SHIPPING ECONOMIC ANALYSIS FOR ULTRA LARGE CONTAINERSHIP

Transcription

1 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 SHIPPING ECONOMIC ANALYSIS FOR ULTRA LARGE CONTAINERSHIP Chaug-Ing HSU Professor Deparen of Transporaon Technology and Manageen Naonal Chao Tung Unversy 1001 Ta Hsueh Road, Hsnchu 300, Tawan, R.O.C Fax: E-al: Yu-Png HSIEH Ph.D. Canddae Deparen of Transporaon Technology and Manageen Naonal Chao Tung Unversy 1001 Ta Hsueh Road, Hsnchu 300, Tawan, R.O.C Fax: E-al: Absrac: Ulra large shps have he advanage of scale econoes, bu wheher hey successfully geng no servce depend on cargo flow, shppng dsance, por effcency and consrans, ec. The sudy consrucs a wo-obecve odel o deerne he opal shp sze and salngs frequency and analyze he shppng econoes of ulra large shps by nzng shppng coss and nvenory coss. The resuls show he Pareo opal soluons of he wo-obecve odel and opal shp sze and salngs frequency wh respec o each level of nvenory coss and shppng coss. The sensvy analyss shows he opal shp ends o be large as roue flow ncreases. Furherore, he econoes and possbly of usng ulra large shps end o ncrease, as por effcency proves, shppng dsance ncreases, he pors of call decreases, or he relave coss of large shps decrease. Key Words: ulra large conanershp, shppng econocs, ul-obecve analyss 1. INTRODUCTION The sze of conanershp ends o be large as world rade expands and cargo raffc grows. The developen srdes of conanershp sze beng large are grea, especally afer The larges shp n he world s 4,400 TEU n 1991, 6,000 TEU n 1996, and 7,500 TEU n The 8,000 TEU shp of OOCL (Oren Overseas Conaner Lne currenly rewres he record, and he shp s he larges shp aong exsng shps used. Moreover, large shps of 9,000+ TEU wll be brough no Asa-Europe and Transpacfc servces soon n he near fuure, and ulra large shps of 12,500+ TEU are also expeced o delver n fve o en years (Frankel, However, wheher hose large shps wll provde servces as well as expecaon depend no only shpbuldng echnology and por accoodaon consrans are overcoe bu also hose large shps us be ore econoc han exsng shps used on curren aor roues. Alhough ulra large shps have he advanage of scale econoes, ha s, he average conaner cos decreases as shp sze ncreases, works only f cargo flow s large enough and salngs frequency s adequae for shppers. Tha s why, n realy, ocean carrers always allance wh each oher or provde her servces usng hub-and-spoke neworks o realze scale econoes. Besdes, key facors such as shppng dsance, por effcency, and he nuber of pors of call also nfluence he exen of scale econoes. Therefore, hs sudy akes hose facors no accoun and consrucs a odel o analyze he shppng econoes of ulra large shps and deerne he nu flows ha realze scale econoes. Prevous sudes on shp sze or ulra large shps were focused largely on econoes of shp 936

2 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 sze. These sudes ndcae ha econoes of shp sze occur a sea, whle dseconoes of shp sze are suffered n por, and ha he choce of opal shp sze nvolves a balancng of he cos per on a sea and he cos per on n por (e.g., Jansson and Shneerson, Recenly, Cullnane and Khanna (1999,2000 ndcae ha he dseconoes of shp sze n por are no apparen and he opal shp sze ends o be large as a resul of provng por producvy. Moreover, McLellan (1997 provded deal dscussons abou he effecs of larger shps on pors. L (1998 dscussed ha shps beng large would pac all shppng ndusry. And Robnson (1998 forecased he shppng servce poson of ulra large shps based on he rend of shppng developen. Dfferng fro prevous sudes, he sudy consders ha ocean carrers no only as a lowerng her shppng coss bu also enhancng her servces, hereby aracng ore shppers. The sudy as o consruc a wo-obecve odel by ndvdually nzng shppng coss and nvenory coss for decson-akng on he opal shp sze and salngs frequency and analyzng he shppng econoes of ulra large shps. The nvenory coss resuled fro he shppng process along he shppng roue and pors usually are he an consderaons of shppers. Invenory cos s coonly regarded as a aor facor affecng shppng servce decson n logscs leraure. These sudes usually deerned he opal shppng frequency by nzng oal shppng and nvenory coss (e.g., Daganzo, 1991; Hall, 1987; ec.. In are sudy, Jansson and Shneerson (1987 also proposed an econoc odel o analyze shppng servce decson by nzng oal shppng and nvenory coss. However, n realy, alhough conaner carrers consder nvenory cos as a decson facor, he wegh placed on nvenory cos s usually no equal o ha on shppng cos. Therefore, he odel proposed heren regards nzng shppng coss and nzng nvenory coss as wo separae obecves. The opal roung, shp sze and salngs frequency wh respec o each level of nvenory cos and shppng cos can be deerned usng he proposed odel. In addon, he proposed wo-obecve odel no only provdes flexbly for conaner carrers n shp sze and salngs frequency decson-akng, bu also provdes a ool o analyze he rade-off beween shppng cos and nvenory cos. Furherore, a sngle-obecve decson could be regard as a specal case of he wo-obecve decson. The reander of hs sudy s organzed as follows. In Secon 2, shppng and nvenory cos funcons are forulaed for a ul-por callng roue. Shppng coss nclude ocean carrers capal and operang cos, fuel cos, and por charge on servng he roue, whle nvenory coss nclude coss due o fregh wang o be shpped n a loadng por and on a shp along he shppng roue. Secon 3 derves a relaonshp equaon for explorng rade-off beween shppng coss and nvenory coss for usng dfferen szes of shps. Based on hs, all feasble soluons and Pareo opal soluons for he wo-obecve odel are deerned, and he opal shp sze and salngs frequency can also be obaned, sulaneously. In Secon 4, a case sudy regardng a ranspacfc conaner servce s ade o analyze shppng econoes for ulra large shps. Shp and por coss relaed o he ranspacfc conaner servce are colleced o consruc cos funcons and ake he opal shp sze decson based on he forulaed odel. Moreover, he nu roue flows ha realze scale econoes for usng ulra large shps on dfferen roues are esaed. And he effecs of key paraeers on he decsons of usng ulra large shps are furher analyzed. Concludng rearks are fnally ade n Secon

