A Mul-Perodc Opmzaon Modelng Approach for he Esablshmen of a Be Sharng Newor: a Case Sudy of he Cy of Ahens G.K.D Sahards, A. Fragogos and E. Zygour Absrac Ths sudy nroduces a novel mahemacal formulaon ha addresses he sraegc desgn of a bcycle sharng newor. The developed pure neger lnear program aes no consderaon daa such as he poenal fuure demand paerns durng he day, he be s populary n a cy, he desred proxmy of he saons and he avalable budge for such a newor. Wh hese npu daa, opmzes he locaon of be saons, he number of her parng slos and he dsrbuon of he bcycle flee over hem n order o mee as much demand as possble and o offer he bes servce o he users. The esmaed demand for he newor s spl no Demand for Pc-Ups and Demand for Drop-offs durng he 24 hours of he day, whch are dscrezed no me nervals. The proposed approach s mplemened on he very cener of he cy of Ahens, Greece. Index Terms be sharng, neger, mahemacal model, mul-perodc B I. INTRODUCTION e sharng newors have receved ncreasng aenon durng he las decades and especally n he 21s cenury as a no-emsson opon n order o mprove he frs/las mle connecon o oher modes of ransporaon, hus faclang he mobly n a densely populaed cy. The be sharng newor consss of docng saons, bcycles and nformaon echnology (IT) nerfaces ha have been recenly nroduced o mprove he qualy offered o he users. There have been hree generaons of be sharng programs over he pas half cenury [1] wh he 3 rd one emergng n 1996 a Porsmouh Unversy (Beabou). However, was no unl 25 ha hs generaon flourshed wh he launch of Velo v wh 15 bes n Lyon. Two years laer, Pars launched Velb and Barcelona launched Bcng, whch are wo of he mos successful newors nowadays. Nowadays, here are 678 programs n Manuscrp receved December 7, 213; revsed January 1, 214. G.K.D Sahards s a Lecurer a he Deparmen of Mechancal Engneerng of he Unversy of Thessaly, Volos, 38834 Greece (emal: sahards@gmal.com) A. Fragogos s a Posgraduae Suden a he Deparmen of Mechancal Engneerng of he Unversy of Thessaly, Volos, 38834 Greece (e-mal: fragogosanonos@gmal.com) E. Zygour s a Posgraduae Suden a he Deparmen of Mechancal Engneerng of he Unversy of Thessaly, Volos, 38834 Greece (e-mal: el.zgour.haf@gmal.com) operaon and 186 n plannng or under consrucon all over he world (Merobe, December 213). Ths expandng rend of be sharng newors necessaes her beer plannng and desgn n order ha hey are successful. The goal of hs paper s o propose a novel mahemacal formulaon o desgn such newors ncorporang he hourly demand esmaon, he fxed coss of nfrasrucure, he proxmy and densy of saons, as well as her sze. Gven a se of canddae locaons of saons and wh a predefned avalable consrucon budge he model decdes he number and he locaon of he saons, how large hey wll be and how many bes should hey have a he begnnng of he day n order o mee he assumed demand. The remander of he paper s organzed as follows. Secon II provdes a bref leraure revew of he man approaches ha have been proposed o solve smlar problems. Secon III presens he developed novel mahemacal model. In secon IV he case-sudy for he cener of Ahens s descrbed followed by he resuls of he mplemenaon of he model on. Fnally, n secon V here s a commenary on he proposed model, s broader applcaon and poenal areas of fuure wor. II. LITERATURE REWIEW Shu e al. (21) [2] proposed praccal models for he desgn and managemen of a bcycle-sharng newor gven he locaon of he saons. A sochasc newor flow model s nroduced n order o predc he flow of bcycles whn he newor and o esmae he number of rps suppored by he sysem, he suable number of bcycles o be deployed and he number of docs needed n each saon examnng he vably of perodc re-dsrbuon of bcycles as well. In he heren research he number of he saons s no predefned, as n [2], bu par of he desgn problem and he demand of each canddae locaon s deermnsc. Fnally, he presen wor addresses he desgn of such newors and no her managemen, so no re-dsrbuon aspecs are aen no consderaon. Ln e al. (211) [3] developed a pure neger non-lnear program for he sraegc desgn of a be sharng newor. Gven a se of orgns, desnaons, canddae bcycle saons and he ravel demands from orgns o desnaons wh specfc demand processes, opmzes he locaon of he saons and bcycle lanes and he requred nvenory
