MEASURING AND RANKING EFFICIENCY OF MAJOR AIRPORTS IN THE UNITED STATES USING DATA ENVELOPMENT ANALYSIS

Transcription

1 MEASURING AND RANKING EFFICIENCY OF MAJOR AIRPORTS IN THE UNITED STATES USING DATA ENVELOPMENT ANALYSIS Myughyu Lee Poect epot submitted to the faculty of the Vigiia Polytechic Istitute ad State Uivesity i patial fulfillmet of the equiemets fo the degee of MASTER OF SCIENCE i Civil Egieeig Atoio A. Tai, Chaima Hesham Rakha Hoog Baik July 8, 24 Blacksbug, Vigiia Keywods: Data Evelopmet Aalysis (DEA), Rakig DEA, GoDEA, TOPSIS Efficiecy of Aipots

2 MEASURING AND RANKING EFFICIENCY OF MAJOR IRPORTS IN THE UNITED STATES USING DATA ENVELOPMENTANALYSIS Myughyu Lee Abstact A aipot is a impotat piece of ifastuctue i ai taspotatio system. This poect focuses o measuig ad akig the efficiecy of aipots i the Uited States usig the basic DEA, Rakig DEA, Goal pogammig ad DEA ad TOPSIS.. I geeal, aipot authoities of elatively iefficiet aipots ae tyig to bechmak the opeatioal stategies of efficiet aipots. This poect focuses o evaluatig hub aipots i the Uited States. ATL, LAX, ad MEM aipots ae elatively efficiet amog foty fou hub aipots i the Uited States based o the pefomaces ad aipot facilities of the 2 yea whe the esults of all applied methods i this poect, the basic DEA akig, the Coss Efficiecy akig, the Adese-Petese akig ad TOPSIS akig method, ae compaed. The implicatio of this poect is that aipot authoities i the Uited States would bechmak these thee aipots to maximize opeatio ad maagemet efficiecy fo thei aipots. I geeal, most of the aipots ae hadlig passeges ad feight. Theefoe, ATL ad LAX would be the most efficiet hub aipots i the Uited States. The capacities of aipot facilities ad moe appopiate iput data like fiacial data should be cosideed i the follow up eseach.

3 TABLES OF CONTENTS LIST OF FIGURE AND TABLES....ⅳ. PURPOSE DEA. 3. DATA COLLECTION AND PROCEDURE OF ANALYSIS DEA MODELS Iequality Case Equality Case GoDEA RANKING DEA MODELS Adese-Petese DEA Coss Efficiecy Rakig Method TOPSIS LIMITATIONS AND CONCLUSIONS... 9 BIBLIOGRAPHY APPENDIX iii

4 LIST OF FIGURE AND TABLES Figue. Efficiecy Scoe i Equality Case...7 Table. Basic DEA Results...8 Table 2. Results of GoDEA.. Table 3. Results of Adese-Petese DEA 3 Table 4. Coss Efficiet Rakig of 2 Aipots..5 Table 5. Results of Coss Efficiecy Rakig..6 Table 6. Results of TOPSIS..8 Appedix : Aipot Code. 2 Appedix 2: Aipot Data..23 Appedix 3: The Example of GoDEA Peemptive Case i Excel Solve...24 iv