3 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , COST FUNCTIONS Consder a ul-por callng roue,, callng a n pors, where n N. The roue sars fro por 1, follows by por 2, por 3 and por n, and hen reurns back o por 1. The pors of call on he roue ay be dfferen or soe of he are roued agan on he reurnng roue as shown by Fgure 1(a and Fgure 1(b, respecvely. On he roue, ocean carrer operaes f salngs frequency per season usng shp ype. In hs sudy, shps are full conaner shps, conaners are dry cargo conaners, and he un of conaners s TEU,.e. weny-foo equvalen un , n 3 1 n 1 n -1 (a (b Fgure 1. Shppng Roues: (a All Pors of Call are Dfferen; (b Soe of Pors are Repeaed Suppose flow fro one por o anoher por on he roue s gven. Le denoe flow fro por o por on roue per season, where, =1,2 n and =0 for =. Then he loadng and unloadng volues n any por per round voyage are respecvely. 2.1 Shppng Cos Funcon Shppng coss can be dvded no hree an caegores: capal and operang coss, fuel cos and por charge. Capal and operang coss represen he oal expenses pad for usng he shp each day, ncludng he cos of ownng he shp, crew wages and eals, shp repar and anenance, nsurances, aerel and supples, and so on. Capal and operang coss ncrease wh shp sze, operang e and salngs frequency. The oal shppng e per round voyage for a shp ncludes lne-haul e a sea and dwellng e n por. The por dwellng e nclude cargo loadng and unloadng e and e a shp spendng on arrval and deparure process a pors. The cargo loadng and unloadng e can be esaed by conaner loadng/unloadng volue and he handlng rae. Le R denoe average gross handlng rae, TEU per day, n por, hen he cargo loadng and 1 unloadng e n any por s ( +. The por arrval and deparure process f R e ncludes e a shp ovng no or ou fro he por and e a shp wang for enerng or leavng a por. The lengh of he e can be esaed by he average shp wang e and he average shp salng e n a por. Le W denoe por arrval and deparure process e n any por, and he un of e s day. Then, e a shp spendng n any por s 1 W + ( +. Moreover, he oal e ha a shp spends on all pors per round f R voyage s he su of he dwellng e of n pors,.e. + W + 1. f R 1 f and 1 f, 938

4 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 Le D denoe shppng dsance beween any consecuve por and por +1 on roue, and V denoe average servce speed for shp ype. Then, shppng e a sea per round 1 voyage s D, and he oal shppng e per round voyage s he su of e spen n V D + all pors and a sea,.e. 1 ( W + +. Furherore, le S denoe V f R average daly capal and operang cos for shp ype. Then, he oal capal and operang cos for a season wh f salngs frequency s D + fs + + ( W S. (1 V R Fuel cos s he expense of fuel consupon by a shp salng a sea and dwellng n por. Fuel cos ncreases wh shp sze eher a sea or n por. Moreover, fuel cos a sea s proporonal o he shppng dsance, snce a shp norally cruses a consan speed a sea. Fuel cos n por s dfferen fro ha a sea, for a shp us decelerae or accelerae when enerng or leavng a por, whle also depends on he dsance a shp ovng n por. If he area of a por s larger, he relave ovng dsance ay be longer and he fuel cos n por s hgher. Therefore, fuel coss for he sae shp n varous pors are dfferen. Le F denoe fuel cos a sea per naucal le by shp ype, and B denoe fuel cos n por by shp ype. Then, he fuel cos per round voyage on roue by shp ype s ( F D + B, and he oal fuel cos for a season wh f salngs frequency s f ( F D + B. (2 Por charge s pad for a shp dwellng n por and can be dvded no charge on shp and sevedorng charge. The forer s pad for servcng he shp, ncludng ploage, owage, lne handlng fee, and berh occupancy charge, ec. The laer s pad for cargo handlng, ncludng conaner loadng and unloadng fee, equpen charge, and ren of conaner yard, ec. The level and srucure of por charge n varous pors are dfferen. In usual, he por charge of a shp depends on he gross onnage or capacy of a shp and also depends on berh occupancy e, so he por charge of a shp ncreases wh shp sze and berh occupancy e. However, ploage, owage, and lne handlng fee are ndependen of berh occupancy e, whle berh occupancy charge s proporonal o berh occupancy e. Le α denoe poron of he por charge of a shp ha s ndependen of berh occupancy e, and β denoe poron of he por charge of a shp ha s proporonal o berh occupancy e, where subscrp and ndcae por and shp ype, respecvely. Then, he oal por charge on he shp servng a roue for a season wh f salngs frequency s β f α + ( +. Le G R denoe average handlng fee per TEU n por. Then, he oal sevedorng charge for a season s + s he su of he oal por charge on shp and he oal sevedorng charge. G (. The oal por charge Tha s 939

