n

jjλ

CCR MODEL Input-Oriented Model Output-Oriented Model

LP ∑=

=s

rrjr yuz

10 0

max

subject to

∑=

=m

iiji xv

11

0 , jj ∀0

njxvyus

r

m

iijirjr ,,2,10

1 1L=≤−∑ ∑

= =

irvu ir ,0 ∀≥

∑=

=m

iiji xvz

10 0

min

subject to

11

0=∑

=

s

rrjr yu , jj ∀0

njxvyus

r

m

iijirjr ,,2,10

1 1L=≤−∑ ∑

= =

irvu ir ,0 ∀≥ DLP (Dual)

jj

sryy

mixx

tosubject

j

rj

n

jrjj

n

jijijj

∀≥

=≥

=≤

∑

∑

=

=

0

1

1

0,

,,2,1

,,2,1

max

0

0

λ

φλ

λ

φ

L

L

jjz

sryyz

mixxz

tosubject

j

n

jrjrjj

n

jijijj

∀≥

=≥

=≤

∑

∑

=

=

0

1

1

0,

,,2,1

,,2,1

min

0

0

L

Lθ

θ

4

where,

rjy : amount of output r from DMU j

ijx : amount of input i from DMU j

ru : the weight given to output r

iv : the weight given to input i

jjz λ, : the weight given to DMUj

s: the number of outputs

m: the number of inputs

n: the number of DMUs

The left-hand side in the first constraint of DLP (Dual LP) represents the hypothetical

DMU which is formed by taking weighted averages of the real DMUs for each input. The

fact that jλ are the same in all of constraints means that each of the inputs and outputs of

the hypothetical DMU is the same weighted average of those of the real DMUs. An

optimal solution of the output oriented model relates to that of the input oriented model

via: . The optimal solution of the input oriented model is not

greater than 1. Therefore, the optimal solution of the output oriented model is not less

than 1. It can be depicted such as and . The higher the value of is, the

less efficient the DMU is. represents the input reduction rate, while describes the

output enlargement rate (Cooper, Seiford and Tone, 2000).

***** /,/1 θλθφ jj z==

1* ≤θ 1* ≥φ *φ

*θ *φ

According to Cooper, Seiford and Tone (2000), reasons for solving the CCR

model using the dual are the following:

- The computational effort of LP (Linear Programming) is increasing in

proportion to powers of the number of constraints. n is larger than (m+s). LP has n

constraints. DLP has (m+s) constraints.

- The pertinent max-slack solution by using LP cannot be found.

- The interpretations of DLP are more straightforward because the solutions are

characterized as inputs and outputs that correspond to the original data where the

multipliers provided by solutions to LP represent evaluations of these observed values.

This project considers two ways in making constraint formulations. One is the

5

inequality constraint of inputs. It is general constraint in DEA. Another is the equality

constraint of inputs. The second method means that inputs are fixed exogenously at each

airport. Input variables are uncontrollable in this case. The reason for this assumption is

that airport authorities could not easily increase or decrease the number of runways and

gates at an airport in a short period of time.

4. DEA MODELS

4.1. Inequality Case

The formulation for the inequality case is shown below. It is the general

formulation of DEA. The left hand side of first constraint represents the hypothetical

DMU formed by taking weighted averages of the real DMUs for each input. This is less

than or equal to the actual input level of DMU.

jj

sryy

mixx

tosubject

j

rj

n

jrjj

n

jijijj

∀≥

=≥

=≤

∑

∑

=

=

0

1

1

0,

,,2,1

,,2,1

max

0

0

λ

φλ

λ

φ

K

K

Ten airports were found in which the relative efficiency score is equal to one. These are

ATL, LAX, EWR, MSP, SEA, HNL, SAN, SJC, MEM and SAT . The efficient score of

BDL is about 0.98. It is a secondary best efficiency score. The worst five airports are PIT,

BWI, IAD, MCO and CLE. PIT and BWI have especially lower score than 0.5.

4.2. Equality Case

The formulation for the Equality case is shown below. The first constraint means

that the input of hypothetical DMU is the same as the actual input. This comes from an

assumption that the number of existing runways and gates of an airport are optimal or

unchangeable for a specific period. Runways and gates can not be easily changeable.

