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1 Avalable ole at SceceDrect Proceda Coputer Scece 31 ( 2014 ) d Iteratoal Coferece o Iforato Techology ad Quattatve Maageet, ITQM 2014 Offshore helcopter routg a hub ad spoe fasho: zg expected uber of fataltes Øyvd Halsau sr.* Molde Uversty College, P.O. Box 2110, NO-6402 Molde, Norway Abstract Helcopters are ofte used for trasportato of worers to ad fro offshore stallatos. Flyg helcopter s a rsy busess ad s ofte cosdered as oe of the a rs factors ths dustry. The preset paper s dealg wth dfferet routg polces for zg the expected uber of fataltes where the trasportato s perfored a hub ad spoe fasho fro a lad based helport to a set of offshore stallatos ether usg the helport as a hub or usg oe or ore offshore stallatos as hubs. Soe theoretcal results are offered as well as a exact odel whe oe operates wth ore tha oe offshore hub Publshed The Authors. by Elsever Publshed B.V. Ope by Elsever access uder B.V. CC BY-NC-ND lcese. Selecto Selecto ad ad peer-revew uder uder resposblty of the of Orgazg the Orgazg Cottee Cottee of ITQM of ITQM Keywords:routg; hub ad spoe; safety; helcopters; offshore petroleu s dustry 1. Itroducto I the offshore ol ad gas dustry ol copaes ost ofte use helcopters order to brg the crews worg o the offshore stallatos out to the platfors ad bac aga. Ths s a farly quc ad effcet way to serve these stallatos both wth the people who operate the o a daly base, but also brgg ateace people ad experts to platfors for shorter or loger tes, perforg specal tass. However, ths type of trasportato s ofte perceved by the worers to be ucofortable ad upleasat due to the ose of the helcopter ad turbulece that ca be volet whe the weather s bad. I addto, flyg helcopter s a farly rsy actvty ad uch ore rsy tha flyg a ordary plae or drvg a car. For ore detals about ths see 1,2,3,4,5,6. The rs durg ladgs ad tae-offs are cosdered to be substatally larger tha durg crusg betwee the helport (HP) ad * Correspodg author. Tel.: ; fax: E-al address: oyvd.halsau@holde.o Publshed by Elsever B.V. Ope access uder CC BY-NC-ND lcese. Selecto ad peer-revew uder resposblty of the Orgazg Cottee of ITQM do: /.procs

2 Øyvd Halsau / Proceda Coputer Scece 31 ( 2014 ) the stallatos or betwee the stallatos. Ths s especally true whe t coes to ladgs or tae-offs o the platfors, where the helcopter dec s arrow wth a lot of equpet le craes ad cotaers create bg challeges for the plots. For statstcs, descrbg the rs of flyg helcopters dfferet coutres, see 7,12. I the scearos treated by 1,2,3,4 rss coected wth both tae offs/ladgs as well as crusg rss are cosdered sultaeously ad dfferet routg polces are cosdered order to ze the expected uber of fataltes. I the preset paper the sae s doe, but cotrast to 1,2,3,4, we cosder hub ad spoe systes. A accdet s called fatal whe oe or ore people de or s serously ured a accdet. Routg of helcopters ca ether decrease or crease the probablty that a uwated fatalty taes place. But as descrbed the artcles etoed above by applyg specal routg polces the expected uber of fataltes ca be reduced. However, ths wll ofte lead to creased costs/creased uber of flyg hours. I 1,2,3,4 several dfferet routg polces are cosdered. Bascally all of the are varatos of classcal vehcle routg probles wth pcup ad delvery deads uder capacty restrctos o the helcopters. All helcopters start fro a HP servg a subset of the offshore stallatos ad retur to the HP wth the people that have bee pced up fro the stallatos. I ay cases the helcopters perfor a flght fro the HP to a sgle custoer, delver whatever uber of people ad pcs up those who are gog bac. I other cases the routes ca be sall cycles vstg two to three stallatos before returg to the HP. All the stallatos such routes are usually vsted exactly oce, that s, the pc-up ad delvery servces are perfored sultaeously. I soe cases a stallatos ay be vsted twce. I such a case the out-boud passegers are delvered o the frst vst ad the hoe-boud passegers are pced up o the secod vst. I the preset paper we wll cosder soe dfferet optos. The frst opto s to perfor the requred servce a hub ad spoe fasho fro the HP. That s, each ad every stallato (custoer ode) s served exclusvely