level for sharng bcycles a each saon o mee demand. The heren model s a pure neger lnear program where no orgn-desnaon flows are assumed, bu every locaon s characerzed by me-dscrezed demand for pc-ups and drop-offs durng a sngle day. Ths approach s consdered o gve mproved and less complcaed smulaon of he newor s fuure usage. Addonally, he be sharng newor s deal wh ndependenly and so he esablshmen of bcycle lanes s no n he scope of he presen research. Sayarshad e al. (211) [4] nroduce a mul-perodc opmzaon formulaon o deermne he mnmum requred be flee sze ha mnmzes smulaneously unme demand, unulzed bes and he need o ranspor empy bes beween renal saons. The heren model, also, uses mulperodc formulaon whou re-dsrbuon concerns because addresses only he newor desgn problem and no s usage, as n [4]. Marnez e al. (212) [5] presen a heursc, encompassng a mxed neger lnear program, whch opmzes he locaon of be saons and he flee dmenson, whle measurng he requred bcycle redsrbuon acves. I consders a mxed flee of regular and elecrc bes and several fare collecon mehods of he sysem. The presen research consders only regular bes assumng ha elecrc ones are ye o come n such a newor. Moreover, ncludes no fare polcy as hs may be decded afer he esablshmen of he be sharng newor. García-Palomares e al. (212) [6] use Geographcal Informaon Sysem (GIS) o calculae he spaal dsrbuon of he poenal demand for rps, locae saons usng locaon-allocaon models, deermne saon capacy and defne he characerscs of he demand for saons. In he heren projec he GIS s no used as access o a respecve sofware could no be graned. The demand daa are derved by he recorded usage daa of already mplemened smlar be sharng newors. A. Problem Defnon III. MODEL FORMULATION Gven a se of canddae locaons of be saons and he me-dependen demand for bes a hese locaons durng an average day s necessary o now where o place he be saons and how many parng slos and bes should each one have. The avalable budge of a cy for he consrucon of he whole be sharng sysem s predefned and so are he coss of a sngle be, a sngle parng slo and a sngle saon. The walng me beween he locaons s anoher parameer of he problem used o manpulae he proxmy of he consruced saons. As regards demand n each locaon, s spl no Demand for Pc-Ups,.e. how many users would le o ae a be from a saon, and Demand for Drop-Offs,.e. how many rders would le o leave a be no a saon. The 24 hours of he day are dscrezed no me nervals of one hour, durng whch dfferen numbers of users come o a saon eher o pc up or drop off a bcycle. B. Mahemacal Model The model ncludes he followng subscrps and ses, npu parameers and decson varables: Subscrps and Ses:, N : he canddae locaons of bcycle saons, p T : he me nervals n a sngle day Inpu Parameers: CB : cos of purchasng a sngle bcycle, CS : cos of esablshng a be saon (whou any parng slos), CTH : cos of consrucng a sngle parng slo no an esablshed saon, APE : walng me from locaon o locaon (n mnues), maxper : maxmum walng me (n mnues) beween wo canddae locaons, of whch he one has an esablshed saon and he oher one does no have a saon. Ths parameer s nroduced n order o manpulae he proxmy of he fnally proposed saons o be esablshed, BDG : oal avalable budge for he esablshmen of he whole be sharng newor, DF : Demand for Pc-Ups from locaon durng me nerval, DE : Demand for Drop-Offs a locaon durng me nerval, DD p : a parameer ha equals 1 f he Demand for Drop- Offs s more han he Demand for Pc-Ups unl me nerval p and oherwse, Z mn : mnmum number of parng slos a saon could have, Z max : maxmum number of parng slos a saon