6

Inputs are regarded as uncontrollable factors in this case.

jj

sryy

mixx

tosubject

j

rj

n

jrjj

n

jijijj

∀≥

=≥

==

∑

∑

=

=

0

1

1

0,

,,2,1

,,2,1

max

0

0

λ

φλ

λ

φ

K

K

As seen in Table1, the numbers of efficient airports are twelve such as ATL, LAX, EWR,

MSP, MIA SEA, CVG, HNL, SAN, SJC, MEM and SAT. Two more airports become

efficient airports compared to the inequality case. MIA and CVG are added to an efficient

airport group as compared with inequality case. Scores of remained airports are same but

only three airports, JFK, STL and MCO, have just a little different scores as compared

with Inequality case. For example, JKF’s relative efficiency is 62.71% at the equality

case, while it is 62.23% at the inequality case. Only the equality case will be considered

after this chapter.

.

0

0.2

0.4

0.6

0.8

1

1.2

ATL

ORD

LAX

DFW

SFO

DEN

PHX

LAS

DTW

EWR

MSPMIAIAH

JFK

STL

MCO

SEA

BOS

LGA

PHL

CLT

CVG

HNL

PIT

BWI

IAD

SLC

TPA

SAN

FLL

DCA

MD

PDX

CLE

SJCMCI

MEM

RDU

MSY

BNA

HOUIND

BDL

SAT

Figure 1. Efficiency Score in Equality Case

7

Table 1. Basic DEA Results.

Airport Efficiency Score in Inequality case

Ranking in Inequality

Efficiency Score in Equality case

Ranking in Equality

ATL 1.0000 1 1.0000 1 ORD 0.8711 16 0.8711 17 LAX 1.0000 1 1.0000 1 DFW 0.8549 18 0.8549 19 SFO 0.6485 34 0.6485 34 DEN 0.7826 20 0.7826 21 PHX 0.7612 23 0.7612 24 LAS 0.7293 27 0.7293 28 DTW 0.5799 39 0.5799 39 EWR 1.0000 1 1.0000 1 MSP 1.0000 1 1.0000 1 MIA 0.9307 14 1.0000 1 IAH 0.7217 29 0.7217 30 JFK 0.6223 37 0.6271 37 STL 0.7708 22 0.7757 22 MCO 0.5576 41 0.5734 40 SEA 1.0000 1 1.0000 1 BOS 0.6682 31 0.6682 32 LGA 0.8121 19 0.8121 20 PHL 0.6292 36 0.6292 36 CLT 0.6410 35 0.6410 35 CVG 0.6679 32 1.0000 1 HNL 1.0000 1 1.0000 1 PIT 0.4639 44 0.4639 44 BWI 0.4996 43 0.4996 43 IAD 0.5407 42 0.5407 42 SLC 0.6019 38 0.6019 38 TPA 0.7279 28 0.7279 29 SAN 1.0000 1 1.0000 1 FLL 0.8614 17 0.8614 18 DCA 0.7425 26 0.7425 27 MDW 0.9585 12 0.9585 14 PDX 0.7504 25 0.7504 26 CLE 0.5686 40 0.5686 41 SJC 1.0000 1 1.0000 1 MCI 0.7739 21 0.7739 23

MEM 1.0000 1 1.0000 1 RDU 0.7084 30 0.7084 31 MSY 0.7557 24 0.7557 25 BNA 0.6500 33 0.6500 33 HOU 0.9411 13 0.9411 15 IND 0.8958 15 0.8958 16 BDL 0.9799 11 0.9799 13 SAT 1.0000 1 1.0000 1

8

5. GoDEA

Goal programming and DEA (GoDEA) gets to the frontier by minimizing

deviation variables related to inputs and outputs. Thanassoulis and Dyson (1992)

developed models which can be used to estimate alternative input-output target levels to

make relatively inefficient DMUs efficient. Their models incorporate preference over

potential improvements to individual input-output levels so that the resultant target levels

reflect the user’s preference over alternative paths to efficiency. Their analysis illustrates

the practical usefulness of the models and emphasizes the alternative measures of relative

efficiency implicit in the models developed. Thanassoulis and Dyson (1992) explain

some DMUs may be able to articulate the targets they would ideally wish to adopt. Such

ideal targets would reflect the degree to which each DMU considers it desirable and/or

feasible to improve each input and /or output level. The ideal targets need not contain

only improvements to current input-output levels. The DMU may be willing to sacrifice

the level of some inputs and /or outputs in order to improve the levels of others. The ideal

targets specified by a DMU may in general be neither feasible nor efficient. Feasible

input-output levels are those which can be expressed as nonnegative linear combinations

of observed input-output levels.

Thanassoulis and Dyson (1992) suggest the model explained in the following

section. The solution of model reveals feasible input-output levels as close as possible to

the ideal targets.

randiandjforkcj

mixckx

sryccy

ts

cwcwkwkwMin

ji

jrj

n

j

tiiiijj

n

j

trrrrjj

m

i

s

rri

s

rriii

m

iii

∀=≥∀≥

==−+

==−+

+++

∑

∑

∑ ∑∑∑

=

=

= =

+

=

+−

=

−

2,10,,0

,,2,1

,,2,1

..