5 . PURPOSE A aipot is a impotat piece of ifastuctue i ai taspotatio system. This poect focuses o measuig ad akig the efficiecy of aipots i the Uited States. The akigs evaluated by diffeet ways such as a Coss Efficiecy Matix ad Adese-Petese s DEA ae compaed i this poect. This poect also povides the akig of TOPSIS (Techique fo Ode Pefeece by Similaity to Ideal Solutio) which is oe techique of Multiple Citeia Decisio Makig (MCDM). The efficiecy akig would be helpful fo decisio makes i.e. aipot authoities ad ai taspotatio policy makes to detemiate aipot stategies ad ai taspotatio policy. I geeal, aipot authoities of elatively iefficiet aipots ae tyig to bechmak the opeatioal stategies of efficiet aipots. This poect focuses o evaluatig hub aipots i the Uited States. I this poect, GoDEA (Goal pogammig ad DEA) is applied to see the shotfalls o excesses of iputs ad outputs ude the specific coditio by miimizig the slacks associated with iputs ad outputs. GoDEA esults ca explai the shotfalls o excesses of iputs ad outputs of aipots i eachig the taget set of iputs ad outputs. 2. DEA Data Evelopmet Aalysis (DEA) is a o-paametic method fo evaluatig the elative efficiecy of decisio-makig uits (DMUs) o the basis of multiple iputs ad outputs. DEA is based o poductivity theoy of micoecoomics. Poductivity models have taditioally bee used to measue the efficiecy of systems. DEA poductivity models fo give DMU use the atio that is based o the amout of outputs pe give set of iputs. DEA is a multi-facto poductivity appoach, which ca coside multiple iputs ad outputs. The advatages of DEA ae that o assumptios ae made about the poductio fuctio ad multiple iputs ad outputs ae aggegated without ay pio specificatio of weights. Accodig to Gille ad Lall (997), methods of measuig efficiecy ae summaized below:

6 - o-paametic methods: idexes of patial ad total facto poductivity, DEA - paametic methods: estimatio of eoclassical ad stochastic cost o poductio fuctios Patial poductivity measues ae ot able to hadle multiple outputs, ad they do ot coside the diffeece i facto pices o do they take accout the diffeece i the othe factos used i poductio. Oe solutio to some of these poblems is to calculate ad compae a idex of total facto poductivity (TFP). TFP ca ot solve completely the shotcomigs of patial poductivity measue. It is ot vey ifomative fo akig maagemet stategies. Extactig ad obtaiig moe ifomatio fom measues of TFP typically depeds o eliace o estimatig paametic eo-classical cost o poductio fuctios. The data equiemets ae moe difficult to aalyze tha patial measues. I additio, data o physical iputs ad outputs, this measue also eeds ifomatio o pices, which is used to aggegate iputs ad outputs. DEA is aothe alteative whe the outputs ae ot easily o clealy defied; fo example i measuig poductivity i schools, hospitals o govemet istitutes. It is also useful i detemiig the efficiecy of fims, especially, as it is difficult to ecogize thei atual pices. DEA is a liea pogammig-based techique. The basic model equies ifomatio o iputs ad outputs. Ideed, this is also a mao weakess of DEA, as it does ot icopoate ay ifomatio of facto pices of poductio. Fo this easo DEA caot be used to aalyze cost efficiecy. Fims may be techically efficiet but cost iefficiet. Additioally, it is possible that fims aked techically iefficiet by DEA may be able to poduce thei outputs at a lowe cost tha those aked as techically efficiet. DEA ca iclude multiple outputs ad iputs. Iputs ad outputs ca be defied i a vey geeal mae without gettig ito poblems of aggegatio. All poductivity measues have the weakess that they do ot diectly iclude use-boe costs. Usig poxies ca iclude these. If moe of a measue is desiable it ca be modeled as output ad if less of somethig is bette, it ca be egaded as iput. This is a attactive featue as i may sevice idusties like a bak. DEA ca also use the poxy outputs icludig output combiatios that would ot be used with othe efficiecy measues. Fo example, goss-to-miles ad ca-miles o goss-to-miles ad eveues ae able to be egaded as alteative measues of outputs i the ail idusty (Gille ad Lall, 997). 2

