AN OPERATIONAL APPROACH FOR GROUND HANDLING MANAGEMENT AT AIRPORTS WITH IMPERFECT INFORMATION

Transcription

1 1 N OPERTIONL PPROCH FOR GROUN HNLING MNGEMENT T IRPORTS WITH IMPERFECT INFORMTION Slm Ftour Trbels (ENC) [email protected] crlos lberto Nunes Cosenz (COPPE) [email protected] Lus Gustvo Zely Cruz (UFF) [email protected] Felx Mor-Cmno (ENC) [email protected] In ths communcton the groun hnlng fleet mngement problem t rports s consere wth the m of mprovng rcrft servce t rrvl n eprture whle the opertonl cost of the groun servce fleets s tken nto ccount. The complexty of the consere problem, s well s, opertonl consertons le to propose n on-lne ecentrlze mngement structure where the crtclty of ech rcrft emn for servce s evlute usng prtculr fuzzy formlsm. Then fter etlng the ssume collbortve scheme between groun hnlng fleet mngers, rlnes n rport uthortes, heurstc pproch s propose to solve ths mult fleet ssgnment problem. cse stuy conserng lrge rport s scusse. Keywors: groun hnlng, mult fleet ssgnment, rport opertons, fuzzy moellng

2 ICIEOM CIO 2013 Vllol, Spn 1 Introucton The groun hnlng opertons represent the rse ctvtes t rports n chrge of processng pssengers, crgo, fcltes n supples t n roun prke rcrft. Most of these opertons re performe by fferent servce provers, usng vehcles whch re specfc to ech type of operton. Groun hnlng s not promnent ctvty wthn the r trnsportton system (RHLG, 2000), however ths ctvty s n mportnt enbler for effcent rport operton n ts mngement s n mportnt ssue. Over the lst eces, the complexty of TS hs ncrese to fce the worlwe growth of r trffc. Toy the operton of ths system nvolves globl ctors (rports, rlnes, r trffc control (TC), r trffc mngement (TM)) s well s locl ctors (groun hnlers, locl supplers ) whose coornton, whle pursung fferent n sometmes contrctory objectves, s ffcult to cheve. The mn objectves of trffc mngement t rports re to mprove opertonl effcency by reucng rcrft elys, to optmze the use of rport resources to reuce operton costs n to mprove the prectblty of r trnsportton opertons (flght rrvls n eprtures). So, to fce the current stuton wth cceptble sfety n effcency stnrs new concept hs been evelope: rport Collbortve ecson Mkng (CM) whch tres to crete common groun for the fferent component of the TS. Ths concept s bse on n mprove communcton between the fferent ctors of the rport. s n exmple, for Rossy-CG rport, where CM hs been mplemente snce 2010, eprture tmes re respecte n more thn 85% of the cses, gnst 80% before, the groun trffc s more flu (txng tmes hve been shortene by 2 to 4 mnutes), reucton of 14.5 tons of fuel n ly consumpton n lso sgnfcnt ecrese n CO 2 emssons (The Boeng Compny, 2000). So fr the mngement of the fferent servce fleets whch perform the turnroun process of groun hnlng hs not been consere specfclly n the CM pproch, even f t hs n mportnt prt n the fluty of rcrft groun movements, however ([3] shows tht 10% of ll the flght elys re cuse by the neffcent mngement of the fferent fleet of the groun hnlng operton. Ths pper fter entfyng possble objectves n essentl constrnts for groun hnlng t rports, proposes ecentrlze structure to cope wth ths mult-fleet ssgnment problem. Conserng tht mny prmeters re mperfectly known, the fuzzy moellng formlsm s ntrouce to tke nto ccount ths mportnt chrcterstc of ths groun hnlng mult-fleet (GHMF) problem. 2 Scope of the Stuy rcrft turnroun efnes the process of servcng n rcrft whle t s on the groun between two successve flghts t opertes. The turnroun term mples fst sequence between n rrvl n eprture, however for mny r trnsport opertons, n prtculr for long hul flghts, lrge tme ntervl my be progrmme between them. urng the turnroun, n rcrft must unergo complex process compose of set of elementry groun hnlng ctvtes such s lnng / borng, unlong / long of luggge, fuellng, cterng, clenng, wter n sntton processes. Fg.1 escrbes the mn groun hnlng opertons tkng plce roun groune rcrft s well s ther preceence constrnts. rrvl n eprture groun hnlng tsks re stngushe. 2