could have, perde : percenage of he demand ha s ransferred from a locaon where a saon s no esablshed o an esablshed saon. I s assumed ha f a saon s no esablshed a a locaon, par of s demand s los ( 1 perde ). Ths parameer s a measure of he czens nclnaon o berdng, CDT : penaly cos per un of demand and per mnue of walng me, f a cusomer has o wal from hs/her locaon wh no esablshed saon o he nearby saon, CDEMAND : penaly cos for a un of unme demand, M : a very large number, m : a very small number, Decson Varables X : bnary varable ha equals 1 f a saon s esablshed a locaon and oherwse, Z : bnary varable ha equals 1 f canddae locaon s served by he esablshed saon a locaon and oherwse, DN : general neger varable ha equals he number of consruced bcycle parng slos a saon, BN : general neger varable ha equals he number of
bcycles ha are avalable a saon a he begnnng of me nerval, BF : general neger varable ha equals he number of bcycles ha could leave saon durng me nerval, where BN bcycles are avalable, BE : general neger varable ha equals he number of bcycles ha could arrve a saon durng me nerval, where are avalable, DN parng slos are esablshed and BN bcycles UDBnF : bnary varable ha equals 1 f a saon canno serve some Demand for Pc-Ups a me nerval and oherwse (no enough avalable bcycles), UDBnE : bnary varable ha equals 1 f a saon canno serve some Demand for Drop-Offs a me nerval and oherwse (no enough avalable parng slos), In Fg. 1 he horough consderaon of he problem s explaned. N locaons are predefned ogeher wh her Demand for Pc-Ups (.e. DF ) and Demand for Drop- Offs (.e. DE ) a all me nervals durng an average day. I s a maer of opmzaon how many be saons wll be esablshed and where, so ha every locaon has a nearby saon. The locaons, where saons are esablshed, s a subse of he locaons. The demand paerns of each canddae locaon express he wll of he locaon s czens o use he newor f a saon were fnally esablshed here. In case a saon s no esablshed a a specfc locaon (no all locaons wll have a saon), he locaon s czens wll have o wal o he one ( perde ). The res of he demand s no served supposng ha hs par of czens wll no ae a be due o he dsance of he saon from her locaon. Objecve Funcon The objecve funcon of he model s a mnmzaon of hree erms: MINIMIZE : CDT * perde * ( DF DE ) * Z * APE CDEMAND * ( DF BF ) CDEMAND * ( DE BE ) The frs erm expresses he amoun of demand ha s ransferred from a locaon o s allocaed saon, whch are a specfc walng me away from one anoher. The second and he hrd erm of he objecve funcon are nroduced n order o mnmze he unme demand. The goal of he model s no only o mee as much demand as possble (second and hrd erm), bu also o provde bes servce o he users. For hs reason, he frs erm s nroduced so ha only few cusomers from locaon wh no saon (.e. perde * ( DF DE ) ) wll have o wal for a mnmum me (.e. APE ) o saon (.e. Z ). Oherwse, whou hs erm he model proposes a soluon where hgh-demand locaons are served by no so close lowdemand saons. The hree erms are mulpled wh a parameer n order o be expressed n he same un ( ). Thus, he uns of CDT are ( /cusomer/mnue) and hose of CDEMAND are ( /cusomer). The second and he hrd erm are mulpled by he same penaly un cos CDEMAND meanng ha no dfferen wegh s gven o eher he Demand for Pc- Ups or he Demand for Drop-Offs. Consrans The mahemacal model s subjec o he followng consrans: CB * BN CS * X CTH * DN BDG (1) (2) X * Z mn DN X * Z max, (3) Fg. 1. Newor srucure of be sharng sysem. neares esablshed saon, whch s maxper walng me away, n order o use he newor. In hs way, s assumed ha locaon s served by saon,.e. Z =1. The percenage of he czens ha are wllng o do hs s expressed by he parameer perde. Ths parameer s assumed o be a measure of he be s populary n a specfc cy. For example, f he czens are een rders, hey would be wllng o wal from her locaon o he neares saon so as o pc up a be and use he newor ( perde 1 ). However, f he be s no a very popular means of ranspor n a cy, hen only few of he demand of a locaon wh no saon would be ransferred o he neares BN DN,, (4) BN BN, (5) BN BN BE BF,, (6) 1 Z X,, (7) X Z, (8) Z 1, (9) maxper Z,,, (1) APE BF BN,, (11)
