Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Mathematca, Computatona, Physca, Eectrca and Computer Engneerng Vo:8, No:9, 2014 Arport Investment Rs Assessment under Uncertanty Eena M. Captanu, Caros A. Nunes Cosenza, Wad E Moudan, Fex Mora Camno Internatona Scence Index, Envronmenta and Ecoogca Engneerng Vo:8, No:9, 2014 waset.org/pubcaton/9999485 Abstract The constructon of a new arport or the extenson of an exstng one requres massve nvestments and many tmes pubc prvate partnershps were consdered n order to mae feasbe such projects. One characterstc of these projects s uncertanty wth respect to fnanca and envronmenta mpacts on the medum to ong term. Another one s the mutstage nature of these types of projects. Whe many arport deveopment projects have been a success, some others have turned nto a nghtmare for ther promoters. Ths communcaton puts forward a new approach for arport nvestment rs assessment. The approach taes expcty nto account the degree of uncertanty n actvty eves predcton and proposes mestones for the dfferent stages of the project for mnmzng rs. Uncertanty s represented through fuzzy dua theory and rs management s performed usng dynamc programmng. An ustraton of the proposed approach s provded. Keywords Arports, fuzzy ogc, rs, uncertanty. I. INTROUCTION IRPORTS are a paramount pece of the goba Anfrastructure puzze, wth a mutper economc, soca and envronmenta mpact at natona, regona and nternatona eve. In a hghy voate and uncertan economc envronment, arports must be capabe to attract suffcent revenues to fnance ther operatons and nvestments whe mantanng a satsfactory quaty of servce for both ther prmary cents: arnes and passengers, and aso mantanng ts roe of economc drver supportng n a sustanabe manner ts oca communty. Arports are asset-ntensve busnesses that requre extensve amount of tme to recover the sgnfcant fnanca nvestments n the specfc nfrastructure, e runways, termnas. Ths aspect forces arports nvestors to mae strategc moves and to carefuy cacuate the rss before tang nvestment decsons. The hghy dereguated and berazed ar transportaton maret determned arports to adopt a more busness e operatona approach, focusng on non-aeronautca actvtes as a strategy to acheve sefreance and fnanca ndependence whch w aow them to deveop n accordance wth the maret needs. Ths process of arport commercazaton shfted the focus towards the passenger as the utmate benefcary of arport nfrastructure. Eena M. Captanu s a Ph Canddate wth the L Ecoe Natonae de L Avaton Cve-ENAC, Lab MAIAA, Tououse, France (+33 06 78 70 83 27; e-ma: eena.captanu@gma.com, eena.captanu-ext@enac.fr). Caros A. Nunes Cosenza s wth the Federa Unversty of Ro de Janero, Lab Fuzzy,Braz (e-ma: cosenzacoppe@gma.com). Wad E Moudan s wth the epartment of Busness Admnstraton, Lebanese Unversty, Trpo, Lebanon (e-ma:wmoudan@hotma.com). Fex Mora Camno s head of the Automaton Research Group wth the MAIAA Lab, Ecoe Natonae de Avaton Cve, (ema:moracamno@hotma.fr). In the ast decades, arports evoved from beng smpy nfrastructure eements to busness orented servce provders, pressured to operate n an optma manner. They proved to be fexbe n turbuent economc tmes, provng they had the capabty to meet the needs of the ar transportaton ndustry, sector that has nown a sustaned hgh rate of growth of approxmatey 5% annuay n the ast decades even through goba economc dsturbances, wth more than 3 bon passengers transported n 2013 [1]. The structure of the artce s as foows: Secton II gves a concse formuaton of the ong term arport pannng probem wth emphass of the fnanca aspects and uncertanty degree, Secton III detas the rss arports are exposed wth partcuar nterest on ther fnanca mpact, n Secton IV s presented the adopted arport pannng context, n secton V s proposed a mathematca mode to address arport nvestment rs assessment and n Secton VI a fuzzy dua dynamc programmng approach s dscussed to tace the consdered arport case study. Fna