3 ICIEOM CIO 2013 Vllol, Spn Fgure 1: Groun hnlng ctvtes t rrvl n eprture Groun hnlng opertons re n generl crre out by fferent servce compnes, usng vehcle whch re specfc to ech type of operton. To perform the turnroun process for ech rcrft wthn the llocte tme, these fferent compnes hve to coornte between ech other whle respectng the constrnts of scheulng tsks for ech rcrft n the constrnts relte to the use of servce vehcles. The urton of ech groun hnlng operton s vrble from one flght to nother n epens n generl of the type of rcrft, the volumes of pssengers/luggge to be processe s well s of other externl fctors such s the current wether contons t the rport. Then the lrge vrblty of elementry tsk urtons shoul be tken nto ccount when mngng the fferent groun hnlng fleets. Ech groun hnlng fleet type s suppose homogenous so tht the sme tsk cn be performe wth the sme effcency by ny vehcle of ech consere groun hnlng fleet. The urton of n elementry tsk t on rcrft () ssgne to flght cn be estmte ether by n rlne groun stton mnger or the corresponng groun hnlng mnger who hs receve nformton bout the lo of the flght from the rlne. It s here suppose tht ths urton s gven by ul fuzzy number t t where s the current t t centrl vlue of the urton of tsk t n s the uncertnty rnge. Prt 3 proves bref t ntroucton to fuzzy ul numbers n ssocte bsc opertons. set of fuzzy rules cn be bult to generte these fuzzy ul tsk urtons where the bckbone s the nomnl processng tmes wth sclng fctors n the fuzzy rules generte the ul prt of the elementry tsk urtons. Ech of the groun hnlng ctvtes mkes use of speclze equpment whch must be turne vlble t the rcrft prkng plce t the rght tme to vo elys. Some of the groun hnlng ctvtes shoul be performe s soon s possble fter the rrvl of the rcrft t ther prkng stn n others must be performe only some tme before eprture from ther prkng stn. epenng of rcrft operton these two sub sets of ctvtes cn be performe n mmete sequence or re seprte by n le pero of vrble urton ccorng to rrvl n eprture scheules of gven rcrft. Fg.2 splys stnr stuton for n rcrft unergong turnroun process where spce s rther scrce resource n some tsks cnnot be performe smultneously (mnly for sfety resons). It ppers tht the effcent opertons of such complex process whch repets wth ech rcrft rrvl or eprture s very ffcult to be cheve whle t s crtcl ssue for rport opertons performnce. Then vnce mngement tools re necessry to cope n stsfctory wy wth ths problem. 3

4 ICIEOM CIO 2013 Vllol, Spn Fgure 2: Groun hnlng rrngement [2]. Few publctons coverng Fuzzy VRP or Fuzzy Scheulng re vlble n the lterture. The Fuzzy VRP hs been ntrouce s VRP problem wth tme wnow constrnts where the customer emn, the servce n the trvel tmes re gven by fuzzy numbers. In (J, 2005), smple escrpton of VRP problem wth fuzzy trvellng tmes s ntrouce n ts soluton s obtne through genetc lgorthm. In (Tng, 2007) where the urton of the tme wnow of VRP problem s consere s fuzzy vrble, the soluton hs been compute wth n nt lgorthm whose montorng s bse on the evoluton of the entropy of the soluton. Wth regr to Fuzzy Scheulng, (ubos, 2003) presents n overvew of fuzzy pproches to scheulng n emphszes the representton of preference profles n the moellng of uncertnty strbutons. 3 Fuzzy ul vrbles n bsc clculus The set of fuzzy ul numbers s the set of numbers (Cosenz 2011) of the form b such s R, b R where s the prml prt n b s the ul prt of the fuzzy ul number. Here s the unty pure ul number. crsp fuzzy ul number wll be such s b s zero, t loses both ts ul n ts fuzzy ttrbutes. The lower n upper bouns of b re gven by: B low ( b) b n B hgh ( b) b (1) grphcl representton of fuzzy ul number s gven below where μ s symmetrcl membershp functon efne over R: 4