1

21

1

21

1 1

22

1

1122

1

11

γ

γ

γ

L

L

where,

:try ideal output level

9

:tix ideal input level

:w user-specified weight

:, kc deviation from target level of output and input respectively

This formulation is modified to be suitable in the uncontrollable input case,

namely the linear GoDEA formulation for forty four airports case is shown below.

jjrccj

sryccy

mixx

tosubject

cwcwMin

rrj

rj

n

jrrrjj

n

jijijj

rr

s

rrr

∀∀≥∀≥

==−+

==

+

∑

∑

∑

=

=

=

021

1

21

1

22

1

11

,0,,0

,2,1

,2,1

)(

0

0

λ

λ

λ

L

L

1rw and are respectively user-specified weights attached to the deviation and

from the target level of output r. is underachievement and is

overachievement of the ideal level of output r.

2rw 1

rc2rc 1

rc 2rc

Pre-emptive and Non-preemptive weighting structure over the deviation of

outputs is used. Pre-emptive GoDEA assumes that the weights of the delay and the

number of passenger are 4 and 2, respectively. Another assumption is that target level of

inputs and outputs is the existing airport facilities and performances. The results are

shown in Table 2. Ck1 in this table means underachievement of output k. Ck2 is

overachievement of output k as k =1, 2, 3, 4 means the number of passenger, the number

of cargo-ton, the number of aircraft departure and total flight delays output respectively.

For example, C11 is the underachievement of the number of passenger in Table 2. C12

means the overachievement of it. As seen in Table 2, fifteen airports have

underachievement or overachievement of outputs; however, the remaining twenty nine

airports do not have it. Twenty nine airports do not have the shortfalls and the excesses of

the corresponding outputs. The under- or over-achievements of fifteen airports are too

small. The slacks for all outputs are almost zero. In preemptive case the slacks for the

delay output of all airports except EWR, HNL and SJC is zero. It would be difficult to

say that the shortfalls or excesses of outputs seem to be apparently in fifteen airports.

10

Table 2. Results of GoDEA

Preemptive C11 C12 C21 C22 C31 C32 C41 C42LAX* 7.451E-13 0 0 0 3.176E-12 0 0 0SFO 6.023E-13 0 0 0 0 0 0 0LAS 7.652E-12 0 0 0 0 0 0 0DTW 0 8.017E-13 0 0 0 5.44E-12 0 0EWR* 0 8.304E-13 9.569E-11 0 0 0 0 4.661E-12JFK 0 0 0 0 0 6.236E-12 0 0 SEA 0 1.766E-12 0 0 5.096E-12 0 0 0BOS 0 1.122E-12 0 0 0 4.187E-11 0 0LGA 1.819E-12 0 0 0 0 0 0 0HNL* 4.297E-13 0 0 0 0 4.182E-12 0 2.212E-12DCA 0 9.449E-13 0 1.009E-11 0 0 0 0 SJC* 1.387E-12 0 0 0 1.127E-11 0 1.736E-11 0HOU 0 5.196E-14 0 3.463E-12 0 0 0 0IND 0 6.04E-13 0 6.173E-13 0 1.148E-12 0 0SAT* 0 1.936E-13 0 0 0 0 0 0

Non-preemptive C11 C12 C21 C22 C31 C32 C41 C42LAX* 7.45E-13 0 0 0 3.18E-12 0 0 0SFO 6.02E-13 0 0 0 0 0 0 0LAS 7.65E-12 0 0 0 0 0 0 0DTW 0 8.23E-14 0 0 0 0 0 2.3E-12EWR* 0 8.3E-13 9.57E-11 0 0 0 0 4.66E-12JFK 0 0 0 0 0 0 0 1.79E-12SEA* 0 1.77E-12 0 0 5.1E-12 0 0 0BOS 0 1.28E-12 0 0 0 2.57E-12 0 1.16E-11LGA 1.82E-12 0 0 0 0 0 0 0HNL* 6.62E-13 0 0 0 0 1.17E-12 0 3.95E-12DCA 0 9.45E-13 0 1.01E-11 0 0 0 0SJC* 0 0 0 0 6.37E-12 0 2.14E-11 0HOU 0 5.2E-14 0 3.46E-12 0 0 0 0IND 0 5.37E-13 0 0 0 2.87E-13 1.28E-12 0SAT* 0 1.94E-13 0 0 0 0 0 0

*: efficient airport in equality case

11

6. RANKING DEA MODELS

DEA efficiency scores cannot generally be used for ranking because these scores are

obtained from different peer group for different DMUs. A ranking method is often needed in

practical and realistic applications.