7 3. DATA COLLECTION AND PROCEDURE OF ANALYSIS The efficiecy of foty fou aipots i the Uited States is measued usig fou outputs ad two iputs i this poect. Foty fou aipots as DMUs ae listed at the Appedix. All thity oe lage hub aipots ae icluded. The used outputs ad iputs ae show below (Appedix 2); - Outputs: the umbe of eplaed passeges, the umbe of eplaed eveuetos (feight + mail), the umbe of aicaft depatue, the umbe of total delays (depatue + aival) - Iputs: the umbe of uways, the umbe of gates All data used i the aalysis ae based o the yea 2. Fo example, the lesse the umbe of total flight delays, the bette the pefomace of the aipot is. The moe outputs except total delays ae, the bette the pefomaces of aipots get. Theefoe, the umbe of total delays eeds to be modified. The appoaches of cosideig udesiable outputs like delay flights at a aipot i DEA ae summaized below: The idiect appoaches: to tasfom the value of the udesiable output vaiables () additive ivese method: f(q) = - Q (2) udesiable output Q ae cosideed as iput (3) lage scala M is added to the udesiable outputs: M-Q (4) multiplicative ivese method: /Q The diect appoaches: to iclude the udesiable output data diectly ito the DEA model, to modify the assumptio of the model The thid method of the idiect appoaches is applied while makig the aalytical basic data i this poect. The poxy, (, the umbe of total delays), is used istead of the umbe of total delays i the aalysis. Delay i aipots is a vey impotat issue ecetly because of the cosume s complait icease ad the esouce limitatio fo aipot facility impovemet. Theefoe, mitigatig delay of aipots is oe of the key policies of FAA. The output-oieted model is coducted because it might be almost impossible fo iputs like a uway ad a gate to be chaged i ode to miimize the opeatig costs of a aipot fo the shot peiod. Whe a aipot ivests ito the ew uway o the ew 3

8 gate i a temial, it might be vey difficult fo aipot maages to disivest to save costs. The costuctio of a uway ad a gate eeds a log peiod. Sometimes seveal yeas ae eeded. The costuctio peiod would be loge if the plaig step wee cosideed i a costuctio peiod. The CCR (Chaes, Coope ad Rhodes) model assumes costat etus to scale ad the BCC (Bake, Chaes ad Coope) model assumes vaiable etus to scale while detemiig the efficiecy scoe of DMUs. The CCR model is applied i this poect because the chage of iputs like a uway o a gate eed a log time as I metioed befoe. The iput-oieted model is to miimize iputs while satisfyig at least the give output levels. The output-oieted model is to maximize outputs without equiig moe of ay of the obseved iput values. This model explais how much outputs ca be iceased without a icease i iputs. It is called as the output iceasig measue of techical efficiecy. The fomulatios of iput-oieted ad output-oieted CCR model ae show below. The BCC model has oe moe costait ( = ) tha the CCR model i the dual fomulatio. λ = CCR MODEL LP DLP (Dual) Iput-Oieted Model max subect to m i= s v i x i s z = u y = =, m u y vi xi =,2, L, = i= u vi, i mi θ subect to z = = z x z y, i θ x y i i =,2, L, m =,2, L, s Output-Oieted Model mi subect to s = s m z = v i = x i i u y, = m u y vi xi =,2, L, = i= u v i, i max subect to = = λ x λ y φ i λ, φ y x i i =,2, L, m =,2, L, s 4

9 whee, y : amout of output fom DMU x i : amout of iput i fom DMU u : the weight give to output v i : the weight give to iput i z λ, : the weight give to DMU s: the umbe of outputs m: the umbe of iputs : the umbe of DMUs The left-had side i the fist costait of DLP (Dual LP) epesets the hypothetical DMU which is fomed by takig weighted aveages of the eal DMUs fo each iput. The fact that λ ae the same i all of costaits meas that each of the iputs ad outputs of the hypothetical DMU is the same weighted aveage of those of the eal DMUs. A optimal solutio of the output oieted model elates to that of the iput oieted model * * * * * via: φ = / θ, λ = z / θ. The optimal solutio of the iput oieted model is ot geate tha. Theefoe, the optimal solutio of the output oieted model is ot less tha. It ca be depicted such as θ * ad φ * *. The highe the value ofφ is, the * * less efficiet the DMU is. θ epesets the iput eductio ate, while φ descibes the output elagemet ate (Coope, Seifod ad Toe, 2). Accodig to Coope, Seifod ad Toe (2), easos fo solvig the CCR model usig the dual ae the followig: - The computatioal effot of LP (Liea Pogammig) is iceasig i popotio to powes of the umbe of costaits. is lage tha (m+s). LP has costaits. DLP has (m+s) costaits. - The petiet max-slack solutio by usig LP caot be foud. - The itepetatios of DLP ae moe staightfowad because the solutios ae chaacteized as iputs ad outputs that coespod to the oigial data whee the multiplies povided by solutios to LP epeset evaluatios of these obseved values. This poect cosides two ways i makig costait fomulatios. Oe is the 5