by a helcopter. Ths soluto ca be very expesve ad te cosug, but t s proved 1,2,3,4 that ths soluto outperfors ay other routg polces treated the tradtoal VRPPD way, whether the servce s sultaeously or o-sultaeously perfored gve that the obectve s to ze the expected uber of fataltes. The ew ad dfferet approach s to select oe or ore of the offshore stallatos as hubs. The out-boud passegers are tae fro the HP to oe of these offshore hubs ad the brought to ther fal destatos fro ths hub by exclusve flghts to each of the spoe odes that are assged to the chose offshore hub. The hoe-boud passegers are brought bac to the offshore hub ad wll wat there utl all the spoe odes are vsted. The fally all the hoe-boud passegers wll be brought bac together to the HP. The rest of ths paper s orgazed as follows: I secto 2 usg the HP as a hub s copared to a stuato where a sgle stallato s chose as a offshore hub. I secto 3, two or ore offshore stallatos are chose as a hub ad a atheatcal odel s offered to decde whch odes to select as hubs ad how to assg the reag odes to the hubs. 2. Two dfferet sgle hub ad spoe solutos t s show that usg a sgle helcopter perforg the servces a hub ad spoe fasho outperforace the results copared to a Haltoa cycle. I the preset paper we wll copare two hub ad spoe stuatos. The frst wll be the stuato where the HP s used as the hub, that s, all the stallatos wll be served drectly fro the HP. I the secod stuato oe of the stallatos wll be chose as a hub. All passegers wll be brought fro the HP to ths stallato ad fro ths ode be brought by sgle flghts to ther fal destatos where the pc-up passegers are collected ad brought bac to the hub. Whe all stallatos have bee vsted, all the pc-up passegers wll be brought bac to the HP wth the helcopter, see Fg. 1 below. The rectagle sybolzes the HP ad the crcles the custoer odes/ stallatos. Notato: We wll deote the odes by = 0,1,2,., where 0 deotes the HP ad the other are the custoers odes. Each ode has a certa delvery dead d, ad a certa pc up dead p, such that d p 0. We wll assue that each of the odes that are ot a hub wll be vsted oly oce, hece, for custoer odes ot chose to be a hub, the servce wll be sultaeous. We wll let d D ad p P 1. Further, we let Q deote the 1 capacty of the helcopter ad assue that D Q ad P Q. I 1,2,3,4

3 1126 Øyvd Halsau / Proceda Coputer Scece 31 ( 2014 ) Fg. 1. (a) frst pcture; (b) secod pcture. Two sgle hub solutos. As etoed the troducto, choosg dfferet routgs for the helcopter(s) ca oly fluece the expected uber of fataltes, ot the probabltes that soe accdet happes due to bad weather, staes ade by the plots or probles based o soe techology brea dow. Utl further otce, we wll ot cosder the probabltes for fatal accdets ether durg crusg te or durg ladgs or tae offs. These probabltes wll be dfferet. It ay eve happe that there are dfferet probabltes for ladg ad tae offs o dfferet stallatos due to the space o the platfor dec ad other equpet close to the helcopter dec. There wll also be dfferet probabltes cocerg the stallatos ad the lad based HP. Hece, there wll be oly three cocepts that wll be of terest. Let C=[ c ] ( 1) x( 1) the cost atrx of travellg fro ode to ode ad c 0,, 0,1,2...,.The costs ca be gve as a dstace, a certa aout of oey or te, but order to avod cofuso we wll terpret these costs as dstaces. Further, we let C \ 0 ) c 1 C) c, 0 R (, that s the row sus the cost atrx C, ad R (, whch s the row sus for the atrx C restrcted to the custoer odes. Costs C HP 2R 0 s the cost of usg helcopter(s) whe the servces are perfored fro the HP a hub ad spoe fasho (fg.1a) C* 2c0, * 2R* ( C \ 0 ) 2R* s the cost of usg helcopter(s) whe the servces are perfored fro stallato *, brgg all out-bod passegers fro the HP to stallato *, * actg as a hub for the other stallatos, collectg all the pc-up deads here before brgg the bac to the HP va the hub (Fg.1b). Nuber of passegers tag part ladgs ad tae offs. d p D P PLHP s the uber of passegers tag part ladgs whe the HP s used as a hub. 1 PL* ( D P) ( D P) ( d* p* ) 2( D P) ( d* p* ) s the uber of passegers tag part ladgs whe stallato * s used as a hub. Nuber of passegers o board the helcopter ultpled wth the flyg dstace they stay o board.