5 ICIEOM CIO 2013 Vllol, Spn Fgure 3: Exmple of ul representton of fuzzy number The fuzzy ul (F) ton of ul fuzzy numbers, wrtten s gven by: ( x1 y1) ( x2 y2) ( x1 x2) ( y1 y2) (2) Its neutrl element s ( 0 0), wrtten 0. Then the sum of rel number x1 n fuzzy ul number x2 y2 s such s: x1 ( x2 y2) ( x1 0) ( x2 y2) x1 ( y1 y2) (2.2) The pseuo norm of ul fuzzy number s gven by: b b R (3) where s shpe prmeter. Fgure 4 splys stnr fuzzy ul numbers wth fferent shpe prmeters. Fgure 4: Exmples of shpes for fuzzy ul numbers The shpe prmeter s gven n generl by: b ( 1/ b ) ( u) u (4) b Let: us efne here the mn n the mx opertors for fuzzy ul numbers: c mx, b (5.1) wth, b R,, R then: c mx, b mx, b b mx (5.2) mn, b (6.1) wth, b R,, R then: mn, b n mn, b b mn, b (6.2) Observe tht here the mx n mn opertors prouce new fuzzy ul numbers. n b, 4 ecentrlze pproch of Groun Hnlng Mult-Fleet Mngement Problem In ths cse, t s consere tht rlnes communcte wth the groun hnlng fleet mngers through ther own groun stton mngers whch re n chrge of montorng the groun hnlng ctvtes t rrvl or eprture of ech flght. For exmple, one of ther objectve wth respect to flght rrvls s to mnmze the wtng tme for e-borng pssengers n luggge, nother one s to mke sure tht pssengers bor the rcrft n ue 5

6 ICIEOM CIO 2013 Vllol, Spn tme before scheule flght eprture tme. So, they wll be n chrge of requestng n ue tme the necessry groun hnlng resources for flght rrvl or eprture processng. In the cse of ecentrlze mngement of the fferent fleets of groun hnlng vehcles, the sze of ech fleet mngement problem s of course smller. Wth respect to the efnton of the corresponng ecson problems, some objectves of the groun hnlng problem cn be expresse s constrnts t the nvul fleet level. Once these constrnts re set, mjor objectve for ech groun hnlng fleet mnger wll consst n mnmzng ts groun hnlng vrble costs relte mnly to the fleet opertons costs. Ths cn be consere to be cheve by mnmzng the trvelle stnce of the corresponng groun hnlng fleet, contrbutng lso to rport envronment protecton (chemcl emssons n nose). To be fesble, ecentrlze pproch, nomnl or on-lne, must be coopertve. Ech groun hnlng fleet ssgnment (GHF) problem must be execute ccorng to sequence comptble wth the orgnzton of the groun hnlng ctvtes (Fg.1). Then ech GHF problem shoul ntegrte tme constrnts generte from the soluton of the uphll GHF problems or from the upte expecte flght rrvl scheules. The groun hnlng servces re elvere n sturbe envronment wth mny opertonl uncertntes. For exmple, the expecte rrvl tmes for flghts re subject to frequent elys, the urton of groun hnlng tsks s senstve to unexpecte events such s tonl trvel tme ue to trffc congeston on rse servce wys or mchne brekown. rport r trffc control servces upte the precte rrvl tmes whch re forwre to rport servces, nclung rlnes n groun hnlng. Ths strts the process of uptng the ssgnment n scheulng of tsks for ech groun hnlng fleet. In the cse n whch repete rcrft rrvl scheule perturbtons re expecte, ccorng for nstnce to meteorology contons, the horzon of fleet mngement cn be commonly lmte to some hours he, whle groun hnlng resources compute from the ly nomnl GHMF problem must remn on the lookout. In theory, ech groun hnlng fleet mnger shoul solve the new nstnce of ech GHF problem by tkng nto ccount the scheulng constrnts generte n prove by the uphll GHF problems or from the upte rcrft rrvl scheule n prkng postons forwre by the rlne. The precte completon tme of hs ctvtes on ech rcrft shoul be sent to the other groun hnlng mngers n the corresponng rlne. Then, when fleet mnger eces to generte new pln he shoul communcte the result to the ownhll groun hnlng opertors so tht they upte ther own plns. However, ths scheme ppers too complex to be opte on n on-lne stuton, speclly when we know tht the urton of the elementry ctvtes t groune rcrft re subject to vrtons. Here we conser tht the estmte rrvl or eprture tme of n rcrft wll be common tme reference for ll nvolve groun hnlng opertors whch wll hve to sen the corresponng servce vehcle to the consere rcrft. Then coornton between the fferent tsks wll tke plce ccorng to the corresponng scheulng constrnts (see for exmple fgure 1). The mmete uphll groun hnlng mngers wll be ble then to compute the estmte tme mrgns for ech tsk by comprng ther processng tme plus the nomnl urton of ther tsk wth the erlest processng tme of the followng tsks n the turnroun process. The ely of servce vehcle to rrve t the prkng poston or to execute ts tsk there my hve two types of consequences: - some followng tsk t ths prkng poston my be elye, - some subsequent ssgnments of ths vehcle to other rrvng or eprtng flghts my be revewe to vo elys. 6