10 iequality costait of iputs. It is geeal costait i DEA. Aothe is the equality costait of iputs. The secod method meas that iputs ae fixed exogeously at each aipot. Iput vaiables ae ucotollable i this case. The easo fo this assumptio is that aipot authoities could ot easily icease o decease the umbe of uways ad gates at a aipot i a shot peiod of time. 4. DEA MODELS 4.. Iequality Case The fomulatio fo the iequality case is show below. It is the geeal fomulatio of DEA. The left had side of fist costait epesets the hypothetical DMU fomed by takig weighted aveages of the eal DMUs fo each iput. This is less tha o equal to the actual iput level of DMU. max φ subect to = = λ x λ y i λ, φ y x i i =,2, K, m =,2, K, s Te aipots wee foud i which the elative efficiecy scoe is equal to oe. These ae ATL, LAX, EWR, MSP, SEA, HNL, SAN, SJC, MEM ad SAT. The efficiet scoe of BDL is about.98. It is a secoday best efficiecy scoe. The wost five aipots ae PIT, BWI, IAD, MCO ad CLE. PIT ad BWI have especially lowe scoe tha Equality Case The fomulatio fo the Equality case is show below. The fist costait meas that the iput of hypothetical DMU is the same as the actual iput. This comes fom a assumptio that the umbe of existig uways ad gates of a aipot ae optimal o uchageable fo a specific peiod. Ruways ad gates ca ot be easily chageable. 6

11 Iputs ae egaded as ucotollable factos i this case. max φ subect to = = λ x λ y i λ, = φ y x i i =,2, K, m =,2, K, s As see i Table, the umbes of efficiet aipots ae twelve such as ATL, LAX, EWR, MSP, MIA SEA, CVG, HNL, SAN, SJC, MEM ad SAT. Two moe aipots become efficiet aipots compaed to the iequality case. MIA ad CVG ae added to a efficiet aipot goup as compaed with iequality case. Scoes of emaied aipots ae same but oly thee aipots, JFK, STL ad MCO, have ust a little diffeet scoes as compaed with Iequality case. Fo example, JKF s elative efficiecy is 62.7% at the equality case, while it is 62.23% at the iequality case. Oly the equality case will be cosideed afte this chapte ATL ORD LAX DFW SFO DEN PHX LAS DTW EWR MSP MIA IAH JFK STL MCO SEA BOS LGA PHL CLT CVG HNL PIT BWI IAD SLC TPA SAN FLL DCA MD PDX CLE SJC MCI MEM RDU MSY BNA HOU IND BDL SAT Figue. Efficiecy Scoe i Equality Case 7

12 Table. Basic DEA Results. Aipot Efficiecy Scoe Rakig Efficiecy Scoe Rakig i Iequality case i Iequality i Equality case i Equality ATL.. ORD LAX.. DFW SFO DEN PHX LAS DTW EWR.. MSP.. MIA IAH JFK STL MCO SEA.. BOS LGA PHL CLT CVG HNL.. PIT BWI IAD SLC TPA SAN.. FLL DCA MDW PDX CLE SJC.. MCI MEM.. RDU MSY BNA HOU IND BDL SAT.. 8

13 5. GoDEA Goal pogammig ad DEA (GoDEA) gets to the fotie by miimizig deviatio vaiables elated to iputs ad outputs. Thaassoulis ad Dyso (992) developed models which ca be used to estimate alteative iput-output taget levels to make elatively iefficiet DMUs efficiet. Thei models icopoate pefeece ove potetial impovemets to idividual iput-output levels so that the esultat taget levels eflect the use s pefeece ove alteative paths to efficiecy. Thei aalysis illustates the pactical usefuless of the models ad emphasizes the alteative measues of elative efficiecy implicit i the models developed. Thaassoulis ad Dyso (992) explai some DMUs may be able to aticulate the tagets they would ideally wish to adopt. Such ideal tagets would eflect the degee to which each DMU cosides it desiable ad/o feasible to impove each iput ad /o output level. The ideal tagets eed ot cotai oly impovemets to cuet iput-output levels. The DMU may be willig to sacifice the level of some iputs ad /o outputs i ode to impove the levels of othes. The ideal tagets specified by a DMU may i geeal be eithe feasible o efficiet. Feasible iput-output levels ae those which ca be expessed as oegative liea combiatios of obseved iput-output levels. Thaassoulis ad Dyso (992) suggest the model explaied i the followig sectio. The solutio of model eveals feasible iput-output levels as close as possible to the ideal tagets. Mi s. t. = = γ t y γ y γ x i m i= whee, w + c + k i i, k i c c c i m s s wi k i + wi c + i= = =, k = = i : ideal output level y x t t i =,2, L, s i =,2, L, m fo =,2 ad w 2+ i c i ad 2 9