BE DN BN,, (12) BF DF ( Z * DF * perde),, (13) BE DE ( Z * DE * perde),, (14) DF ( Z * DF * perde) BN * m UDBnF 1 DF ( Z * DF * perde) BN * m,, DE ( Z * DE * perde) ( DN BN ) * m UDBnE 1 DE ( Z * DE * perde) ( DN BN ) * m,, DF ( Z * DF * perde) M * UDBnF BF DF ( Z * DF * perde) M * UDBnF,, BN M * (1 UDBnF ) BF BN M * (1 UDBnF ),, DE ( Z * DE * perde) M * ( UDBnE DD ) BE DE ( Z * DE * perde) M * ( UDBnE DD ),, ( DN BN ) M * (1 UDBnE DD ) BE ( DN BN ) M * (1 UDBnE DD ),, X Z (15) (16) (17) (18) (19) (2) {,1}, (21) {,1},, (22) UDBnF {,1},, (23) UDBnE {,1},, (24) DN BN BE BF, general neger (25),, general neger (26),, general neger (27),, general neger (28) Consran (2) warrans ha he oal cos for he esablshmen of all saons, he consrucon of all parng slos n hem and he purchase of all bes does no exceed he avalable budge. Consran (3) ensures ha he bcycle parng slos (.e. DN ) a each consruced saon are beween he permssble mnmum and maxmum value (.e. Z mn and Z max ). Consran (4) ensures ha a all me nervals, each saon canno have more bes han he number of s parng slos. Consran (5) means ha a all me nervals he oal number of bcycles a all saons wll no exceed he oal number of bcycles a he frs me nerval. Ths consran s nroduced because he frs me nerval s assumed o be 4-5am, so a 4am all bes are consdered o be pared no he saons and no user eeps a be away. Durng he day a user can eep a be for more han he duraon of he me nerval (e.g. one hour) and reurn o a saon a a laer me nerval. So n a gven me nerval due o more Demand for Pc-Ups han Demand for Drop-Offs he oal number of avalable bes a all saons wll be less han he nal number. Aferwards, n a laer me nerval > due o more Demand for Drop-Offs han Demand for Pc-Ups he avalable bes a all saons wll be more han hose n me nerval, bu no greaer han he oal number of bes n. Ths consran also ensures ha he model does no add bes o he newor durng he day,.e. he be sharng newor s a closed newor. Consran (6) expresses ha he number of bcycles a saon a he begnnng of me nerval +1 s equal o he ones had a he begnnng of me nerval plus he bes ha arrve mnus he ones ha leave durng me nerval. Consran (7) guaranees ha a locaon canno be served by locaon, f a saon s no bul n locaon. Consran (8) warrans ha f a saon s consruced a locaon hs locaon wll be served by s own saon. Consran (9) ensures ha each locaon may be served by exacly one be saon. Consran (1) expresses ha a consruced saon can serve only locaons whch are locaed whn a maxmum walng me away from. Consran (11) guaranees ha a every me nerval he bcycles ha can leave he saon can be no more han he avalable ones. Consran (12) ensures ha a every me nerval he bes ha can come o a saon can be no more han he free parng slos. Consran (13) expresses ha a every me nerval he bes ha can leave a saon can be no more han he demand for pc-ups of hs saon plus a percenage of he demand of all oher locaons hs saon serves. Consran (14) expresses he same as he prevous one, bu for he demand for drop-offs. Consrans (15) and (16) force he varables UDBnF and UDBnE o be 1 f a saon canno serve some Demand for Pc-Ups or Demand for Drop-Offs respecvely durng me nerval and oherwse. Consrans (17) and (18) guaranee ha f here s unsasfed Demand for Pc-Ups, all avalable bes wll leave he saon and f here s no unsasfed Demand for Pc-Ups, he whole demand wll be me. Consrans (19) and (2) guaranee ha f here s unsasfed Demand for Drop-Offs, all bes wll fll he avalable slos and f here s no unsasfed Demand for Drop-Offs, he whole demand wll be me. These wo consrans are relaxed f he Demand for Drop-Offs s more han he Demand for Pc-Ups unl me nerval p (.e. DD p 1), whch s a deformaon of he assumed demand (unl me nerval he oal number of users ha wan o drop off a be a all saons canno be more han he ones ha have already pced up one). The be sharng newor s a closed newor and wh hs parameer a hese wo consrans he model s no oblged o mee he whole Demand for Drop-Offs a he me nervals a whch hs deformaon happens. Fnally he consrans (21), (22), (23), (24), and (25), (26), (27), (28) are he negraly and he non-negavy