4 Øyvd Halsau / Proceda Coputer Scece 31 ( 2014 ) PC HP 1 whe the HP s used as a hub. PC c0 d p s the uber of passegers ultpled wth the flyg dstace they stay o board d p ( D P c c s the uber of passegers ultpled wth the flyg te they stay o * ) 0, * 1 *, board whe stallato * s used as a hub. Note that the two last deftos ca be terpreted as trasportato wor, perfored by the helcopter ad wll be referred to as trasportato wor below. Fro the forulas above the followg expressos are straghtforward, startg wth the stuato that the HP s the hub. Iequalty (1) gves sple upper ad lower bouds o the trasportato wor perfored by the helcopter: d p R 0 PCHP axd p R 0 (1) Cobg (1) wth the cost/dstaces travelled fro the HP, we get the followg equaltes: 1 2 PC HP 1 d p axd p (2) C 2 HP gvg upper ad lower bouds for the fracto of the trasportato wor relatve to the fled dstace. Fro the forula for trasportato wor fro the HP we ca obta the equaltes (3) c D P PC axc D P 0 0 HP (3) whch cobato wth the forula for the passeger ladgs fro HP ca be trasfored to PC HP c c (4) 0 ax PLHP 0 Iequalty (4) gves a upper ad lower boud for the fracto of the trasportato wor relatve to the uber of passegers tag part ladgs ad tae-offs. If the offshore odes are farly equdstat fro the HP, the upper ad lower boud wll be close to each other. The forula for the trasportato wor for a offshore hub ca easly be reforulated to (5), gvg upper ad lower bouds for the trasportato wor perfored fro the chose hub * to the other stallatos. d p R ( C \ 0 ) PC ( D P) c axd p R ( \ ) 0 ( D P) c0, * * * 0, * * C (5) Further, equalty (5) shows that f oe wats to have as sall upper boud as possble, the hub should be chose such that the su of the dstaces fro the hub to the other offshore stallatos should be as sall as possble. A reasoable terpretato of ths wll be to choose the hub aog the stallatos located the ddle of all the offshore stallatos. O the other had, ths upper boud wll crease f the chose hub s far fro the HP. Lea 1 If oe chooses a custoer ode as a hub, the uber of passeger ladgs wll be zed by choosg a ode

5 1128 Øyvd Halsau / Proceda Coputer Scece 31 ( 2014 ) such that d p d p ax. Proof: The result follows drectly fro the forula of passeger ladgs whe usg a offshore ode as a hub. Hece, t s straght forward to fd the best offshore hub f we restrct ourselves oly to loo at the uber of passeger ladgs. Above we have looed at the two stuatos HP as a hub ad a offshore stallato as a hub separately. Below two leas are gve sayg soethg about the relatoshp betwee the two choces. Lea 2 If the tragle equalty holds for the cost atrx C, the followg equalty holds for ay choce as a hub aog the custoer odes: PC PC HP ad PL PLHP. Proof: Regardg the frst equalty we have: PC ( D P) c d p c, d p c 0. d p d p c 0 c d p c0 PC HP. 1 0, The secod equalty follows edately by coparg the uber of passeger ladgs for the two stuatos. Hece, as a cosequece, choosg the HP as a hub wll always outperfor choosg a custoer ode as a hub ters of uber of passeger ladgs ad trasportato wor. Above we have dscussed two of three cocepts, aely the uber of passeger ladgs ad the trasportato wor. The thrd cocept s the dstace the helcopter has to fly or the te t has to be the ar. Coparg the flght hours whe the HP s used as a hub wth the flght hours used whe a custoer ode s used as a hub s dffcult ad wll rely heavly o how the custoer odes ad the HP s located relatvely to each other. I offshore ol ad gas actvty the HP s ofte located close to the coast wth all the stallatos out the sea - broadly speag the sae drecto. Hece, ths case the flght hours eeded to serve the stallatos usg the HP as hub ofte wll lead to a large uber of flyg hours ad uch bgger tha f soe cetrally located stallato s used as a hub. Actually the ode wth the sallest row su the cost atrx C wll be the optal locato for the hub f oe wats to ze the uber of flyg hours. Ths wll ot ecessarly be the HP but could ofte be a stallato out the sea. Hece, whe t coes to costs t ay be beefcal to operate wth a hub that s ot the HP. Further, t ay happe that soe of the stallatos are located so far fro the HP that t could be dffcult to reach the drectly fro