14 t xi : ideal iput level w : use-specified weight c, k : deviatio fom taget level of output ad iput espectively This fomulatio is modified to be suitable i the ucotollable iput case, amely the liea GoDEA fomulatio fo foty fou aipots case is show below. Mi subect = = λ x λ y s = λ i ( w = to x c + c i, + w c c i =,2, L m 2 c, c 2 = 2 2 ) y =,2, L s, 2 w ad ae espectively use-specified weights attached to the deviatio ad w c 2 c 2 fom the taget level of output. is udeachievemet ad is c c oveachievemet of the ideal level of output. Pe-emptive ad No-peemptive weightig stuctue ove the deviatio of outputs is used. Pe-emptive GoDEA assumes that the weights of the delay ad the umbe of passege ae 4 ad 2, espectively. Aothe assumptio is that taget level of iputs ad outputs is the existig aipot facilities ad pefomaces. The esults ae show i Table 2. C k i this table meas udeachievemet of output k. C k2 is oveachievemet of output k as k =, 2, 3, 4 meas the umbe of passege, the umbe of cago-to, the umbe of aicaft depatue ad total flight delays output espectively. Fo example, C is the udeachievemet of the umbe of passege i Table 2. C2 meas the oveachievemet of it. As see i Table 2, fiftee aipots have udeachievemet o oveachievemet of outputs; howeve, the emaiig twety ie aipots do ot have it. Twety ie aipots do ot have the shotfalls ad the excesses of the coespodig outputs. The ude- o ove-achievemets of fiftee aipots ae too small. The slacks fo all outputs ae almost zeo. I peemptive case the slacks fo the delay output of all aipots except EWR, HNL ad SJC is zeo. It would be difficult to say that the shotfalls o excesses of outputs seem to be appaetly i fiftee aipots.

15 Table 2. Results of GoDEA Peemptive C LAX* SFO LAS DTW EWR* JFK SEA BOS LGA HNL* DCA SJC* HOU IND SAT* C2 C2 C22 C3 C32 C4 C E E E E-2 8.7E E E E- 4.66E E-2.766E E-2.22E E-.89E E E E E-3.9E-.387E-2.27E-.736E- 5.96E E-2 6.4E E-3.48E-2.936E-3 No-peemptive C C2 C2 C22 C3 C32 C4 C42 LAX* 7.45E-3 3.8E-2 SFO 6.2E-3 LAS 7.65E-2 DTW 8.23E-4 2.3E-2 EWR* 8.3E E- 4.66E-2 JFK.79E-2 SEA*.77E-2 5.E-2 BOS.28E E-2.6E- LGA.82E-2 HNL* 6.62E-3.7E E-2 DCA 9.45E-3.E- SJC* 6.37E-2 2.4E- HOU 5.2E E-2 IND 5.37E E-3.28E-2 SAT* *: efficiet aipot i equality case.94e-3

16 6. RANKING DEA MODELS DEA efficiecy scoes caot geeally be used fo akig because these scoes ae obtaied fom diffeet pee goup fo diffeet DMUs. A akig method is ofte eeded i pactical ad ealistic applicatios. 6.. Adese-Petese DEA The basic DEA models evaluate the elative efficiecy of DMUs. Thee ae multiple efficiet DMUs i the esults of the basic DEA. I the aipot aalysis efficiet DMUs which have efficiet scoe equals uity ae twelve at the equality case. Theefoe, the akig of twelve aipots is same like the st akig (Table ). The basic DEA models do ot povide the akig of efficiet uits themselves. This facto has a weakess of basic DEA models. Accodig to Adle, Fiedma ad Siuay-Ste (22), Adese ad Petese developed a ew pocedue fo akig efficiet uits by modifyig the basic model fomulatio. The basic idea of Adese-Petese model is to compae the uit ude evaluatio with a liea combiatio of all othe uits i the sample, amely the calculated DMU is excluded fom the pee goup. Adese-Petese model makes a exteme efficiet uit k achieve a efficiecy scoe less (geate) tha oe by emovig the kth costai i output (iput)-oieted DEA fomulatio. The dual fomulatio of Adese-Petese model is show below. max = k = k λ φ λ x k subect to i λ y = xik φ y k i =,2, L, m =,2, L, s k - k is the efficiet DMU i the basic DEA aalysis The pimal fomulatio is show below. 2