7 ICIEOM CIO 2013 Vllol, Spn In both cses, the groun hnlng fleet mnger of the elye vehcle shoul communcte n estmte of ths ely to the other groun hnlers n to the nvolve rlne. Then they wll be ble to check the fesblty of the current plnne ssgnment scheme of ech groun hnlng fleet. In the cse current ssgnment scheme s no more fesble wthout tonl ely, ressgnment of the corresponng groun hnlng fleet shoul be cheve n communcte to the other prtes f nvolvng confrme elys. Fgure 5: Informton flows structure for GHMF operton 5 Fuzzy Heurstc for the On-lne GHMF ssgnment The problem for ech groun hnlng fleet s here to ssgn groun hnlng vehcles to rrvng or eprtng rcrft so tht ech rcrft s servce by vehcle whle, ccorng to the current opertonl stuton, no ely or mnmum ely s prouce. For tht, the rlne groun stton mngers generte resources requests to the groun hnlng fleet mngers. The prouce scheules re bse on the precte rrvl tmes s well s the scheule eprture tmes. These scheules tke not only nto conserton the possble vrton of the groun hnlng tsks urtons by usng fuzzy ul formlsm (Cosenz, 2012), but conser lso the crtclty of the flght. Ths crtclty epens on the current precte ely s well s the opertonl consequences on other flghts. Then more crtcl flghts my get ther groun hnlng soluton trete before erler less crtcl scheule flghts. The followng nottons re opte: Ech tsk of the turnroun process t 1,...,T s crre out on n rcrft () ssocte to flght, I, (I=I I, I s the set of rrvng flghts n I s the set of eprtng flghts) by specfc servce prover k 1,..., K. 5.1 Fuzzy-bse rnkng of flghts The frst step of the propose heurstc conssts n performng n ntl orerng of the flghts n ccornce wth ther current precte rrvl tme tˆ t ther ssgne prkng mene by conserng ther crtclty. To ech rrvng flght I, cn be ssgne the fference t tˆ t between the precte rrvl tme tˆ n the scheule rrvl tme t. Here tˆ n t cn be ether rel numbers or fuzzy ul numbers, where tˆ s prove by the TC. Ech rrvng flght must cope wth two types of opertonl constrnts: Connecton constrnts when rrvng pssengers must rech wthout ely nother eprtng flght. 7