5 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 f β α + + G ( +. (3 R Fro eqns. (1-(3, he oal shppng cos for a season wh f salngs frequency on roue usng shp ype, TC1, s he su of capal and operang coss, he fuel cos, and he por charge. Tha s S β S TC1 = f α SW + B + D + F G ( +. (4 V R R And average shppng cos per TEU, AC1, s he oal shppng cos, TC1, dvded by he oal flow on he roue,. Tha s S β S f α S W + B + D + F G ( + V R R AC1 =. (5 2.2 Invenory Cos Funcon Invenory coss represen opporuny cos or loss of value due o cargos canno be used or sold n he shppng process, and are posvely correlaed wh he cargo volue, he value of cargo, and he lengh of rans and sorage e. In hs sudy, only nvenory coss relaed o conaner shppng process are aken no accoun, nvolvng he wang e cos n he loadng por and he shppng e cos ha conaners are n-rans and shpped on a shp. However, he nvenory cos ha occurred n he unloadng por s no aken no accoun due o s no drecly relaed o he conanershp shppng servce and relavely sall. The wang e cos s he cos relaed o salngs frequency due o schedule delay eher conaner fregh wang n he loadng por or a he place of producon or orgn. The denser he salngs frequency s, he lower he wang cos s. Assue he arrval process of conaners a each loadng por follows a unfor dsrbuon, hen he average wang e per TEU n a loadng por s one half of he shppng e cycle. Le H denoe he daly value of e per TEU, and suppose one season approxaes o 13 weeks or 91 days, hen he oal wang e cos per season for conaners shpped along roue s 91H 2 f. (6 The shppng e cos s relaed o e whle conaners are shpped on a shp, and ncreases wh he shppng e. Le T denoe he shppng e of conaners fro por o por on roue. I ncludes e ha a shp spends on roung hrough all lnks and pors on he pah fro por o por. Snce e ha conaners spend n unloadng pors s no easy o esae and s relavely sall as copared wh he oal shppng e. So e ha conaners spend n loadng and unloadng pors s approxaely esaed as e spen n loadng pors only, hen T s represened as D k 1 k k W k + + k V f k l R k = ( T kl + lk. (7 940

6 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 Where k s defned as 1, f pah fro por o conanes a lnk beween por k and k + 1; k = (8 0, oherwse. Then, he oal shppng e cos per season for conaners shpped on roue s equal o H (, and can be expressed furher by eqn (7 as: H T. (9 V f k l Rk D k H k + k Wk + ( + lk kl k Fro eqns. (6 and (9, he oal nvenory cos for a season for conaners shpped along roue by shp ype, TC2, can be expressed as he su of he oal wang e cos and he oal shppng e cos. Tha s: 91H D k H k TC2 = + H k Wk + + ( + lk.(10 2 f kl k V f k l Rk And average nvenory cos per TEU, AC2, s he oal nvenory cos, TC2, dvded by he oal flow on he roue,. Tha s D k k H k Wk + H ( kl + lk 91H k = + V k l Rk AC2 +. (11 2 f f 3. SHIP SIZE DECISION There s a rade-off beween average shppng cos and average nvenory cos as shown by eqns. (5 and (11, respecvely. Tha s, shppng conaners along a dense salngs frequency roue, he average nvenory cos s low and he average shppng cos s hgh, whle on a hn salngs frequency roue, he average shppng cos s low and he average nvenory cos s hgh. However, a coplee opal soluon does no exs when one obecve aed a nzng he average shppng cos whle he oher obecve aed a nzng he average nvenory cos due o wo obecves conflc wh each oher. Insead of a coplee opal soluon, he Pareo opaly concep s nroduced heren. The Pareo opaly s he soluon where no obecve can be reached whou sulaneously worsenng a leasng one of he reanng obecves. (Cohon, 1978 A rade-off equaon beween he average shppng cos and he average nvenory cos s derved fro eqns. (5 and (11. However, varables heren are splfed furher. Le 11, 21, and denoe he fxed coponens of average shppng cos and average nvenory 12, 22, cos for shp ype on roue, respecvely, and le and denoe he argnal shppng cos and nvenory cos for ncreasng one ore salngs frequency, respecvely. 11, 21, 12, 22, Then,,,, and can be expressed as: 941