concusons are presented n Secton VII. II. THE LONG TERM AIRPORT PLANNING PROBLEM As the word economy s sowy recoverng from the most powerfu economc downturn, the ar transport ndustry w contnue to grow steady on the ong run. Snce demand n ar transportaton sector s hghy mpacted by economc actvty t s expected that the ndustry w recover ts sustanabe growth. Arport ong term pannng has at ts core the foowng objectves: optmzed nfrastructure deveopment costs and functonaty, optmzed economc and operatona performance and a hgh degree of fexbty n order to ntegrate a the shfts n demand and potenta dsturbances accordngy to the arport future needs and eve of growth. The new busness cuture concepts that arports need to embrace ncude strong ar servce compettor advantages, capabty of tang ong term rss, adoptng the staehoder coaboratve decson mang cuture, dversfyng the revenues sources and most of a puttng the passenger at the core of the busness. The constructon of a new arport or the extenson of an exstng one requres huge nvestments and many tmes pubc prvate partnershps were consdered n order to mae feasbe such projects. One characterstc of these projects s uncertanty wth respect to the fnanca and envronmenta mpacts on the medum to ong term. Another one s the mutstage nature of these types of projects. Whe many arport deveopment projects have been a success, e Munch Arport [2], some others have turned nto a nghtmare for ther promoters e the ghost arport of Cudad Rea, Span. Internatona Schoary and Scentfc Research & Innovaton 8(9) 2014 1230 schoar.waset.org/1999.7/9999485
Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Mathematca, Computatona, Physca, Eectrca and Computer Engneerng Vo:8, No:9, 2014 Internatona Scence Index, Envronmenta and Ecoogca Engneerng Vo:8, No:9, 2014 waset.org/pubcaton/9999485 Arports were tradtonay seen as the responsbty of governments to manage and operate, typcay n ne wth strategc economc and defense poces [3]. In the more recent economc envronment, a paradgm shft occurred were prvate staehoders emerged as nvestors evovng from decson maers n arport pannng and deveopment to fu owners and operators. Prvatzaton of arports emerged as the too to go to for governments oong for strateges to mae the oca avaton maret more dynamc and to acheve ther ong term pannng goas when the costs of fundng new nfrastructure or mantanng the exstng one exceeds ther resources. The prvatzaton of arports maes for a fuzzy governance space where dfferent governance modes ntersect and overap as noted n [3]. The ong term arport pannng process s a compex endeavor due to the ntrcaces of the arport system, staehoders nvoved and the sgnfcant degree of uncertanty. In a hghy voate economc context the pannng process needs to be constanty adjusted to the reates of the maret the arport w serve. Notons e demand and capacty need to be rethought n order to accuratey compute the operatona parameters of the future arport. Overa, we need to acnowedge the fact that ong term arport pannng s a mutbon busness nvestment requrng a systemc and fexbe approach. The demand for ar transport servces has rsen much faster than demand for most other goods and servces n the word economy. Snce 1970, ar trave demand, measured by Revenue Passenger Kometers fown (RPKs) has rsen 10 fod compared to a 3-4 fod expanson of the word economy. Ar cargo demand, both refectng and factatng the gobazaton of busness suppy chans and economes generay, rased 14 fod [4]. An economcay sustanabe ndustry has to cover the costs of operatons and provde a reasonabe return on nvestment so that capta can be renewed [5]. The arport sector had a substanta growth n annua nvestment, from US 308 bon n 2009 to US 463 bon n 2011, representng an mportant 36% of the tota nvestment n the avaton vaue chan for 2011[4]. Accordng to Arports Counc Internatona 2011 Annua Report, tota revenue for arports wordwde was $102 bon n 2011 [6]. III. AIRPORT RISK ANALYSIS The rss arports are contnuousy facng due to the hghy dynamc envronment they are exposed to, can be categorzed as exo-ndustry and endo-ndustry rss. The man exo-ndustry rss are: 1) Voatty of the economc envronment wth major maret shfts: The tradtonay strong and robust North Amercan and European marets have become stagnant whe emergent Asan and Latn Amercan marets are soarng. Ar traffc evouton foows economc trends. 