17 mi subect to m z k = i= v i x ik s = u y k = s u y m = i= u v x i i fo v : uesticted i i =,2, L,. k As see i Table, twelve aipots ae efficiet i the equality case. The akig ad φ -value of these aipots ae at the Table 3 though the Adese-Petese model. HNL has the fist akig. MEM ad ATL ae secod ad thid espectively. SEA has the lowest akig amog twelve aipots. Table 3. Results of Adese-Petese DEA Aipot φ -value Adese-Petese Rakig ATL LAX EWR MSP MIA SEA CVG.58 5 HNL.456 SAN SJC.962 MEM.42 2 SAT Coss Efficiecy Rakig Method Accodig to Adle, Fiedma ad Siuay-Ste (22), Coss Efficiecy is a two stage pocess. Fist, the basic DEA model is u. Coss Efficiecy the compaes evey DMU with all 3

18 othe DMUs, applyig the weights of the othe DMUs, fom the oigial DEA estimatio, to the DMU ude cosideatio to ascetai the effect this has o the oigial DMU s efficiecy atig. It would be expected that aveage coss efficiecy scoes would be lowe tha the oigial scoes, as a DMU caot have a coss efficiecy scoe highe tha the oigial DEA scoe, as this shows each DMU i its best possible light. (Table 5) The coss efficiecy simply calculates the efficiecy scoe of each DMU by usig the optimal weights evaluated by basic DEA which has a stadad LP fom. The esults of all the DEA coss efficiecy scoes ca be summaized i a coss efficiecy matix as show below. h k = s = m i= u v k ik y x i, k =,2, L,, =,2, L,. h k epesets the scoe give to uit i the DEA u of uit k i.e. uit is evaluated by the weights of uit k. all the elemets i a coss efficiecy matix ae betwee zeo ad oe, h hkk k, ad the elemets i the diagoal, h, epeset the oigial DEA efficiecy scoe, = fo efficiet uits ad h < fo iefficiet uits. kk The coss efficiecy akig method i the DEA utilizes the esults of the coss efficiecy matix kk i ode to ak scale the uits. The aveage coss efficiecy scoe, h k = = h k /, is used i akig the uits. The h k scoe bette epesets the uit evaluatio sice it measues the oveall atios ove all the us of all the uits. The maximum value of h k is, which occus if uit k is efficiet i all the us i.e. all the uits evaluate uits k as efficiet. I ode to ak the uits, the uit with the highest scoe is assiged a ak of oe ad the uit with the lowest scoe a ak of. This poect calculates two akigs. Oe is the akig of all aipots. The akig of all aipots is compaed with the akig of the basic DEA ad TOPSIS metioed at the ext chapte. Aothe is the akig of efficiet twelve aipots i the basic DEA by usig the aipot pefomaces ad weights of oly twelve aipots. The akig of twelve aipots is calculated i ode to compae it with the akig of Adese-Petese DEA. While the DEA scoes, h kk, ae o-compaable, sice each uses diffeet weights, the h k scoe is compaable because it 4