7 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 β S G + + ( + R R 11 =, (12, D k H k Wk + k = V 21,, (13 S α + S W + B + D + F V 12 =, (14, k H ( + lk kl 22, 91H k l Rk = +. (15 2 And average shppng and nvenory cos funcons (eqns. (5 and (11 can be expressed as: 11, 12, AC1 = + f, (16 21, 22, ( 1 AC2 = + f. (17 Then, a rade-off equaon beween average shppng cos and average nvenory cos can be derved fro eqns. (16 and (17. Tha s 11, 21, 12, 22, AC1 AC2 =. (18 ( ( Eqn. (18 ndcaes clearly ha here exss a rade-off beween average shppng cos and average nvenory cos. When flow, shp relaed varables, and por relaed varables are hold consan, average shppng cos per TEU for any ype of shp decreases as average nvenory cos per TEU ncreases, and he subsue rae beween wo coss s decreasng. 11, 11, Average shppng cos per TEU s approachng o,.e. AC1, when average nvenory cos per TEU s approachng nfne,.e. AC2. Slarly, average nvenory cos per TEU also decreases as average shppng cos per TEU ncreases, and he 21, subsue rae s decreasng. And AC2 when AC1. Eqn. (18 s a hyperbolc funcon, an eleenary geoery as crcle, ellpse, or parabola. Hyperbolc funcon wh cener, verex, focus, focal lengh and asypoe can be shown exacly n wo-densonal space. Fgure 2 llusraes he hyperbolc funcon for any shp ype n obecve value space wh horzonal denson represenng average nvenory cos per TEU and vercal denson represenng average shppng cos per TEU, whle cener, verex, focal lengh, horzonal asypoe and vercal asypoe of he hyperbolc funcon 21, 11, 21, 12, 22, 11, 12, 22, 12, 22, 11, are (,, ( +, +, 2, AC1 = 0, 21, and AC2 = 0, respecvely. The hyperbolc funcon llusraes no only rade-off relaonshps beween average shppng cos and average nvenory cos, bu also soluons for he wo-obecve odel for any shp ype. However, snce cargo loaded on a shp canno exceed s capacy on any voyage lnk, salngs frequency for any shp ype us be larger han or equal o he axu lnk flow dvded by shp capacy, ha s 942

8 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 f Max k U k n. Moreover, le f denoe he nu salngs frequency, Max k k n f =, and le AC1 and AC 2 denoe he nu average U shppng cos and he axu average nvenory cos when a shp s operang wh he nu salngs frequency, respecvely. And naes he pon ( AC 2, AC1 n obecve value space he nu salngs frequency pon. Then he feasble soluons for he wo-obecve odel are locaed a he hyperbolc funcon curve, whch AC1 values are hgher han ha of he nu salngs frequency pon, ( AC 2, AC1, as shown n Fgure 2. AC1 asypoe ( AC2 21, = 0 cos rade-off curve 11, cener, (, 21, 21, 12, 22, 11, 12, 22, verex ( +, + Focus lengh ( AC2, AC1 2 12, 22, 21 11, asypoe ( AC1 11, = 0 AC2 Fgure 2. Feasble Soluons for Any Shp Type The Pareo opal soluons are he feasble soluons n he case ha here s only one ype of shp. Snce shp-relaed varables, such as por charges, α and β, and average daly capal and operang cos, S, and fuel coss, F and B, and servce speed, V, all change wh shp ype, herefore he hyperbola curve and he nu salngs frequency pon for each ype of shp s dfferen. Consequenly, Pareo opal soluons are locaed along he envelope of dfferen curves, whch are he closes soluons o orgn (0,0 aong all feasble soluons for all ypes of shps. 4. SHIPPING ECONOMIC ANALYSIS A Transpacfc Norhwes Servce (TPN servce, on whch ulra large shps are possbly appled, s consdered heren o deonsrae decson-akng on he opal shp sze and salngs frequency and analyzng shppng econocs for ulra large shps. The roue of he TPN servce sars a Kaohsung, passes Hong Kong, Osaka, Tacoa, Vancouver, and backs o Kaohsung. I calls a 5 pors n oal and oal dsance per round voyage s 11,945 naucal les, as shown n Fgure 3. There are 5,652 TEU conanershps currenly used o provde shppng servces on he roue. 943