6.1. Andersen-Petersen DEA

The basic DEA models evaluate the relative efficiency of DMUs. There are multiple

efficient DMUs in the results of the basic DEA. In the airport analysis efficient DMUs which

have efficient score equals unity are twelve at the equality case. Therefore, the ranking of twelve

airports is same like the 1st ranking (Table 1). The basic DEA models do not provide the ranking

of efficient units themselves. This factor has a weakness of basic DEA models. According to

Adler, Friedman and Sinuany-Stern (2002), Andersen and Petersen developed a new procedure

for ranking efficient units by modifying the basic model formulation. The basic idea of

Andersen-Petersen model is to compare the unit under evaluation with a linear combination of all

other units in the sample, namely the calculated DMU is excluded from the peer group.

Andersen-Petersen model makes an extreme efficient unit k achieve an efficiency score less

(greater) than one by removing the kth constrain in output (input)-oriented DEA formulation.

The dual formulation of Andersen-Petersen model is shown below.

0

,,2,1

,,2,1

max

kj1

kj1

≥

=≥

==

∑

∑

≠=

≠=

j

rkk

n

jrjj

n

jikijj

k

sryy

mixx

tosubject

λ

φλ

λ

φ

L

L

- k is the efficient DMU in the basic DEA analysis

The primal formulation is shown below.

12

∑=

=m

iiki xvz

1kmin

subject to

11

=∑=

s

rrkr yu

kjnjforxvyus

r

m

iijirjr ≠=≤−∑ ∑

= =

.,,2,101 1

L

iedunrestrictvru

i

r

∀∀≥

:0

As seen in Table 1, twelve airports are efficient in the equality case. The ranking and φ -value of

these airports are at the Table 3 through the Andersen-Petersen model. HNL has the first ranking.

MEM and ATL are second and third respectively. SEA has the lowest ranking among twelve

airports.

Table 3. Results of Andersen-Petersen DEA

Airport φ -value Andersen-Petersen Ranking

ATL 0.4484 3 LAX 0.7187 6 EWR 0.9307 9 MSP 0.7780 7 MIA 0.8998 8 SEA 0.9906 12 CVG 0.5810 5 HNL 0.0456 1 SAN 0.4676 4 SJC 0.9612 11

MEM 0.4002 2 SAT 0.9328 10

6.2. Cross Efficiency Ranking Method

According to Adler, Friedman and Sinuany-Stern (2002), Cross Efficiency is a two stage

process. First, the basic DEA model is run. Cross Efficiency then compares every DMU with all

13

other DMUs, applying the weights of the other DMUs, from the original DEA estimation, to the

DMU under consideration to ascertain the effect this has on the original DMU’s efficiency rating.

It would be expected that average cross efficiency scores would be lower than the original scores,

as a DMU cannot have a cross efficiency score higher than the original DEA score, as this shows

each DMU in its best possible light. (Table 5)

The cross efficiency simply calculates the efficiency score of each DMU by using the optimal

weights evaluated by basic DEA which has a standard LP form. The results of all the DEA cross

efficiency scores can be summarized in a cross efficiency matrix as shown below.

.,,2,1,,,2,1,

1

1 njnkxv

yuh m

iijik

s

rrjrk

kj LL ===

∑

∑

=

=

kjh represents the score given to unit j in the DEA run of unit k i.e. unit j is evaluated by the

weights of unit k. all the elements in a cross efficiency matrix are between zero and one,

, and the elements in the diagonal, , represent the original DEA efficiency score,

=1 for efficient units and < 1 for inefficient units.

10 ≤≤ kjh kkh

kkh kkh

The cross efficiency raking method in the DEA utilizes the results of the cross efficiency matrix

in order to rank scale the units. The average cross efficiency score, ∑=

=n

jkjk nhh

1

/ , is used in

ranking the units. The kh score better represents the unit evaluation since it measures the

overall ratios over all the runs of all the units. The maximum value of kh is 1, which occurs if

unit k is efficient in all the runs i.e. all the units evaluate units k as efficient. In order to rank the

units, the unit with the highest score is assigned a rank of one and the unit with the lowest score a

rank of n.