19 utilizes the weights of all the uites equally. The coss efficiecy akig of twelve efficiet aipots i the basic DEA is i Table 4 cotaied Adese-Petese akig to compae it with the coss efficiecy akig based o the aveage of the efficiecies fom the coss efficiecy matix fo each efficiet aipot. As see i Table 4, the aipots ae aked diffeetly by usig these two appoaches. Oly oe aipot, MEM, has the same akig. SAT ad MIA ae aked similaly i the two appoaches. Table 4. Coss Efficiet Rakig of 2 Aipots Aipot Aveage Efficiecy Coss-Efficiecy Rakig Adese-Petese Rakig ATL LAX EWR MSP MIA SEA CVG HNL SAN 4 SJC MEM SAT.654 The aveage coss efficiecy ad its akig ae show i Table 5. As see the aveage coss efficiecy is less tha the efficiecy scoe of the basic DEA usig the equality case. SAN has the highest aveage coss efficiecy (.9724). The high akig goup aipots ae MPS, LAX, HNL, ad SJC. MIA ad CVG ae two of twelve efficiet aipots whose efficiecy scoe is i the basic DEA. But the aveage coss efficiecies of these aipots ae.587 ad.429, espectively. The akigs of these aipots i the aveage coss efficiecy ae 2th ad 4st espectively. The akig of CVG betwee the aveage coss efficiecy ad the efficiecy scoe of the basic DEA is highly diffeet, 4st ad st. 5

20 Table 5. Results of Coss Efficiecy Rakig AIRPORT Efficiecy Scoe i Equality case Aveage Coss Efficiecy Coss Efficiecy Rakig Basic DEA Rakig ATL* ORD LAX* DFW SFO DEN PHX LAS DTW EWR* MSP* MIA* IAH JFK STL MCO SEA* BOS LGA PHL CLT CVG* HNL* PIT BWI IAD SLC TPA SAN* FLL DCA MDW PDX CLE SJC* MCI MEM*..656 RDU MSY BNA HOU IND BDL SAT*..65 6

21 6.3. TOPSIS Accodig to Yoo ad Hwag (995), TOPSIS (Techique fo Ode Pefeece by Similaity to Ideal Solutio) is based o the cocept that the chose alteative should have the shotest distace fom the positive ideal solutio ad the logest distace fom the egative ideal solutio. TOPSIS defies a idex called similaity (o elative closeess) to the positive ideal solutio by combiig the poximity to the positive ideal solutio ad the emoteess fom the egative ideal solutio. The the method chooses a alteative with the maximum similaity to the positive ideal solutio. TOPSIS assumes that each attibute takes eithe mootoically iceasig o mootoically deceasig utility. That is, the lage the attibute outcome, the geate the pefeece fo beefit attibutes ad the less the pefeece fo cost attibutes. I this poect beefit attibutes ae outputs ad cost attibutes ae iputs. The weight to each attibute i TOPSIS should be assiged. This TOPSIS aalysis assumes two ways i assigig weights. Oe is that the weight of delay output is.4, that of umbe of passege is.2 ad fou emaiig outputs ad iputs have each. weight (TOPSIS ). The sum of weights i TOPSIS must be oe. The fist way is elated to the facto that aipot authoities ae the most iteested i the aipot cogestio ad the secoday impotace is the passege pefomace at a aipot. The weight impotace i TOPSIS has the same popotio as i GoDEA. Fo example, the weight of delay is twice as that of umbe of passege. Aothe is all attibutes have same weights like about.667(topsis 2). The esults of the fist ad secod way ae TOPSIS akig ad 2 espectively (Table 6). The top five aipots i TOPSIS ae the same as ATL, ORD, LAX, DFW ad MEM. Fou of them have the highe the umbe of passeges tha othes ad MEM of five aipots has the highest cago pefomace. The akig of ORD ad DFW is geatly diffeet compaed with that of DEA. 7

22 Table 6. Results of TOPSIS. AIRPORT TOPSIS Rakig TOPSIS2 Rakig2 Coss Efficiecy Rakig Basic DEA Rakig i Equality Case ATL ORD LAX DFW SFO DEN PHX LAS DTW EWR MSP MIA IAH JFK STL MCO SEA BOS LGA PHL CLT CVG HNL PIT BWI IAD SLC TPA SAN FLL DCA MDW PDX CLE SJC MCI MEM RDU MSY BNA HOU IND BDL SAT