8 ICIEOM CIO 2013 Vllol, Spn eprture scheule when the rrvng rcrft must be rey to strt new flght wth tght scheule. When conserng connecton constrnts, let C be the set of eprtng flghts connecte to rrvng flght. The fuzzy tme mrgn between flght n ech flght j n C s gven by: m j t j tˆ mx b T j, ul j j C (7) Here T n j re respectvely the connectng ely for pssengers n luggge between j flghts n j. The mrgn between rrvl flght n eprture flght j whch re servce n mmete successon by the sme rcrft s: m t tˆ wth j () (8) j j j where s the mnmum fuzzy ul urton of groun hnlng roun rrvl of flght n j eprture of flght j. Here () proves the number of the next flght servce by the rcrft opertng flght. Then, ccorng to fgure 1: ul fu ll b c b j mx (9) pb b cl b s w Then, the fuzzy mrgn of the rrvng rcrft s gven by: m mn m (10) jc ( ) j The mene rrvl tme for flght s then gven by: t tˆ m (11) To ech eprtng flght I, cn be ssgne the fference t tˆ t between the precte eprture tme tˆ n the scheule eprture tme t. Here lso, tˆ n t cn be ether rel numbers or fuzzy ul numbers. Symmetrclly, ech eprtng flght must cope wth opertonl constrnts relte wth successve flghts by the sme rcrft n flght connectons for pssengers n crgo. In the cse n whch the groun hnlng tsks re reltve to eprtng flght j, the mene precte tme to strt grn hnlng ctvtes t the corresponng prkng poston s now gven by: (12) t j t wth j mn 1 jc n ( j) m m j fu ll ( ) mx c b w pb Then, to ech flght, ether rrvng or eprtng, s ssgne tme prmeter such s: low ( B t ) for rrvng flghts (14.) low B ( t j ) for eprtng flghts (14.b) Then the flghts, ether rrvng or eprtng, present n the consere pero of operton cn be rnke ccorng to n ncresng nex. Let the nteger r () be the mene rnk of flght. 5.2 Groun Hnlng Fleets ssgnment to flghts Ech groun hnlng fleet mnger wll process the fferent flghts ccorng to the prouce orer r () but tkng nto ccount tht the estmte rrvl (eprture) tme s stll tˆ ( tˆ ), where groun hnlng vehcles re ssgne to the corresponng rcrft. In the cse (13) 8