This project calculates two rankings. One is the ranking of all airports. The ranking of all

airports is compared with the ranking of the basic DEA and TOPSIS mentioned at the next

chapter. Another is the ranking of efficient twelve airports in the basic DEA by using the airport

performances and weights of only twelve airports. The ranking of twelve airports is calculated in

order to compare it with the ranking of Andersen-Petersen DEA. While the DEA scores, , are

non-comparable, since each uses different weights, the

kkh

kh score is comparable because it

14

utilizes the weights of all the unites equally.

The cross efficiency ranking of twelve efficient airports in the basic DEA is in Table 4

contained Andersen-Petersen ranking to compare it with the cross efficiency ranking based on

the average of the efficiencies from the cross efficiency matrix for each efficient airport. As seen

in Table 4, the airports are ranked differently by using these two approaches. Only one airport,

MEM, has the same ranking. SAT and MIA are ranked similarly in the two approaches.

Table 4. Cross Efficient Ranking of 12 Airports

Airport Average Efficiency

Cross-EfficiencyRanking

Andersen-Petersen Ranking

ATL 0.7033 8 3 LAX 0.8362 3 6 EWR 0.7544 6 9 MSP 0.8062 4 7 MIA 0.6828 10 8 SEA 0.8035 5 12 CVG 0.4967 12 5 HNL 0.6922 9 1 SAN 1 1 4 SJC 0.7223 7 11

MEM 0.8497 2 2 SAT 0.6154 11 10

The average cross efficiency and its ranking are shown in Table 5. As seen the average

cross efficiency is less than the efficiency score of the basic DEA using the equality case. SAN

has the highest average cross efficiency (0.9724). The high ranking group airports are MPS,

LAX, HNL, and SJC. MIA and CVG are two of twelve efficient airports whose efficiency score

is 1 in the basic DEA. But the average cross efficiencies of these airports are 0.5871 and 0.4291,

respectively. The rankings of these airports in the average cross efficiency are 20th and 41st

respectively. The ranking of CVG between the average cross efficiency and the efficiency score

of the basic DEA is highly different, 41st and 1st.

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Table 5. Results of Cross Efficiency Ranking

AIRPORT Efficiency Score in Equality case

Average Cross Efficiency

Cross Efficiency Ranking

Basic DEA Ranking

ATL* 1.0000 0.6762 8 1 ORD 0.8711 0.5907 19 17 LAX* 1.0000 0.7902 3 1 DFW 0.8549 0.6105 15 19 SFO 0.6485 0.4746 35 34 DEN 0.7826 0.6134 14 21 PHX 0.7612 0.5779 24 24 LAS 0.7293 0.5316 31 28 DTW 0.5799 0.4644 36 39 EWR* 1.0000 0.6668 9 1 MSP* 1.0000 0.8422 2 1 MIA* 1.0000 0.5871 20 1 IAH 0.7217 0.5848 21 30 JFK 0.6271 0.4626 37 37 STL 0.7757 0.5799 23 22 MCO 0.5734 0.4206 42 40 SEA* 1.0000 0.7469 6 1 BOS 0.6682 0.5005 32 32 LGA 0.8121 0.5480 27 20 PHL 0.6292 0.4869 33 36 CLT 0.6410 0.5633 26 35

CVG* 1.0000 0.4291 41 1 HNL* 1.0000 0.7891 4 1

PIT 0.4639 0.3920 44 44 BWI 0.4996 0.4206 42 43 IAD 0.5407 0.4441 40 42 SLC 0.6019 0.4772 34 38 TPA 0.7279 0.5834 22 29

SAN* 1.0000 0.9724 1 1 FLL 0.8614 0.6826 7 18 DCA 0.7425 0.5757 25 27 MDW 0.9585 0.6397 13 14 PDX 0.7504 0.5973 18 26 CLE 0.5686 0.4442 39 41 SJC* 1.0000 0.7739 5 1 MCI 0.7739 0.6062 17 23

MEM* 1.0000 0.6561 10 1 RDU 0.7084 0.5429 28 31 MSY 0.7557 0.5404 30 25 BNA 0.6500 0.4554 38 33 HOU 0.9411 0.6088 16 15 IND 0.8958 0.5427 29 16 BDL 0.9799 0.6443 12 13 SAT* 1.0000 0.6510 11 1

16

6.3. TOPSIS

According to Yoon and Hwang (1995), TOPSIS (Technique for Order Preference by

Similarity to Ideal Solution) is based on the concept that the chosen alternative should have the

shortest distance from the positive ideal solution and the longest distance from the negative ideal

solution. TOPSIS defines an index called similarity (or relative closeness) to the positive ideal

solution by combining the proximity to the positive ideal solution and the remoteness from the

negative ideal solution. Then the method chooses an alternative with the maximum similarity to

the positive ideal solution. TOPSIS assumes that each attribute takes either monotonically

increasing or monotonically decreasing utility. That is, the larger the attribute outcome, the

greater the preference for benefit attributes and the less the preference for cost attributes. In this

project benefit attributes are outputs and cost attributes are inputs.