23 7. LIMITATIONS AND CONCLUSIONS I this poect oly the umbe of uways ad gates was cosideed. It meas that the capacity of uway is ot cosideed i the model. As oly the umbe of uways ad gates ae cosideed lage aipots ca have moe advatages because moe passeges ca be hadled i lage aipots as well as moe passeges pe flight ca be caied. The efficiet aipots usig the equality case ae twelve. Thee of them, SJC, MEM, ad SAT, ae medium hub aipot. MEM is a ai feight oieted aipot. If MEM was ot cosideed due to the ai feight aipot, oly two medium aipots ae efficiet. This seems to be a limitatio of the aalysis. MEM aipot is a hub of Fedeal Expess which is a all-cago ailie. The pefomace of the cago hub is the lagest amog all aipots. It is twice moe tha the secod highest cago pefomace aipot (BOS). This facto might cause MEM to be efficiet aipot. As we kow, DEA shows the elative efficiecy scoe. If we wee to study aipots except MEM the efficiet aipots might be diffeet. Some aipots do ot have cufew like MEM which ca opeate twety fou hous a day. Cufew may affect the pefomace of a aipot geatly. This facto should be cosideed i DEA study of aipots. Iput o output vaiables would be modified if they ae highly coelated. Oly two physical iputs of evey aipot wee cosideed i this poect. If fiacial data such as eveues ad maageial costs at each aipot ae cosideed as iputs o outputs i DEA, the aalytical esults would explai the situatio of aipots moe ealistic. If time seies data cosideed, the esults would explai the sequetial chage of efficiecy i foty fou aipots ove time. ATL, LAX, ad MEM aipots ae elatively efficiet amog foty fou aipots i the Uited States based o the pefomaces ad aipot facilities of the 2 yea whe the esults of all applied methods i this poect, the basic DEA akig, the Coss Efficiecy akig, the Adese-Petese akig ad TOPSIS akig method, ae compaed. The implicatio of this poect is that aipot authoities i the Uited States would bechmak these thee aipots to maximize opeatio ad maagemet efficiecy fo thei aipots. I geeal, most of the aipots ae hadlig passeges ad feight. Theefoe, ATL ad LAX would be the most efficiet hub aipots i the Uited States. The capacities of aipot facilities ad moe appopiate iput data should be cosideed i the follow up eseach. 9

24 BIBLIOGRAPHY Nicole Adle, Lea Fiedma ad Zilla Siuay-Ste (22). Review of akig methods i the data evelopmet aalysis cotext. Euopea Joual of Opeatioal Reseach 4, Mila Matic ad Godaa Savic (2). A applicatio of DEA fo compaative aalysis ad akig of egios i Sebia with egads to social-ecoomic developmet. Euopea Joual of Opeatioal Reseach 4, Joseph Sakis (2). A aalysis of the opeatioal efficiecy of mao aipots i the Uited States. Joual of Opeatios Maagemet 8, Ethaassoulis ad R.G.Dyso (992). Estimatig pefeed taget iput-output levels usig data evelopmet aalysis. Euopea Joual of Opeatioal Reseach 56, David Gille ad Ashish Lall (997). Developig Measues of Aipot Poductivity ad Pefomace: A Applicatio of Data Evelopmet Aalysis. Taspotatio Reseach E, Vol.33, No. 4, William W. Coope, Lawece M. Seifod ad Kaou Toe (2). Data Evelopmet Aalysis, Kluwe Academic Publishe. K. Paul Yoo ad Chig-Lai Hwag (995). Multiple Attibute Decisio Makig: A Itoductio, Sage Publicatios. FAA (2), OPSNET: Rakig Repot

25 Appedix : Aipot Code Code Aipot City State 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 Hub Categoy 2

26 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 Souce: 22

27 Appedix 2: Aipot Data AIRPORT (o) PAX (o) cago tos (o) A/C ope. (o) delays delay (I) uway (I) gate ATL ORD LAX DFW SFO DEN PHX LAS DTW EWR MSP MIA IAH JFK STL MCO SEA BOS LGA PHL CLT CVG HNL PIT BWI IAD SLC TPA SAN FLL DCA MDW PDX CLE SJC MCI MEM RDU MSY BNA HOU IND BDL SAT Souce: FAA (2) OPSNET: Rakig Repot, each aipot website. 23

28 Appedix 3: The Example of GoDEA Peemptive Case i Excel Solve 24