9 ICIEOM CIO 2013 Vllol, Spn of n rrvng flght, groun hnlng rrvl tsks (unlong luggge, e-borng, clenng n sntton) re cope wth by ssgnng the corresponng vehcles n ccornce to ther prevous ssgne tsks wth other rcrft, ther current vlblty, n ther current stnce to the consere rcrft. Here the common reference tme scheule for the groun hnlng rrvl tsks s tˆ, I. In the cse of eprtng flght, groun hnlng eprture tsks (fuellng, cterng, luggge long, borng, wter n push bck) re lso cope wth by ssgnng the corresponng vehcles n ccornce to ther prevous ssgne tsks wth other rcrft, ther current vlblty, n ther current stnce to the consere rcrft. Here the common reference tme scheule for the groun hnlng eprture tsks s tˆ, j I. In both cses t s consere tht the whole set of fferent groun hnlng vehcles necessry t rrvl or eprture s ssgne by conserng the common reference tme scheule. Ths ssgnment of vehcles to flghts ether rrvng or eprtng s performe on greey bse by conserng the closest vehcle vlble to perform the requre tsk. Ths wll mke tht t the strt of groun hnlng ctvtes for n rrvl or eprture flght, ll necessry resources wll be nerby the prkng plce n tht scheulng constrnts between elementry groun hnlng tsks (see fg. 1) wll be cope loclly by the vehcle opertors wthout nee of communcton between the fferent groun hnlng fleet mngers. Ths s rther smple greey heurstc whch proves for ech fleet fcng the current servce emn complete soluton through reuce computtonl effort. So there s no lmtton n cllng bck ths soluton process, nclung the crtclty rnkng of flghts, ny tme sgnfcnt perturbton occurs. In generl, ths process wll be clle bck systemtclly ny tme new rcrft enters set I or set I. Observe tht the rnkng of flghts n I I B s globl rnkng whch shoul be opte by the groun hnlng fleet mngers s constrnt wth respect to the globl performnce of the rport wth respect to flghts. Gven ths rnkng, t s up to ech groun hnlng fleet mnger to mnmze ts opertons costs whle meetng ths overll common soft constrnt. The sets I n I re upte ccorng to current tme t. It s consere tht ssgnment of groun hnlng vehcles to rrvng or eprtng flghts s efntve t tme. Then t tme, I or I wll be upte epenng f s n rrvng or eprtng flght: I I or I I (15) When tˆ t becomes nferor to ely, then: I I n when tˆ t becomes nferor to ely, then: I I. epenng on the ntensty of trffc, the elys n cn be extene (low trffc stuton) or retrcte (hgh trffc stuton). 6 Cse Stuy To vlte the propose cooperton scheme n the ssocte heurstcs rel trffc t from Plm e Mllorc (PM) rport hs been consere. PM rport s, wth respect to rcrft n pssengers trffc, the thr lrgest Spnsh rport. urng the summer pero t s one of the busest rports n Europe, wth 22.7 mllon of pssengers n The rport s the mn bse for the Spnsh crrer r Europ n lso focus rport for Germn crrer r Berln. It occupes n re of 6.3 km2 (2.4 sq m). ue to rp growth of rcrft trffc n pssenger flows long the lst eces, tonl nfrstructure hs been e to the two orgnl termnls (1965) n B (1972). PM rport s compose now of two runwys, four termnls n 180 prkng stns (27 of them t prons) [20]. It cn hnle up to 25 mllon pssengers per yer, wth cpcty to sptch 12,000 pssengers per hour. Fgure 6 splys the hourly trffc of rrvng n eprtng rcrft on typcl 9

10 ICIEOM CIO 2013 Vllol, Spn summer y t ths rport. It ppers tht rcrft trffc remns ntense from erly mornng untl the begnnng of nght hours. Fgure 6: 01/08/2007 PM rport rcrft Hourly Trffc The evluton of the propose ecentrlze pproch hs been performe usng rcrft trffc t for 24h pero wth groun hnlng ctvtes tkng plce t the four prkng res relte wth the four termnls of PM rport. Except for rcrft styng t nght t the rport, lrge mjorty of groun hnlng opertons re one n the context of fst turnroun opertons. fferent szes for ech of the groun hnlng fleets hve been consere n vrous scenros. Fg.7 splys one of the consere compostons for groun hnlng fleets, whle fgure 8 splys the fuzzy ul urtons opte for full 320 rplne. Perturbtons hve been lso ntrouce for some rrvng rcrft wth upte prectons vlble wth ffteen mnutes he. The propose heurstc pproch hs been teste for the rcrft trffc t 1 st of ugust, 2007 (345 rcrft turnrouns on tht y). The resultng erlest eprture tme for rcrft hve been compre wth the rel tme eprture t, showng tht wth rther reuce groun hnlng fleets, vlble t ech termnl, the propose ecentrlze heurstc, oes not generte tonl elys. The pplcton of the propose heurstc pproch hs le to elys wth respect to eprture scheule nvolvng only 36 rcrft, wth mxmum ely of 16 mnutes. Fgure 7: Exmple of composton of groun hnlng fleets 10