The weight to each attribute in TOPSIS should be assigned. This TOPSIS analysis

assumes two ways in assigning weights. One is that the weight of delay output is 0.4, that of

number of passenger is 0.2 and four remaining outputs and inputs have each 0.1 weight (TOPSIS

1). The sum of weights in TOPSIS must be one. The first way is related to the factor that airport

authorities are the most interested in the airport congestion and the secondary importance is the

passenger performance at an airport. The weight importance in TOPSIS has the same proportion

as in GoDEA. For example, the weight of delay is twice as that of number of passenger. Another

is all attributes have same weights like about 0.1667(TOPSIS 2). The results of the first and

second way are TOPSIS ranking1 and 2 respectively (Table 6). The top five airports in TOPSIS

are the same as ATL, ORD, LAX, DFW and MEM. Four of them have the higher the number of

passengers than others and MEM of five airports has the highest cargo performance. The ranking

of ORD and DFW is greatly different compared with that of DEA.

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Table 6. Results of TOPSIS.

AIRPORT TOPSIS1 Ranking1 TOPSIS2 Ranking2 Cross

Efficiency Ranking

Basic DEA Ranking in

Equality Case ATL 0.5995 2 0.5006 3 8 1 ORD 0.5270 4 0.4847 5 19 17 LAX 0.6543 1 0.5812 2 3 1 DFW 0.5623 3 0.4963 4 15 19 SFO 0.3979 16 0.3285 16 35 34 DEN 0.4426 7 0.3423 12 14 21 PHX 0.4078 14 0.3333 15 24 24 LAS 0.4021 15 0.2967 30 31 28 DTW 0.4124 11 0.3276 17 36 39 EWR 0.4162 9 0.4372 6 9 1 MSP 0.4347 8 0.3718 9 2 1 MIA 0.4585 6 0.4100 7 20 1 IAH 0.3886 17 0.3203 18 21 30 JFK 0.4101 13 0.3545 11 37 37 STL 0.3845 19 0.3059 23 23 22 MCO 0.3829 20 0.2755 40 42 40 SEA 0.4109 12 0.3556 10 6 1 BOS 0.4151 10 0.3982 8 32 32 LGA 0.2727 44 0.3052 24 27 20 PHL 0.3575 27 0.3409 13 33 36 CLT 0.3735 22 0.3022 26 26 35 CVG 0.3600 25 0.2907 33 41 1 HNL 0.3848 18 0.3194 19 4 1 PIT 0.3443 33 0.2487 44 44 44 BWI 0.3455 32 0.2593 43 42 43 IAD 0.3372 39 0.2809 38 40 42 SLC 0.3685 23 0.2971 29 34 38 TPA 0.3545 28 0.2942 31 22 29 SAN 0.3738 21 0.3361 14 1 1 FLL 0.3603 24 0.3091 21 7 18 DCA 0.3456 31 0.2903 34 25 27 MDW 0.3363 40 0.2806 39 13 14 PDX 0.3590 26 0.3066 22 18 26 CLE 0.3317 42 0.2703 41 39 41 SJC 0.3539 29 0.3126 20 5 1 MCI 0.3500 30 0.2988 28 17 23

MEM 0.5044 5 0.5822 1 10 1 RDU 0.3419 36 0.2895 36 28 31 MSY 0.3416 37 0.2902 35 30 25 BNA 0.3315 43 0.2702 42 38 33 HOU 0.3357 41 0.2851 37 16 15 IND 0.3385 38 0.2929 32 29 16 BDL 0.3429 34 0.3024 25 12 13 SAT 0.3420 35 0.3008 27 11 1

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7. LIMITATIONS AND CONCLUSIONS

In this project only the number of runways and gates was considered. It means that the

capacity of runway is not considered in the model. As only the number of runways and gates are

considered large airports can have more advantages because more passengers can be handled in

large airports as well as more passengers per flight can be carried. The efficient airports using the

equality case are twelve. Three of them, SJC, MEM, and SAT, are medium hub airport. MEM is

an air freight oriented airport. If MEM was not considered due to the air freight airport, only two

medium airports are efficient. This seems to be a limitation of the analysis.