2) Potca pocy and reguaton regardng envronment, taxaton, securty reguatons, and batera and open ses agreements, a have the potenta to be a major constrant for future arport deveopment. 3) Bac swans are events or occurrences that devate beyond what s normay expected of a stuaton and that woud be extremey dffcut to predct. Ths term was popuarzed n [7]. The foowng events can be categorzed as such: the terrorst attacs of September 2011, the SARS outbrea (2003), the Indan Ocean tsunam (2004), Hurrcane Katrna (2005), the goba fnanca crss (2008), the vocanc erupton of Eyjafjaajöu (2010). 4) Soca and cutura aspects have a powerfu mpact on oca communtes. Pubc awareness on avaton envronmenta mpact, the prevaence of Internet vdeo conferencng over busness trave, the vng standard, a these factors mpact decsvey the propensty to fy. The man endo-ndustry rss are: 1) The arport performance s strongy dependent on arne operatons. Arports are mpacted by the operatona, fnanca and overa busness modes of arnes (egacy, ow-cost, start-up). To a these aspects the trendng arnes aance mode can rapdy turn from an opportunty or strength, to a weaness or a threat, dependng on the context the arport fnds tsef n. Powerfu aances offer to the arport the opportunty to reach a arger and more dverse maret but aso nterna nstabty wthn an aance can sgnfcanty compcate arport future deveopment pans. In concuson, arports shoud tae a the necessary steps to mnmze the dsruptons to whch the arne ndustry s exposed to. 2) The emergence of prvate nvestors n the arport maret, rangng from parta prvatzaton to fu ownershp and operaton, brngs a new degree of uncertanty and rs to the system due to the compexty of nvestor varety and to the fact they no onger see arports as a very secure and proftabe endeavor, compared wth the pre-fnanca crss era. 3) Arport competton s emergng as a serous pressure pont n the ndustry wth more vsbty between prmary and secondary arports and even more pronounced for cargo arports; 4) Technoogca advancements determne arports to adjust ther nfrastructure n order to eep up wth the new arcrafts whch gan popuarty n a far more acceerated pace than the specfc arport nfrastructure (Arbus A380, Arbus A350, Boeng 787). Aso major operatona mprovements e A-CM (Arport Coaboratve ecson Mang), SESAR (Snge European Sy ATM Research) or NextGen are pushng arports forward n terms of nfrastructure and operatona advancements. 5) Forecastng errors, statstca and modeng errors, msnterpretaton of data, errors n the data, are addng to the overa error margn for md and ong term forecastng. In ths context, arport deveopment projects are exposed to a very compex and dynamc envronment, characterzed by a sgnfcant degree of uncertanty and rs. Internatona Schoary and Scentfc Research & Innovaton 8(9) 2014 1231 schoar.waset.org/1999.7/9999485
Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Mathematca, Computatona, Physca, Eectrca and Computer Engneerng Vo:8, No:9, 2014 Internatona Scence Index, Envronmenta and Ecoogca Engneerng Vo:8, No:9, 2014 waset.org/pubcaton/9999485 IV. AOPTE AIRPORT PLANNING CONTEXT The startng pont of any arport pannng project and ts fnancng s the potenta demand forecast and ts evouton. The forecast generay covers the tme horzon of the project and ncudes potenta demands for the annua voumes of nternatona and domestc schedued and non-schedued passenger, freght and arcraft movements. Aso, day and monthy traffc dstrbutons are requred n order to dentfy traffc trends and peang patterns aong wth the feet mx. Of