consrans, respecvely. A hs pon s necessary o explan how he model decdes he number of a saon s parng slos (.e. and s bes a frs me nerval (.e. BN DN ) ). Gvng a value a hese wo varables deermnes he values of UDBnF and UDBnE (consrans (15) and (16)). The laer varables deermne he values of he bes ha wll leave or come o he saon a he frs me nerval (.e. BF and BE, consrans (17) o (2)). The las ones deermne he avalable bes of he saon a he begnnng of he nex me nerval 1 (.e. BN 1, consran (6)) and so goes on. Headng o mnmze unme demand he model proposes hose values of DN and BN a each saon ha wll resul no havng he suable number of avalable bes and free parng slos n he followng me nervals gven he saon s dfferen dsrbuon of demand durng he day. A. Daa sengs IV. ATHENS CASE-STUDY Generally, should be noced ha he goal of hs research s o develop a globally applcable modelng approach for he desgn of he be sharng newor and no he esmaon of demand. However, so as o esmae he poenal demand of a be sharng newor for he cy of Ahens, he hree exsng n he leraure papers were analyzed and one of hem was Fg. 2. a ) The hourly Demand for Pc-Ups of each cluser durng a weeday n Ahens, b) The hourly Demand for Drop-Offs of each cluser durng a weeday n Ahens. aen no consderaon. Froehlch e al. (29) [7] provde spaoemporal analyss of he bcycle saon usage n Barcelona s shared bcyclng newor, called Bcng. Laha e al. (212) [8] analyze he usage daa of he London Barclay Cycle Hre newor. Fnally, Eenne e al. (212) [9] propose a model o form clusers of he saons of he Velb newor of Pars based on her usage daa. The las one was consdered more helpful due o he ampler way descrbes saons dynamcs. In converng he usage daa of he Velb newor n whole Pars no poenal demand of a fuure be sharng newor n he 1s Muncpal Dsrc of Ahens, he auhors oo no consderaon several facors, such as populaon densy, [1] and [11], saons proxmy o he cy cener and urban characerscs. The canddae locaons n he problem of Ahens are caegorzed no four clusers dependng on her locaon. Fg. 2 depcs he mean demand values of each one of he four clusers of saons durng he weedays n Ahens. Based on he urban desgn and he ransporaon newor characerscs of he cener of Ahens, he auhors of hs paper chose 5 canddae locaons where be sharng saons could be esablshed. These 5 locaons were caegorzed no he prevously descrbed 4 clusers and each one was gven a scalng facor of.25 (depcs a low-acvy Parameer locaon) o 2 (depcs a hgh-acvy locaon). The values of he res of he npu parameers for he case sudy of Ahens are shown n Table I. B. Resuls Value TABLE I DATA CB 5 CS 12, CTH 9 BDG 1,, maxper 7 mnues Zmn 8 parng slos Zmax 7 parng slos CDT 1 /cusomer/mnue CDEMAND 3 / los cusomer The problem was formulaed as a pure neger lnear problem and was solved usng CPLEX opmzer hrough a C++ code. The code was mplemened on a lapop compuer (Inel 2.67 GHz Core 5 and 4GB of RAM). In hs paragraph, he resuls of 2 solved cases of he problem wll be presened. In he frs one s consdered ha he be s a very popular means of ranspor among he Ahenans ( perde 1) and n he second one ha s no so popular ( perde.5 ). Wheher he frs or he second scenaro s acually he case s somehng o be decded by a socal survey n he cener of Ahens, whch s no n he scope of hs paper. All oher parameers are he same for boh cases. Fg. 3 and 4 depc he proposed esablshed be saons n case 1 and 2 respecvely. The shape of each do corresponds o he saon s cluser, whereas s sze represens he number of parng slos each saon should have.