MEM airport is a hub of Federal Express which is an all-cargo airline. The performance

of the cargo hub is the largest among all airports. It is twice more than the second highest cargo

performance airport (BOS). This factor might cause MEM to be efficient airport. As we know,

DEA shows the relative efficiency score. If we were to study airports except MEM the efficient

airports might be different. Some airports do not have curfew like MEM which can operate

twenty four hours a day. Curfew may affect the performance of an airport greatly. This factor

should be considered in DEA study of airports. Input or output variables would be modified if

they are highly correlated.

Only two physical inputs of every airport were considered in this project. If financial

data such as revenues and managerial costs at each airport are considered as inputs or outputs in

DEA, the analytical results would explain the situation of airports more realistic. If time series

data considered, the results would explain the sequential change of efficiency in forty four

airports over time.

ATL, LAX, and MEM airports are relatively efficient among forty four airports in the

United States based on the performances and airport facilities of the 2000 year when the results

of all applied methods in this project, the basic DEA ranking, the Cross Efficiency ranking, the

Andersen-Petersen ranking and TOPSIS ranking method, are compared. The implication of this

project is that airport authorities in the United States would benchmark these three airports to

maximize operation and management efficiency for their airports. In general, most of the airports

are handling passengers and freight. Therefore, ATL and LAX would be the most efficient hub

airports in the United States. The capacities of airport facilities and more appropriate input data

should be considered in the follow up research.

19

BIBLIOGRAPHY

Nicole Adler, Lea Friedman and Zilla Sinuany-Stern (2002). Review of ranking methods in the data envelopment analysis context. European Journal of Operational Research 140, 249- 265.

Milan Martic and Gordana Savic (2001). An application of DEA for comparative analysis and ranking of regions in Serbia with regards to social-economic development. European Journal of Operational Research 140, 249-265.

Joseph Sarkis (2000). An analysis of the operational efficiency of major airports in the United States. Journal of Operations Management 18, 335-351.

Ethanassoulis and R.G.Dyson (1992). Estimating preferred target input-output levels using data envelopment analysis. European Journal of Operational Research 56, 80-97.

David Gillen and Ashish Lall (1997). Developing Measures of Airport Productivity and Performance: An Application of Data Envelopment Analysis. Transportation Research E, Vol.33, No. 4, 261-273.

William W. Cooper, Lawrence M. Seiford and Kaoru Tone (2000). Data Envelopment Analysis, Kluwer Academic Publisher.

K. Paul Yoon and Ching-Lai Hwang (1995). Multiple Attribute Decision Making: An Introduction, Sage Publications.

FAA (2000), OPSNET: Ranking Report. http://www.faa.gov/arp/planning/vphubs.htm http://www.faa.gov/arp/planning/vphubs.pdf