9 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 Osaka 4,557 Vancouver 154 1,376 5,516 Tacoa Hong Kong 342 Kaohsung Source of shppng dsance: Caney and Reynolds (1995. Fgure 3. The TPN Servce (nubers represen lnk dsance n naucal les The sudy consders four ypes of large/ulra large shps, ncludng 5,652 TEU shps whch are currenly used on he TPN roue, 7,500 TEU shps whch are alos he larges shps aong exsng shps used, 9,000 TEU shps whch wll be brough no servce soon, and fuure 12,500 TEU ulra large shps. Table 1 shows capacy, gross onnage, draf, servce speed, daly capal and operang coss, fuel cos per naucal le, and fuel cos n por for each ype of shp. Table 2 shows fxed and varable por charges, and average cargo handlng fee per TEU for each ype of shp. In addon, Table 3 shows cargo flows beween any wo pors of call. Snce ocean carrers ake shp sze decson ay no ake he cargo flow nsde one regon no consderaon, herefore he sudy assues cargo flows beween any wo pors nsde eher Far Eas regon or U.S. Wes Coas are zero for he TPN roue and consders erely cargo flows beween Far Eas and U.S. wes coas. Cargo flows are esaed by he conaner loadng and unloadng volues of he TPN roue n por of Kaohsung a he second season n 2001 and Conanersaon Inernaonal Yearbook 2002 (2003. Besdes, he average gross handlng rae, R, and por arrval and deparure es, W, are 1,680 TEU per day and day, respecvely, whch are esaed fro relaed daa of Kaohsung. Table 1. Capacy, Gross Tonnage, Draf, Servce Speed, Daly Capal and Operang Cos, Fuel Cos per Naucal Mle, and Fuel Cos n Por for Each Type of Shp Types of shps T1 T2 T3 T4 Capacy, U (TEU 5,652 7,500 9,000 12,500 Gross onnage (G.T. 69,245 94, , ,000 Draf ( Servce speed, V (naucal les per day Daly capal and operang cos, S (US$ 25,813 27,675 29,187 32,715 Fuel cos per naucal le, F (US$ Fuel cos n por, B (US$ Noe: Daly capal and operang cos and fuel coss are esaed by daa n Wang (1998. Table 2. Fxed and Varable Por Charges and Average Cargo Handlng Fee per TEU for Each Type of Shp Types of shps T1 T2 T3 T4 Fxed por charge,α 4,241 5,827 7,177 10,820 Varable por charge,β 4,302 5,455 6,545 9,091 Average cargo handlng fee per TEU, G Noe: Suppose values of α, β and G are dencal n all pors of call and esaed by he por charge of Kaohsung Harbor (Kaohsung Harbor Bureau,

10 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 Table 3. Cargo Flows beween Any Two Pors (TEU Orgn\Desnaon Kaohsung Hong Kong Osaka Tacoa Vancouver Kaohsung ,663 8,166 Hong Kong ,553 19,904 Osaka 0 0-1,918 1,621 Tacoa 6,026 14,689 1,196-0 Vancouver 5,093 12,413 1, The Opal Shp Sze The sudy furher apples he odels n Secons 2 and 3 o deerne he rade-off equaon, nu salngs frequency, nu shppng cos per TEU, and axu nvenory cos per TEU for each ype of shp on servng he TPN roue. The resuls are shown n Table 4, and he feasble soluons are llusraed n Fgure 4. Table 4 shows ha larger shps have he hgher advanage of shp sze econoes on servng he TPN roue and he nu shppng cos per TEU decreases as shp sze ncreases. Ocean carrers gh provde servces wh he nu salngs frequency o reduce her shppng coss and oban he advanage of shp sze econoes f hey gnore he nvenory cos and salngs frequency consrans. However, he nu salngs frequency for shp ypes T4, T3, and T2 are 5.186, 7.203, and per season for curren deand flow, respecvely, and hose servce frequences are lower han he weekly servce,.e. 13 per season. However, an ocean carrer ha provdes such levels of servces usng large shps gh no copee wh oher ocean carrers usng curren shp sze and salng frequency. In Fgure 4, four curves represenng shp ypes fro T1 o T4 are shown fro lef o rgh, and he shapes of curves are hyperbolc funcons as derved n Secon 3. The curve of shp ype T1 s he one closes o orgn (0,0, and hen shp ype T2, shp ype T3, and shp ype T4. I shows ha he shppng cos for shp ype T1 s he lowes one for he sae nvenory cos level aong all shp ypes. Table 4. Trade-Off Equaon, Mnu Salngs Frequency, Mnu Shppng Cos per TEU, and Maxu Invenory Cos per TEU for Each Type of Shp for he TPN Roue Mnu Mnu Maxu Shp salngs Trade-off equaon shppng cos nvenory cos ype frequency (US$/TEU (US$/TEU per season T1 (AC (AC = T2 (AC (AC = T3 (AC (AC = T4 (AC (AC = Pareo opal soluons n an obecve value space are he envelope of he feasble soluon curves, whch are closes o orgn (0,0 and deerned by coparng he feasble soluons beween all ypes of shps. As a resul, he Pareo opal soluons for he TPN roue are ade up of all feasble soluons of shp ype T1 and par of feasble soluons of shp ypes T2, T3 and T4, as shown by sold lnes of Fgure 5. Fgure 5 shows ha he opal shp szes of he TPN roue are T4, T3, T2 and T1, for four dfferen values of average nvenory cos per TEU,.e. whou consran, lower han U.S. dollars, lower han U.S. dollars, and lower han U.S. dollars, respecvely. 945