the HP wthout refuelg the helcopter. It ay also be coveet to have a offshore hub for a perso gog fro oe stallato to aother va ths hub, stead of havg to retur to the HP to be brought out to the secod stallato fro the HP. Algorth for fdg the best offshore hub sgle hub case. Let L ad C be the probabltes for a fatal accdet durg ladgs/tae offs ad crusg, respectvely. We wat to ze the followg obectve, the total probablty (TP) of havg a fatal accdet, TP. TP LPL C PC L 2 D P d p C ( D P) c0, d p c, (6) 1 Sce we have offshore stallatos, we ca calculate (6) for each of the ad choose the oe wth the sallest probablty. Hece, the algorth s polyoal wth coplexty. The optal soluto wll of course deped partly 1 c

6 Øyvd Halsau / Proceda Coputer Scece 31 ( 2014 ) o the dead patter. As a cosequece the offshore hub ca chage for oe te horzo to the ext. It ay also happe that soe of the offshore stallatos are ot suted as a hub due to dfferet reasos le specal actvtes gog o ag hdraces for frequet ladg ad tae offs, that the uber of people o board the platfor s too bg copared to the capacty of the lfe boats or that a platfor does ot have equpet for re-fuelg the helcopter. Of course such platfors have to be excluded fro the calculatos above, eve f they otherwse are good caddates for a teporarly hub. A sgle helcopter perforg all the vsts ay ru out of te durg the gve te horzo. If ths s the case we eed two or ore helcopters to perfor the servces. Ths stuato wll be treated the ext secto. 3. Multple helcopters ad ultple hubs aog the custoer odes I ths secto we wll assue that we have two or ore helcopters perforg the pc-up ad delvery servce. We wll assue that the servce s perfored sultaeously, that s, every ode s vsted oe ad oly oe te by a helcopter except the chose hubs whch of course have to be vsted several tes. There wll be three bascally dfferet stuatos: 1. All the helcopters use the HP as a hub, vstg dsuctve sub-sets of the custoers. 2. Each helcopter has dfferet offshore stallato as ts hub, startg fro the HP wth the delvery deads that belog to ther specfc dsuctve sub-sets of the custoers a hub ad spoe fasho ad brgg all the pc-up deads bac to the HP. 3. A subset of the helcopters s usg the HP as a hub ad the reag subset of the helcopters s usg specfc custoer odes as ther hubs. 3.1All the helcopters are usg the HP as a hub. I ths case the flyg dstace, the uber of passeger ladgs ad the trasportato wor wll be the sae as the sgle helcopter case. The flyg dstace or the te used to serve the offshore stallato ay becoe large, but usg the HP as a hub havg several helcopters wll stll outperfor case 2 ad 3 whe t coes to passeger ladgs ad trasportato wor. Usg ore tha oe helcopter oe tactly assues that there s soe restrcto o te (or dstace) that each helcopter ca use to perfor ts servce. If ths te restrcto s sall, the oe ay have to use helcopters, oe for each of the offshore stallatos. If t s soewhat bgger a helcopter ca serve ore tha oe stallato durg the gve te horzo. It wll be a separate proble to fd whch stallatos to cobe such that the uber of ecessary helcopters wll be zed. Usg several helcopters each choosg a custoer ode as a hub Assue that we have =1,2,, helcopters. Let be the custoer ode chose as the hub for helcopter uber. Let N be a subset of N \ 0 such that N Nl Ø, l ad N1 N2... N N \ 0. N deotes the custoer odes that s served by helcopter, startg fro the HP wth all the passegers that are gog to the odes N, the usg ode as a hub brgg all the delvery deads fro to the other odes N ad brgg the pc-up deads bac to ad brgg all pc up deads bac to the HP. The dfferet cocepts for ths stuato are gve the expressos (7) (9) below. C 1 C 1 2 c 2 c (7) 0, 1 N, PL 1 D P PL ds ps d p 1 sn D P d p 2( D P) d p 1 1 N 1 (8)