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Appendix 1: Airport Code

Code Airport City State Hub Category

ATL THE WILLIAM B HARTSFIELD AT ATLANTA GA L

ORD CHICAGO O'HARE INTL CHICAGO IL L

LAX LOS ANGELES INTL LOS ANGELES CA L

DFW DALLAS/FORT WORTH INTERNATI DALLAS-FORT WORTH TX L

SFO SAN FRANCISCO INTERNATIONAL SAN FRANCISCO CA L

DEN DENVER INTL DENVER CO L

PHX PHOENIX SKY HARBOR INTL PHOENIX AZ L

LAS MC CARRAN INTL LAS VEGAS NV L

DTW DETROIT METROPOLITAN WAYNE DETROIT MI L

EWR NEWARK INTL NEWARK NJ L

MSP MINNEAPOLIS-ST PAUL INTL/WO MINNEAPOLIS MN L

MIA MIAMI INTL MIAMI FL L

IAH GEORGE BUSH INTERCONTINENTA HOUSTON TX L

JFK JOHN F KENNEDY INTL NEW YORK NY L

STL LAMBERT-ST LOUIS INTL ST LOUIS MO L

MCO ORLANDO INTL ORLANDO FL L

SEA SEATTLE-TACOMA INTL SEATTLE WA L

BOS GENERAL EDWARD LAWRENCE LOG BOSTON MA L

LGA LA GUARDIA NEW YORK NY L

PHL PHILADELPHIA INTL PHILADELPHIA PA L

CLT CHARLOTTE/DOUGLAS INTL CHARLOTTE NC L

CVG CINCINNATI/NORTHERN KENTUCK COVINGTON/CINCINNATI KY L

HNL HONOLULU INTL HONOLULU HI L

PIT PITTSBURGH INTERNATIONAL PITTSBURGH PA L

BWI BALTIMORE-WASHINGTON INTL BALTIMORE MD L

IAD WASHINGTON DULLES INTERNATI CHANTILLY VA L

SLC SALT LAKE CITY INTL SALT LAKE CITY UT L

TPA TAMPA INTL TAMPA FL L

SAN SAN DIEGO INTL-LINDBERGH FL SAN DIEGO CA L

21

FLL FORT LAUDERDALE/HOLLYWOOD I FORT LAUDERDALE FL L

DCA RONALD REAGAN WASHINGTON NA ARLINGTON VA L

MDW CHICAGO MIDWAY CHICAGO IL M

PDX PORTLAND INTL PORTLAND OR M

CLE CLEVELAND-HOPKINS INTL CLEVELAND OH M

SJC SAN JOSE INTERNATIONAL SAN JOSE CA M

MCI KANSAS CITY INTL KANSAS CITY MO M

MEM MEMPHIS INTL MEMPHIS TN M

OAK METROPOLITAN OAKLAND INTL OAKLAND CA M

RDU RALEIGH-DURHAM INTL RALEIGH/DURHAM NC M

SJU LUIS MUNOZ MARIN INTL SAN JUAN PR M

MSY NEW ORLEANS INTL/MOISANT FL NEW ORLEANS LA M

BNA NASHVILLE INTL NASHVILLE TN M

HOU WILLIAM P HOBBY HOUSTON TX M

SMF SACRAMENTO INTERNATIONAL SACRAMENTO CA M

SNA JOHN WAYNE AIRPORT-ORANGE C SANTA ANA CA M

IND INDIANAPOLIS INTL INDIANAPOLIS IN M

BDL BRADLEY INTL WINDSOR LOCKS CT M

AUS AUSTIN-BERGSTROM INTL AUSTIN TX M

DAL DALLAS LOVE FIELD DALLAS TX M

SAT SAN ANTONIO INTL SAN ANTONIO TX M

Source: www.faa.gov/arp/planning/vphubs.htm

22

Appendix 2: Airport Data

AIRPORT (o) PAX (o) cargo tons (o) A/C oper. (o) delays delay (I) runway (I) gate ATL 39278 371027 417876 71771 28229 4 189 ORD 33846 477891 382631 42455 57545 7 151 LAX 32168 741896 269156 82859 17141 4 118 DFW 28275 565828 388986 79362 20638 7 151 SFO 19557 301988 146557 75522 24478 4 114 DEN 18383 242695 200555 98823 1177 5 89 PHX 18094 173489 200335 85976 14024 3 108 LAS 17425 64864 161512 95822 4178 4 92 DTW 17327 315929 228023 90220 9780 6 130 EWR 17212 527162 230854 62868 37132 3 107 MSP 16959 198449 224956 93342 6658 3 70 MIA 16489 538065 144533 94151 5849 3 110 IAH 16358 135566 217944 86215 13785 4 95 JFK 16155 458133 126932 86070 13930 4 117 STL 15288 112702 210024 91163 8837 5 85

MCO 14832 120199 136371 97703 2297 3 129 SEA 13876 222961 177512 95347 4653 2 81 BOS 16614 576581 151449 75880 24120 5 107 LGA 12697 39171 134577 38880 61120 2 67 PHL 12294 416852 150921 78479 21521 4 102 CLT 11469 124260 138381 97252 2748 3 78 CVG 11224 269940 163580 92640 7360 3 147 HNL 11175 228076 84796 99992 8 6 29 PIT 9872 66227 123764 98305 1695 4 100 BWI 9676 73232 101396 97819 2181 4 82 IAD 9643 127581 79151 90661 9339 3 76 SLC 9522 255688 89588 99280 720 4 75 TPA 7970 48456 76180 99565 435 3 48 SAN 7898 67810 85143 99480 520 1 38 FLL 7818 112524 69943 98906 1094 3 39 DCA 7518 24279 97368 97273 2727 3 52 MDW 7060 11837 88908 96446 3554 5 33 PDX 6755 162977 98965 99836 164 3 55 CLE 6270 63475 134796 96206 3794 3 87 SJC 6170 107897 68151 98288 1712 3 30 MCI 5903 87512 81699 99759 241 3 45

MEM 5685 1368635 121006 99857 143 5 84 RDU 5191 51969 77199 99388 612 3 48 MSY 4936 39253 57572 99867 133 3 42 BNA 4480 27157 63647 99841 159 4 48 HOU 4355 10416 65019 99361 639 4 31 IND 3834 32323 33265 99753 247 3 33 BDL 3652 81264 47472 99485 515 3 30 SAT 3529 56536 44277 99810 190 3 28

Source: www.faa.gov/arp/planning/vphubs.pdf, FAA (2000) OPSNET: Ranking Report, each airport website.

23

Appendix 3: The Example of GoDEA Preemptive Case in Excel Solver

24