11 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 Fgure 4. Feasble Soluons for Four Types of Shps for he TPN Roue Fgure 5. Pareo Opal Soluons and Praccal Soluons for he TPN Roue Moreover, consder, n realy, ha salngs frequency for he lner servce generally s weekly and salngs frequency less han fornghly are coonly regarded as nadequae. The sudy deernes he opal shp sze and salngs frequency ha could be possbly chosen by ocean carrers n realy. Those praccal resuls are shown n Table 5 and depced by he dscree pons n Fgure 5. I s shown ha he 5,652 TEU shps of shp ype T1 are opal-sze shps when ocean carrers would lke o provde servce frequency equal o or hgher han he weekly salngs servce. And ocean carrers ay use he 7,500 TEU shps of shp ype T2, f hey prefer provdng 3 salngs frequency per onh. Weekly salngs frequency Table 5. Praccal Shppng Servces for he TPN Roue (US$/TEU Weekly Opal Shppng Invenory Opal Shppng salngs shp ype cos cos shp ype cos frequency Invenory cos 0.5 Infeasble T T T T T T T T T In suary, he Pareo opal soluons, he praccal soluons n realy, and he opal shp sze wh respec o each level of shppng coss and nvenory coss for he TPN roue usng four ypes of shps can be deerned by applyng he odel. If oher ypes of shps are aken no consderaon or oher roues are analyzed, he opal soluons can also be obaned. For nsance, f one ype of shp wh he sae servce speed bu wh capacy less han 5,652 TEU s consdered, s rade-off curve us be locaed on he lef hand sde of he curve of he 5,652 TEU shp. Then he Pareo opal soluons us conan he curve of he saller shp. However, wheher conaner carrers use he saller shp or no wll depend on he salngs frequency n realy or he shppng and nvenory coss. 4.2 Cargo Flow Effecs As shown above, alhough he bgger shps,.e. he 9,000 or 12,500 TEU shps, have ore advanage of shp sze econoes, he saller shps,.e. he 5,652 or 7,500 TEU shps, have ore copeve advanage. However, opal shp sze endng o be larger s assued as cargo flows ncrease wh he world rade expands. And can be shown by furher usng he 946

12 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 proposed odel o deerne he crcal flow when he 9,000 or 12,500 TEU shps are used. Frs, he nfluences of roue flows on he opal soluons are analyzed. Le denoe roue flow, and suppose he share of cargo flow beween wo pors s consan. Then, he sudy furher analyzes varaons n he rade-off equaon, he nu shppng cos per TEU, and he axu nvenory cos per TEU due o changes n roue flows and suarzes he resuls n Table 6. Table 6 shows ha as roue flow ncreases, he cener pon and asypoes of he rade-off equaon do no change bu he focal lengh decreases; as a resul, he curve oves oward he cener pon. Moreover, he nu shppng cos per TEU s ndependen of roue flow, and he axu nvenory cos per TEU decreases as roue flow ncreases. Consequenly, he nu salngs frequency pon ( AC2, AC1 s shfed o he lef. The resul of he nu shppng cos per TEU for each ype of shp beng ndependen of roue flow ples ha he relave econoes of dfferen shp szes do no change as roue flow vares. Fgure 6 furher llusraes an exaple regardng a 5,652 TEU shp,.e. shp ype T1. Table 6. Varaons n he Trade-Off Equaon, he Mnu Shppng Cos per TEU, and he Maxu Invenory Cos per TEU as Roue Flow Changes Mnu Maxu Shp Trade-off equaon shppng cos nvenory cos ype (US$/TEU (US$/TEU * *10 T1 ( AC ( AC = 16, * *10 T2 ( AC ( AC = 18, * *10 T3 ( AC ( AC = 20, * *10 T4 ( AC ( AC = 25, Fgure 6. Varaons n Trade-Off Equaon for Shp Type T1 as Roue Flow Changes Fgure 7. Opal Shp Sze wh Respec o Invenory Cos and Roue Flow Moreover, he opal shp sze of he TPN roue wh respec o roue flow and nvenory cos per TEU can be deerned usng he rade-off equaon and he nu salngs frequency pon for each ype of shp, as shown n Fgure 7. When boh he nvenory cos per TEU 947

13 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 and roue flow are low, he opal shp sze s shp ype T1; when eher nvenory cos per TEU or roue flow ncreases, he opal shp sze ends o becoe large and changes fro shp ype T1 o T2, T3 or T4. Besdes, f weekly servce s provded on he roue, he opal shp szes are T1, T2, T3 and T4, for four cases ha he roue flow less han 143,272 TEU; fro 143,272 TEU o 182,385 TEU; fro 182,385 TEU o 257,883 TEU; and larger han 257,883 TEU, respecvely. Therefore, he roue flow beng an poran facor for shp sze decson-akng s clearly shown, and he opal shp sze ends o becoe large as he roue flow ncreases. In realy, f ocean carrers ncrease roue flows by allance wh ohers or usng hub-and-spoke neworks, he average shppng cos wll be lower. As a resul, he opal shp sze wll becoe larger, and he ulra large shp wll be brough no he servce sooner. 4.3 Sensvy Analyss In addon o ncreases n cargo flows, shpbuldng cos s assued o decrease when echnology s advanced, and por effcency s also assued o prove when faser loadng/unloadng equpen or new operang ehods are used n he fuure. These wo facors agan are key facors pushng conaner carrers o use ulra large shps. However, he proposed odel can show he effecs of changes n hese key facors on he carrers decsons on usng ulra large shps. Besdes, oher key facors such as shppng dsance, he nuber of pors of calls, and he cargo flow balance facor, are analyzed a he sae e. Table 7 shows he nu average shppng cos, AC1, for each ype of shp, he dfference n he nu average shppng cos beween any wo ypes of shps, and he nu roue flow for shp ypes T2, T3 and T4 when weekly servce are provded. Therefore, decsons-akngs on wheher usng ulra large shp are approprae or no can be ade by hese hree ndexes. Frs, he nfluence of he change n por effcency s evaluaed. The nu shppng coss for all ypes of shps decrease ye he dfference beween any wo consecuve ypes of shps expands as por effcency ncreases, n parcular, when he cargo handlng rae, R, s proved up o 140 TEU per hour and he por arrval and deparure process e, W, s decreased o 1 hour. Thus, shp sze econoes ncrease and he possbly of usng ulra large shp also ncreases when he relave advanages of larger shps becoe large. Moreover, hese are also shown by he rend ha he values of he nu roue flows for usng shp ypes T2, T3 and T4 for weekly servce are decreasng. On he oher hand, he nu shppng coss for all ypes of shps ncrease as por effcency decreases, n parcular, when he cargo handlng rae, R, s reduced o 35 TEU per hour and he por arrval and deparure process e, W, s ncreased o 6 hour. Therefore, he value of he nu shppng cos for shp ype T4 s larger han he value for shp ype T3, consequenly, neher shp ype T4 has he advanage of shp sze econoes, nor shp ype T4 s he opal shp sze for any roue flow. Second, he producon coss of ulra large shps wll be decreased as echnology advances, so he relave daly capal and operang coss of ulra large shps wll be decreased as well. Suppose he relaonshp beween he daly capal and operang coss and shp capacy s a logarh curve (e.g., Jansson and Shneerson, 1987, hen he daly capal and operang coss for four ypes of shps can be esaed as 25,042, 25,750, 26,186, and 26,973 U.S. dollars, respecvely. As a resul, as shp buldng echnology advances, he dfference beween any wo consecuve ypes of shps ncreases, and he nu shppng coss and roue flows for he weekly servces of all ypes of shps decrease. Therefore, shp sze econoes ncrease 948