11 ICIEOM CIO 2013 Vllol, Spn Fgure 8: Fuzzy ul urton of hnlng tsks for 320 rcrft The verge ely mong elye rcrft hs been of 7 mnutes. Hstorcl t from 01/08/2007 t Plm e Mllorc rport ncte tht bout 200 rcrft eprtures where elye for multple resons, nclung one of the mn resons, groun hnlng elys. Fgure 9 splys the hourly strbuton of elye rcrft t eprture resultng from the pplcton of the propose ecentrlze pproch. Clerly, the occurrence of these elys correspons to the busest rcrft trffc peros t the rport. Fgure 9: Hourly strbuton of resultng elys 7 Concluson In ths communcton the problem of mngng n ecentrlze wy rport groun hnlng hs been consere. Then, optng ecentrlze mngement structure, where rlne stton mngers n groun hnlng fleet mngers nterct, n heurstc tkng explctly nto ccount the uncertnty bout elementry processng tmes hs been evelope. Ths heurstc s bse on the cooperton between the fferent tctcl ecson mkers, provng n effcent rectve groun hnlng mult fleet mngement structure. Ths cooperton scheme ppers to be comptble wth n overll collbortve ecson mkng pproch for the rse mngement t rports. cse stuy conserng rcrft n groun hnlng trffcs t PM rport urng typcl summer y hs been evelope through smulton, showng the nterest of the propose pproch. References RHLG-Report of the Hgh Level Group (2000) Sngle Europen Sky. The Boeng Compny (2004), Boeng. B777-rplne Chrcterstcs for rport Plnnng C. 11

12 ICIEOM CIO 2013 Vllol, Spn Jw J.,. Oon, H. N. Psrfts, n N. H. M. Wlson (1986), heurstc lgorthm for the mult-vehcle vnce request l--re problem wth tme wnows, Trnsportton Reserch Prt B, Vol. 20, pp Correu J.F. n G. Lporte (2003), tbu serch heurstc for the sttc mult-vehcle l-re problem, Trnsportton Reserch Prt B, Vol. 37, pp Bon L.. n T. Sexton (1986), The mult-vehcle subscrber l--re problem, TIMS Stues n Mngement Scence, Vol. 26, pp ngnostks I., H. R. Irs, J.-P. Clrke, E. Feron, R. J. Hnsmn,. Oon, n W.. Hll (2000), conceptul esgn of eprture plnner ecson, 3r US/Europe r trffc mngement R& semnr, Nples, Itly. Crr F., G. Thes, J.-P. Clrke, n E. Feron (2005), Evluton of mprove pushbck forecsts erve from rlne groun opertons t, Journl of erospce Computng, Informton, n Communcton, Vol. 12, pp Kuhn K. n S. Loth (2009), rport Servce Vehcle Scheulng, 8th US/Europe r Trffc Mngement Reserch n evelopment Semnr, June 29 July 02; Np, Clforn, US. Ftour.Trbels S., F.Mor-Cmno n C.Mncel (2012), Moélston es opértons escle sur une plteforme éroporture en vue e leur geston. Proceeng of the 13th Congress of Esys Ph stuent Esys2012, Februry 9-10; Toulouse, Frnce. J J., N.Lu n R.Wng (2008). Genetc lgorthm for Fuzzy Logstcs strbuton Vehcle Routng Problem, In proceeeng Interntonl Conference on Servce Opertons n Evolutonry Computng.IEEE. Tng L., W.Cheng, Z.Zhng, B.Zhong (2007). nt Colony lgorthm Bse on Informton Entropy Theory to Fuzzy Vehcle Routng Problem.In proceeng ISKE, seres: vnces n Intellgent Systems Reserch. ubos., H.Frger n P.Fortemps (2003). Fuzzy scheulng: Moellng flexble constrnts vs. copng wth ncomplete knowlege. Europen Journl of Opertonl Reserch 147, pp Cosenz C..N. n Mor-Cmno, F. (2011) Nombres et ensembles uux flous et pplctons, Techncl repport, LMF lbortory, COPPE/UFRJ, Ro e Jnero, ugust. Cosenz C..N., Lenguerke O. n Mor-Cmno F. (2012) Fuzzy sets n ul numbers: n ntegrte pproch, Proceengs of 9th Interntonl Conference on Fuzzy Sets n Knowlege scovery, Chongqng, pp The EN, Plm e Mllorc rport, 12