paramount mportance s the ntegraton of uncertanty n demand forecastng snce the decsons taen at a specfc step of the deveopment pan can have a ong term mpact over the genera outcome of the project. Long term arport pannng can expand up to 20 years as a tme horzon wth a proposed sx months ncrementa mestone n order to accuratey montor the progress of the deveopment project. In ths way, an mportant degree of adaptabty s nsured whch w aow arport paners to tae better nformed decsons over a more controabe tme frame wth far more reduced uncertanty degree. Let the eve of predcted potenta demand for traffc type aong the pannng horzon be gven by:, I, {1,2,..., K}, where I s the set of traffc actvtes. The necessary arcraft traffc to cope wth a demand eve s gven by: T /( S ) (1),, where T,, are rea numbers. Here S s the mean capacty of arcraft type at tme corrected by the mean oad factor. The rates of return, r assocated wth the traffc of type at tme, depend on the nvestments made unt that perod. The potenta arport passenger processng capacty s P wrtten C and the avaabe potenta arcraft movements T processng capacty s wrttenc. Then the actua eve of demand of type at perod : T mn{, C P, S C } (2) Let L be the number of canddate upgrades whch can be performed for traffc type at the consdered arport. Let be the perod at whch upgrade for traffc type s panned to be done. When a project s retaned, the correspondng vaue s wthn the set {1, 2,,K} and when t s not retaned =K+1, {1,2,, L }. Technca consderatons mpose, n genera, sequence constrants, so t s supposed that constrants such as: ', ' 1,, L1, I: (3) can be encountered. Aso there are excuson constrants such as f project s retaned. A set of concurrent or contradctory projects w be dsmssed: {1, 2,..., K} K 1, ' 1,, L (4) ' Snce the dfferent types of traffc mae use of common resources n the arport, goba capacty constrants must be satsfed. Let be the set of projects whch have been retaned unt perod so the correspondng capactes are: P T C ( ) and C ( ). c ( ) s defned as the cost of upgrade when performed at perod and r( ) represents the rate of return at perod for traffc type. V. MATHEMATICAL FORMULATION AN SOLUTION APPROACH The adopted strategy deveops at frst a determnstc approach whch eads to the formuaton of an optmzaton probem. Then the parameters and varabes subject to uncertanty are ponted out and a fuzzy-dua based mode of ther uncertanty s estabshed. Fnay a fuzzy dua formuaton of the arport pannng probem s proposed. A determnstc formuaton of the optma programmng probem assocated to arport pannng can be such as: max ([ ], 1,, L, I (5) under constrants (3) and (4). Here the current return s gven by: ([ ], 1,, L, I K L r ( ) c ( ) I 1 (1 ) 1 (1 ) K where ρ s the fnanca rate of actuazaton. Here t s consdered that uncertanty regardng the actua eves of demand, the rates of return and the upgrade costs can be represented by fuzzy dua numbers. A fuzzy dua number a. b s composed of a ey vaue a and a degree of uncertanty b, ε representng the pure dua number such that 2 0 [8]. Then et the fuzzy dua representatons of the actua eves of demand, the rates of return and the upgrade costs be gven by: (6) L r ( ) r ( ) r ( ) (7) (8) L L c ( ) c ( ) c ( ) (9) where the ey components are ndexed by L and the dua components are ndexed by. In many stuatons, the ey components can be assocated wth mean estmated vaues Internatona Schoary and Scentfc Research & Innovaton 8(9) 2014 1232 schoar.waset.org/1999.7/9999485
Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Mathematca, Computatona, Physca, Eectrca and Computer Engneerng Vo:8, No:9, 2014 Internatona Scence Index, Envronmenta and Ecoogca Engneerng Vo:8, No:9, 2014 waset.org/pubcaton/9999485 whe the dua components can be assocated wth the correspondng standard devatons. Then the expresson of the fuzzy dua return s gven by: where ([ ], 1,, L, I) L ([ ], 1,, L, I) ([ ], 1,, L, I) L ([ ], 1,, L, I) K L L L r ( ) c ( ) I 1 (1 ) 1 (1 ) K L (10) (11) and ([ ], 1,, L, I) (12) K L L L r ( ) r ( ) c ( ) I 1 (1 ) 1 (1 ) K Now, the optma programmng probem assocated to arport pannng whch taes nto account the eve of uncertanty can be formuated as: L max ([ ], 1,, L, I) (13) under constrants (3) and a goba uncertanty eve constrant such as: max ([ ], 1,, L, I) (14) where max represents the maxmum eve of uncertanty. Observe here that the souton of probem (13) wth (3), (4), and (14) s not straghtforward snce the actua eves of demand and ther assocated degree of uncertanty are dependent of the tmng and sze of nvestment reazatons (see (2)). When sovng ths probem, the nvestment w be consdered safe f: L* ([ ], 1,, L, I) * ([ ], 1,, L, I) A rs eve, r, can be attached to the souton: L* * 0 f 0 L* * * L* * L* 100 ( ) / (2 ) f 0 r 100 (1 ( ) / (2 )) f 0 L* * * L* L* * L* * 100 f 0 (15) (16) VI. CASE STUY AN FUZZY UAL YNAMIC PROGRAMMING APPROACH For the numerca ustraton the case of a regona arport expected to gan an nternatona poston has been consdered. Mean potenta passenger demand s supposed to doube every eght years wth an nta traffc of 300,000 passengers per year whe mean cargo potenta demand s supposed to doube every fve years. The arport has been supposed to be managed under a BOT agreement (Bud Operate Transfer) over a perod of thrty years. In ths stuaton, the BOT project fnancng nvoves a prvate entty whch has receved a concesson from the pubc sector to fnance, desgn, construct, and operate the compex of arport nfrastructure factes, accordng to the concesson contract. The fnanca rs of the concessonare s to not be abe to recover ts nvestment, operatng and mantenance expenses n the project. In ths type of stuaton, the project proponent s facng a sgnfcant amount of rs that needs to be assessed and mtgated. The project s composed of three man phases: 1) An nta phase where the exstng runway and termna are renewed. 2) A second phase where arport ar traffc contro tower and reated equpment are upgraded, the ength of the runway s augmented whe passenger and cargo termnas capactes are ncreased. 3) A thrd phase where a new runway and a new passengers and cargo termnas are but. In each phase, a prepannng of arsde and andsde factes s necessary. It has been supposed that no new and acquston s necessary to perform the proposed pan. The fuzzy dua formasm has aowed consderng three scenaros wth respect to each type of demand (ow, medum and hgh). Ths has ed to a pannng probem wth 20 decson varabes ncudng tmng and sze of subprojects resutng n a set of rather sma scae optmzaton probems. In ths case, to sove probem (13), (3), (4), and (14) wth (2), ynamc Programmng has been consdered snce as stated n [9] ynamc Programmng s a mathematca technque for mang a sequence of nterreated decsons, provdng a systematc procedure for determnng the optma combnaton of resources. ynamc Programmng buds an optma souton step by step by consderng that any parta souton up to any ntermedate stage must be optma to that stage to be a canddate part for the goba souton (Beman prncpe). So, ony optma ways to reach each possbe state at each stage are mantaned n the search process. The ony mathematca condton for appcabty of ynamc Programmng s the separaton of the objectve functon and of the eve constrants wth respect to the decson varabes, and then ynamc Programmng may produce an exact souton through a rather effcent computatona process even for combnatora probems. Many dfferent approaches to mae use of ynamc Programmng (drect or reverse ynamc programmng) and extensons (stochastc ynamc Programmng, Fuzzy ynamc programmng) have been deveoped to face dfferent characterstcs of sequenta decson mang. Fuzzy dua programmng has been ntroduced recenty [10] to provde a genera framewor for deang wth uncertanty approached through the fuzzy dua formasm. The paradgm of ynamc Programmng has been Internatona Schoary and Scentfc Research & Innovaton 8(9) 2014 1233 schoar.waset.org/1999.7/9999485