14 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 and he possbly of usng ulra large shps also ncreases, due o he coparave advanage n he average shppng cos of larger shp s large. Table 7. Resuls of Sensvy Analyses (US$; TEU Mnu roue flow Mnu shppng cos, AC1 Scenares for weekly servce T1 T2 T3 T4 T2 T3 T , , ,883 Curren suaon (9.066 (3.325 (1.643 Por effcency ncreases , , ,035 (W=1hr.;R=140TEU/hr. ( (4.760 (5.098 (- (- (- Por effcency decreases , ,040 - (W =6hr.; R =35TEU/hr. (5.816 (0.398 ( (+ (+ Relave coss of , , larger shps decrease ( (5.577 (6.498 (- (- (- Nuber of pors of , , ,766 calls decreases (n=2 (8.911 (3.258 (1.623 (- (- (- Nuber of pors of , , ,062- calls ncreases (n=10 (9.325 (3.435 (1.677 (+ (+ (+ Shppng dsance , decreases (ΣD =5000 (1.859 ( ( (+ Shppng dsance , , ,674 ncreases (ΣD =15,000 ( (4.939 (3.904 (- (- (- Balance flow , ,614 - (Rao=50% (6.685 (2.116 ( (+ (+ Unbalance flow , , ,221 (Rao=70% ( (4.202 (2.855 (- (- (- Moreover, he nfluence of he change n he nuber of pors of calls s evaluaed. Resuls show ha as he nuber of pors of calls decreases, he nu average shppng coss for all ypes of shps ncreases slghly; he dfference beween any wo consecuve ypes of shps also ncreases slghly; and he nu roue flows for usng shp ypes T2, T3 and T4 all ncrease. However, snce he exen of he effec s relavely sall as copared wh hose of oher facors on shp sze econoes and he possbly of usng ulra large shps. Therefore, he nuber of pors of calls s no a sgnfcan pac facor. The sudy furher perfors wo sensvy analyses, n whch he oal shppng dsance s decreased down o 5,000 naucal les and ncreased up o 15,000 naucal les, respecvely. Resuls show ha as he oal shppng dsance ncreases, he nu shppng coss for all ypes of shps ncrease, he dfference beween any wo consecuve ypes of shps ncreases, and he nu roue flows for he weekly servces usng shp ype T2, T3 and T4 decrease. Consequenly, shp sze econoes and he possbly of usng ulra large shps ncrease as he oal shppng dsance ncreases. Addonally, he nu shppng coss for shp ypes T3 and T4 beng larger han ha for shp ype T2 ples ha hese wo ypes of shps do no have he advanage of shp sze econoes. Fnally, he nfluence of flow balance s furher analyzed. On he TPN roue, he flow fro Far Eas o U.S. Wes Coas s hgher han he reverse flow fro U.S. Wes Coas o Far Eas, and he share of one-drecon flow o oal roue flow s 61.59%. Suppose he oal roue 949