7 1130 Øyvd Halsau / Proceda Coputer Scece 31 ( 2014 ) PC 1 sn 0, s s c, s (9) 1 sn s d p c d p s s Now, assug that oe wats two or ore offshore hubs, the followg two decsos have to be ade uder the restrcto of ot volatg the helcopters capactes: 1. Whch stallatos to choose as offshore hubs? 2. Whch stallatos should be assged to whch hub? We wll assue that the deads durg the te horzo are gve as D ad P, but are so bg that they caot be hadled by a sgle helcopter. Further, t s assued that the uber of helcopters s the sallest teger, such that, where Q s the capacty for a sgle helcopter, all helcopters are ufor. Lea 4 For a gve choce of offshore stallatos, the uber of passeger ladgs wll be depedet of the way the spoe odes are assged to the offshore hubs. Proof: Follows drectly by (8). A exact odel for decdg whch offshore stallato that should be chose as hubs, whe the uber of helcopters, that s the uber of offshore hubs, s gve. I addto to the otato already gve the followg otato wll be used: s a paraeter deotg the uber of helcopters. Varables: PL the uber of passeger ladgs PC the trasportato wor U 1 f ode s chose as a offshore hub ad 0 otherwse, = 1,2,, W 1f ode s served fro the offshore hub, ad 0 otherwse,, =1,2,, The odel ( LPL C PC) Subect to d p PL 2 ( D P) U (10) PC 1 1 c 1 0, d p W c d p W (11) U (12) W U,, 1,2,..., (13)

8 Øyvd Halsau / Proceda Coputer Scece 31 ( 2014 ) d W p W d U Q, 1,2,... pu Q, 1,2,... (14) (15) 1 1 d W d U D (16) 1 1 p W p U P The obectve zes the expected uber of fataltes depedg o the uber of passeger ladgs ad crusg dstace ultpled wth the uber of passeger o board. (10) ad (11) gve the uber of passeger ladgs ad trasportato wor, respectvely. Costrat (12) specfes the uber of helcopters. Costrat (13) says that f a offshore stallato s ot selected as a hub, o trasportato ca tae place fro ths hub to ay of the other offshore stallatos. Costrats (14) ad (15) esure that the capactes of the helcopters are ot volated, ether for the out-boud or the hoeboud deads, respectvely. Fally, Costrats (16) ad (17) esure that all the ecessary trasportato tae place, both for the out-boud ad the hoe boud traffc, respectvely. The above odel s a 0/1 progra. As the uber of stallatos creases, the uber of 0/1 varables wll also crease ad solvg the odel to optalty ay becoe dffcult or tae too log te, eve f the odel s treated as a tactcal or strategc tool. O the other had, the uber of stallatos assged or served fro a specfc HP, wll ay real lfe stuatos ot be very bg ad the odel ca be solved to optalty. If the odel s used o a day to day bass where the hubs ca be chaged fro oe day to the ext, te for solvg the odel ca be lted, ad a qucer way to fd feasble solutos ay be ecessary. It s the ecessary to rely o soe heurstcs to fd feasble solutos. But fdg ad dscussg such heurstcs are beyod the scope of ths paper. Refereces (17) 1. Qa F, Grbovsaa I, Halsau Ø. Helcopter routg the Norwega Offshore Ol Idustry: Icludg Safety Cocers for Passeger Trasport. Iteratoal Joural of Physcal Dstrbuto & Logstcs Maageet 2011; 41: Qa F, Grbovsaa I, Laporte G, Halsau sr. Ø. Passeger ad Plot Rs Mzato Offshore Helcopter Trasportato. Oega 2012; 40: Qa, F.: A ult-obectve Offshore Helcopter Routg Proble for Passeger Trasportato. Artcle 3 Passeger Rs Mzato Helcopter Trasportato for the Offshore Petroleu Idustry. PhD thess, Molde Uversty College; Qa F, Strusevch V, Grbovsaa I, Halsau Ø. Mzato of Passeger Taeoff ad Ladg Rs Offshore Helcopter Trasportato: Models, Approaches ad Aalyss. Artcle 4 Passeger Rs Mzato Helcopter Trasportato for the Offshore Petroleu Idustry. PhD Thess, Molde Uversty College; Subtted to Oega. 5. Grbovsaa I, Halsau Ø, Kovyalov M. Mzg taeoff ad ladg rss helcopter pcup ad delvery operatos. Subtted to Oega. 6. Meezes F, Porto O, Res ML, Moreo M, Pogg de Arago M, Uchoa E, Abeledo H, Carvalho do Nasceto N. Optzg helcopter trasport of ol rg crews at Petrobras. Iterface 2010; 40: Nasceto N, Maudara A, Jarvs S. Nghtte approaches to offshore stallatos Brazl: Safety shortcogs expereced by helcopter plots. Accdet aalyss ad Preveto 2012; 47: Avato trasport accdet statstcs, OGP report No March

9 1132 Øyvd Halsau / Proceda Coputer Scece 31 ( 2014 ) Key helcopter statstcs. Helcopter Aual 2009;55: Helbe J, Schwalbe M, Neuhaus C, Wetsch WA, Gezwurer HV. Icdets, accdets ad fataltes 40 years of Gera helcopter eergecy edcal syste operatos. Europea Joural of Aesthesology 2011; 28(11): Safety statstcs. Helcopter Assocato Iteratoal safetystatsstcs.aspx. 12. Statstcal suary, Avato Occurreces Trasportato Safety board of Caada. eg/stats/avato/2010/ss10.pdf.