Word Academy of Scence, Engneerng and Technoogy Internatona Journa of Mathematca, Computatona, Physca, Eectrca and Computer Engneerng Vo:8, No:9, 2014 Internatona Scence Index, Envronmenta and Ecoogca Engneerng Vo:8, No:9, 2014 waset.org/pubcaton/9999485 extended to ths stuaton by adoptng the comparson operators between fuzzy dua numbers detaed n the appendx. VII. CONCLUSIONS Ths communcaton after anayzng the ong term arport pannng probem has deveoped a new approach for arport nvestment rs assessment. Ths approach taes expcty nto account the degree of uncertanty n the predcton of actvty eves whe proposng mestones for the dfferent stages of the project for mnmzng rs. Uncertanty s represented through fuzzy dua theory whch aows mtng probem compexty as we as the computatona burden of ts souton. Here rs management s performed usng a fuzzy dua extenson of dynamc programmng and the appcabty of the proposed approach s dscussed through a case study. APPENIX A set of fuzzy dua numbers s defned as the set of numbers of the form a. b, where a s the prma part and b s the dua part of the fuzzy dua number, ar, b R. represents the unty pure dua number. A fuzzy dua number oses both ts dua and fuzzy attrbutes f b equas zero. The ower and upper bounds of a. b are gven by ow hgh B ( a. b) a b and B ( a. b) a b. Fg. 1 Graphca representaton of a tranguar fuzzy number The pseudo norm of a fuzzy dua number s gven by a. b a. b R, where 0 s the shape parameter. The shape parameter s gven by (1 / b) ( u) du, where µ s the membershp functon. The foowng propertes of the pseudo norm are mantaned no matter the vaues the shape parameters tae: b b a. b : a. b 0 (17) ar, b R a. b 0a b 0 (18) wrtten can be defned over by: a. b, a. b : a. b a. b a. b a. b (21) 1 1 2 2 1 1 2 2 1 1 2 2 The wea parta order wrtten can be defned over by: a1. b1, a2. b2 : a1. b1 a2. b2 (22) a b a b and a b a 2 2 1 1 1 1 2 The fuzzy equaty between two fuzzy dua numbers, symbozed by, s defned: a1. b1, a2. b2 : a1. b1 a2. b2 a a b a b a a b a b.,. and.,. 2 1 1 1 1 1 2 2 2 2 (23) Then any two fuzzy dua numbers can be raned as ether strongy dfferent, weay dfferent or rather equa and a fuzzy ranng can be estabshed between them as we as max and mn operators over subsets of. REFERENCES [1] Internatona Ar Transport Assocaton - IATA, Fact sheet: Economc and soca benefts of ar transport (Web page), accessed Juy 2014. [2] M. Strec, M. Rossbach, scontnuous nnovaton, (Boo stye), 2013, pp. 419-422 [3] T. onnet, R. Keast, Fttng arport prvatzaton to purpose: agnng governance, tme and management focus, Issue 11(2), 2011, pp.98-114, www.ejtr.tbm.tudeft.n. [4] Internatona Ar Transport Assocaton - IATA, B. Pearce, IATA Economcs Brefng Nº10 Proftabty and the ar transport vaue chan, June 2013, v 1.1. www.ata.org. [5] M. Tretheway, K. Marhvda, Arports n the avaton vaue chan: fnancng, returns, rs and nvestment, scusson paper 2013-15, Internatona Transport Forum, May 2013, Germany. [6] Arports Counc Internatona, 2011 Annua report, pp. 12, www.ac.aero. [7] N.N. Taeb, The Bac Swan: The mpact of hghy mprobabe (Boo stye), 2007, 1 st ed., Random House, New Yor, USA. [8] C.A.N. Cosenza, O. Lengere, F. Mora Camno, Fuzzy sets and dua numbers:an ntegrated framewor, (Pubshed Conference Proceedngs stye) 9 th Fuzzy Sets and Knowedge scovery Conference, Chonqng, Chna, 2012. [9] S.F. Her, J.G. Leberman, Introducton to operatons research, p.424, 9 th ed., McGraw H Internatona Edton, Sngapore, 2010. [10] C.A.N Cosenza, F. Mora Camno, Programmng wth fuzzy dua uncertanty, (Pubshed Conference Proceedngs stye) CLAIO Congreso Latno-Ibero-Amercano de Investgacon Oeprtva, Ro de Janero, Braz, 2012. a. b. a. b. a, R, b, R (19). a. b. a. b ar, b, R (20) Parta orders between fuzzy dua numbers can be ntroduced usng the above pseudo norm. The strong parta Internatona Schoary and Scentfc Research & Innovaton 8(9) 2014 1234 schoar.waset.org/1999.7/9999485