15 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 flow does no change, whle wo cases wh he shares of 50% and 70% are esed, respecvely. Resuls show ha as he roue flow s ore unbalanced, he nu shppng coss for all ypes of shps are larger and he dfferences beween any wo consecuve ypes of shps are larger as well whle he nu roue flows for weekly servce usng shp ypes T2, T3 and T4 are all saller. Consequenly, shp sze econoes and he possbly of usng ulra large shps all ncrease, as he roue flow s ore unbalanced. In suary, shppng econoes enhance and he possbly of usng ulra large shps end o ncrease as he por effcency ncreases, he shppng coss of larger shps decrease, he oal shppng dsance ncreases, he nuber of pors of calls decreases, or flow s unbalanced. In fac, he ulra large shps us be ore and ore econoc n he fuure as he cargo flow ncreases, shpbuldng cos decreases, and he por effcency proves. They are expeced o delver frsly n lnes wh he longes shppng dsance, such as he Asa-Europe servce or he Transpacfc servce. In addon, he nuber of pors of call wll only be a few. The nuercal resuls obaned usng he proposed odel are dencal o he udgen of expers. However, he sudy can asss conaner carrers n decson-akng by consderng all key facors coprehensvely. Also he resuls of he sudy can furher show conaner carrers how o fnd he opal ng of usng 9,000 TEU, 12,500 TEU, or oher larger shps and undersand deeply he effecs of shppng dsance, he pors of call, he relave coss of large shps, ec. 5. CONCLUSIONS Ths sudy develops a wo-obecve odel for decson-akng on he opal shp sze and salngs frequency by nzng shppng coss and nvenory coss. Shppng and nvenory cos funcons are forulaed for a ul-por callng roue. Shppng coss nclude ocean carrers capal and operang coss, fuel cos, and por charge on servng he roue, whle nvenory coss nclude coss due o fregh wang o be shpped n a loadng por and on a shp along he shppng roue. Besdes, he cos funcons forulaed heren are flow-dependen. Moreover, hs sudy derves a relaonshp equaon for explorng he rade-off beween shppng coss and nvenory coss for usng dfferen szes of shps and shows all feasble soluons of shp sze and salngs frequency. The relaonshp equaon s furher denfed as a hyperbolc funcon, whch could be shown n obecve value space. Accordngly, Pareo opal soluons of he wo-obecve odel are hen deerned, and he opal shp sze and salngs frequency wh respec o dfferen nvenory coss and shppng coss are shown. Then, a case sudy regardng he TPN roue s ade o analyze shppng econoes for ulra large shps. Feasble soluons for dfferen ypes of shps, Pareo opal soluons, and praccal soluons n realy are deerned. And he opal shp sze and salngs frequency wh respec o nvenory cos and roue flow are shown. The resuls show ha f he weekly servce s provded, he opal shp s he 5,652 TEU shp ha s he sae as he shp currenly beng used on he roue. Addonally, he opal shp ends o be large as roue flow ncreases. Fnally, he sensvy analyss shows ha shppng econoes enhance and he possbly of usng ulra large shps end o ncrease, as por effcency ncreases, he shppng coss of larger shps decrease, he oal shppng dsance ncreases, he nuber of pors of calls decreases, or he roue flow s unbalanced. The nuercal resuls can asss conaner carrers n decson-akng by consderng all key facors coprehensvely and furher o fnd he opal ng of usng ulra large shps. Furherore, because co-operaons or copeons beween conaner carrers ake cargo 950

16 Journal of he Easern Asa Socey for Transporaon Sudes, Vol. 6, pp , 2005 flows change, analyzng hese wo sraeges n he fuure sudy s suggesed. ACKNOWLEDGEMENTS The auhors would lke o hank he Naonal Scence Councl of he Republc of Chna for fnancally supporng hs research. REFERENCES Caney, R.W. and Reynolds, J. E. (1995 Reed s Marne Dsance Tables. Thoas Reed Publcaons, Prned n Grea Bran. Cohon, J.L. (1978 Mulobecve Prograng and Plannng. Acadec Press, New York. Conanersaon Inernaonal (2003 Conanersaon Inernaonal Yearbook Cullnane, K. and M. Khanna (1999 Econoes of scale n large conaner shps, Journal of Transpor Econocs and Polcy, Vol. 33, Par 2, Cullnane, K. and M. Khanna (2000 Econoes of scale n large conanershp: opal sze and geographcal, Journal of Transpor Geography, Vol. 8, Daganzo, C. F. (1991 Logscs Syse Analyss. Sprnger-Verlag Press, Berln, Hedelberg. Frankel, E.G. (2002 New generaon conaner ernal echnology, Por Technology Journal, Edon 15, Secon 1. Hall, R. W. (1987 Drec versus ernal fregh roung on a nework wh concave coss, Transporaon Research B, Vol. 21, No. 4, Jansson, J.O. and Shneerson, D. (1987 Lner Shppng Econocs. London: Chapan and Hall. Kaohsung Harbor Bureau, Mnsry of Transporaon and Councaons, ROC (2002 Por of Kaohsung: Tarff of Por Charges. Kaohsung Harbor Bureau Publcaons, Republc of Chna. L, S.M. (1998 Econoes of scale n conaner shppng, Mare Polcy and Manageen, Vol. 25, No. 4, McLellan, R.G. (1997 Bgger vessels: how bg s oo bg? Mare Polcy and Manageen, Vol. 24, No. 2, Robnson, R. (1998 Asan hub/feeder ne: he dynacs of resrucurng, Mare Polcy and Manageen, Vol. 25, No. 1, Wang, H.J. (1998 Conaner Transshpen Analyss for he Por of Kaohsung as a Transshpen Cener. Deparen of Shppng and Transporaon Manageen, Naonal Tawan Ocean Unversy, Maser Thess. (n Chnese 951