Fg. 3 The esablshed saons of he soluon of he 1 s case caegorzed n clusers and wh her sze. (Reference: hp://www.bng.com/maps/) Fg. 4 The esablshed saons of he soluon of he 2 s case caegorzed n clusers and wh her sze. (Reference: hp://www.bng.com/maps/) In he frs case he oal number of docng saons s 34 and he number of parng slos s 517 mang a mean value of 517/34=15.2 slos per saon. The oal number of bes n he newor s 253 and her dsrbuon over he esablshed saons a he frs me nerval of he day shows ha saons of he cluser Housng are nearly full of bes n order o mee he ncreased Demand for Pc-Ups durng he mornng pea. On he oher hand, he saons of he cluser Employmen do no have many bes. Ths resuls n havng more free parng slos n order o mee he ncreased Demand for Drop-Offs durng he mornng pea. In he second case he esablshed saons are 4 wh a oal number of 461 parng slos. Ths maes a mean value of 461/4=11.525 slos per saon. The purchased bes are 21. The same noce as regards he be dsrbuon over he saons a he frs me nerval can be made n hs case as well. Comparng he resuls of he wo cases, should be menoned ha here s a dfference beween hem n he number and he sze of he esablshed saons. In he frs case he locaons wh no esablshed saon ransfer her whole demand o he nearby saon ( perde 1). So he model proposes fewer bu larger saons o mee he added demand by nearby locaons. In he second case wherever he model does no esablshed a saon and serves he specfc locaon from a nearby saon, loses 5% of s demand ( 1 perde 1.5 5% ). For hs reason, he second soluon proposes more saons han he frs one havng less money o buld enough parng slos and hus mang hem smaller. V. CONCLUSION I s crucal ha he be sharng newors are desgned accordng o he demand hey are o mee n he fuure. The nowledge ganed from he already mplemened newors can and should be used for he desgn of fuure ones. In hs paper he auhors modfed he usage daa from he Velb newor of Pars so as o predc demand n Ahens and desgn a suable be sharng newor o mee ha demand. However, he value of hs paper les raher on he mahemacal formulaon self han on s mplemenaon. The mahemacal formulaon allows he user o aler dfferen parameers of he fuure be sharng newor (such as he demand paerns, maxper, perde, he budge ec.) and ae a soluon of how hs newor should be. In hs paper a sensvy analyss over one parameer ( perde ) was provded o show he changes on he soluon. The values of hese parameers need o be drawn from a socal survey of he under-sudy regon and hen nsered no he mahemacal model o ge an opmal desgn of a be sharng newor. Moreover, dfferen runs of he developed code can be made o ge a soluon, where he avalable budge s changed or he demand profles approxmae he seasonal dfferences (wner-summer) or he wee dfferences (weedays-weeend). The dfferen soluons aen can hen be combned n order o ge a beer newor desgn. Ths combnaon mgh be a maer of a fuure wor. REFERENCES [1] P. DeMao, Be sharng: Hsory, Impacs, Models of Provson, and Fuure, Journal of Publc Transporaon, vol. 12, No 4, 29, pp. 41-56. [2] J. Shu, M. Chou, Q. Lu, C-P Teo and I-L Wang, Bcycle-Sharng Sysem: Deploymen, Ulzaon and he Value of Re-dsrbuon, Naonal Unversy of Sngapore, 21. [3] J-R Ln and T-H. Yang, Sraegc desgn of publc bcycle sharng sysems wh servce level consrans, Transporaon Research Par E, vol. 47, 211, pp. 284-294. [4] H. Sayarsad, S. Tavassol and F. Zhao, A mul perodc opmzaon formulaon for be plannng and be ulzaon, Appled Mahemacal Modellng, vol.36, 211, pp. 4944-4951. [5] M. L. Marnez, L. Caeano, T. Ero and F. Cruz, An opmzaon algorhm o esablsh he locaon of saons of a mxed flee bng sysem: an applcaon o he cy of Lsbon, Proceda- Socal and Behavoral Scences, vol. 54, 212, pp. 513-524. [6] C. J. Garca-Palomares, J. Guerrez and M. Laorre, Opmzng he locaon of saons n be sharng programs: A GIS approach, Appled Geography, vol. 35, 212, pp. 235-246. [7] J. Froehlch, J. Neumann and N. Olver, Sensng and Predcng he Pulse of he Cy hrough Shared Bcyclng, Proceedngs of he 21s Inernaonal Jon Conference on Arfcal nellgence, USA, 29, pp. 142 1426. [8] N. Laha, S. Ahmed and L. Capra, Measurng he mpac of openng he London shared bcycle scheme o casual users, Transporaon Research Par C, vol. 22, 211, pp. 88-12. [9] C. Eenne and L. Ouhellou, Model-based coun seres cluserng for Be sharng sysem usage mnng, a case sudy wh he Velb sysem of Pars, Transporaon Research-Par C Emergng Technologes, vol. 22, 212, pp. 88. [1] Insu Naonal de la Sasque e des Éudes Économques. Présenaon de la régon Ile-de-France. hp://www.nsee.fr/fr/regons/df/defaul.asp?page=fasechffres/pre senaon/presenaon.hm. Accessed Nov. 1, 213. [11] Hellenc Sascal Auhory (EL.STAT). Populaon. hp://www.sascs.gr/poral/page/poral/esye/pagehemes?p_param=a162. Accessed Nov. 1, 213.