SLOT EXCHANGE AND PURCHASE PLANNING OF SHORT SEA SERVICES FOR LINER CARRIERS

Transcription

1 Jounal of Maine Science and Technology, Vol. 18, No. 5, pp (2010) 709 SLOT EXCHNGE ND PURCHSE PLNNING OF SHORT SE SERVICES FOR LINER CRRIERS Hua-n Lu*, Shu-Ling Chen**, and Pete Lai*** Key wods slot exchange, slot puchase, shot sea sevice, slot allocation. STRCT In a slot exchange co-opeation, paticipating caies see to benefit in which thei suplus of contolled capacities can be shaed to exchange slots belong to patnes fo thei shotages. To each paticipant, whethe the exchanged conditions can bing oe benefits is based on its slot allocation planning. This pape intoduces a pactical slot exchange contact fo ultiple shot sea loops between two co-opeative caies. Two intege pogaing odels fo axiizing the concened pofits ae poposed to satisfy the expected deand level and shipping popeties. One of the odels eely consides slot exchange as the pactical planning, and the othe one includes slot puchase additionally. Decision esults can assist the studied copany to pusue an optial allocation with consideation of exchanged slots fo the involved lines. Moeove, sensitivity analyses including fixed exchanged condition, swap allowance influence, and puchase pice assessent ae caied out fo easuing the ipact of elevant vaiables to the pofits. I. INTRODUCTION In contepoay line shipping industy, alliance coopeation has been a popula appoach adopted by caies fo extending sevice scopes and/o educing investent iss. Concete eans of collaboation lie joint fleet, slot chate, slot puchase, and slot exchange ae noally eployed in pactice. This eseach focuses on a eal-wold case of slot exchange aong shot sea sevices. Slot exchange allows paticipating caies to use the ecognized capacities of the Pape subitted 02/13/09; evised 07/09/09; accepted 09/28/09. utho fo coespondence Hua-n Lu (e-ail halu@ail.ntou.edu.tw). *Depatent of Shipping and Tanspotation Manageent, National Taiwan Ocean Univesity, #2, Pei-Ning Rd., Keelung 202, Taiwan, R.O.C. **Depatent of Maitie and Logistics Manageent, ustalian Maitie College Loced ag 1397Launceston, Tasania, 7250, ustalia. ***usiness Division-sia Sevice Depatent, Yang Ming Maine Tanspot Copoation, #271, Ming De 1 st Rd., Cidu, Keelung 206, Taiwan, R.O.C. involved lines not opeated by own self, accoding to the contents of the ageeent. In such co-opeation, paticipating caies expect to benefit in which thei suplus of contolled slots can be shaed to exchange capacities fo thei shotages. ccodingly, the exchanged condition ust have a fai and ecipocal calculation aong the involved lines between paticipants. If the nube of exchanged slots cannot satisfy a caie s estiated deand, exta available slots could be puchased fo its patne as long as the deal is accepted by all of the. Fo fulfilling the benefit fo the alliance contact as expectation, the caie has to ae an ideal slot allocation plan to undestand the poposal of exchanged conditions. This eseach exploes how to constuct a beneficial poposal fo the paticipating caie. The co-opeative stuctues aong line copanies began fo confeences and consotia to the ecent stategic alliances. Seveal studies have been devoted on the stategic alliances fo diffeent pespectives such as the exploation of coopeative pupose [7], otivations and successful easons [14], and the ain diving factos to yield the high degee of instabilities in the beginning of stategic alliances [12]. It was found that the obvious changes in the opeations of line shipping copanies because of stategic alliances wee the sevice netwos and fleet coposition and deployent [13, 16]. Slot allocation anageent is closely lined to containe delivey that includes containe oveent contol and epty containe epositioning eithe sea sevices [2, 4, 8, 9, 15] o inland tanspots [3, 6, 10]. Howeve, the availability of seabone containe oveent depends on the planning of enough slot capacities. few studies have teated the distibution of slot esouces with the concept of evenue anageent o yield anageent fo single pot pai [5, 11], but this ethod fits fo applying to the shot-te planning befoe ship visiting duing each voyage. Recently, ng et al. [1] pesented a yield axiization poble in consideing cagos with vaious consigned peiods fo one pot of oigin to ultiple pots of destinations. They foulated this poble as a ulti-diensional ultiple napsac odel liited by the available epty containes, volue capacities and weight capacities. This eseach can only apply to the outbound slots distibution fo a loading pot. To the best of ou cuent nowledge, thee is no desciption

2 710 Jounal of Maine Science and Technology, Vol. 18, No. 5 (2010) and foulation fo pactical slot exchange planning and alliance slot allocation. Ting and Tzeng [18] descibed the slot allocation poble of a line sevice and poposed an intege pogaing odel to obtain ideal allocated esults fo single diectional taffic flows. This odel can be only conducted on the case with the chaacteistics of the taffic patten lie an ocean-going sevice. Song and Panayides [17] suggested obseving the opeations of line shipping stategic alliances fo a co-opeative gae theoy. They pesented the siple exaples fo assessing the bette coalition sevices in the cases of two playes and oe than two. Nevetheless, this conceptual intoduction cannot povide the caie a concete planning pocedue o stuctue applied to the pactice yet. In tes of the intoduction of a pactical case of slot exchange contact between two co-opeative caies, this study poposes two optiized allocation odels stood at the viewpoint of one of paticipating caies. The fist odel eely consides the slot exchange as the tes in the contact, while anothe one includes the allowance of slot puchase to satisfy the studied caie s expectation. These two odels can assess the level of concened incoe unde given pat of infoation of its patnes. The est of this pape will intoduce the teated poble in the next section, and then the contents and explanation of foulated odels ae followed. The assessent and paaete analysis of the consideed case, which involves in total eight shot sea sevices within sia, will be epoted fo the viewpoint of the studied caie. The final section concludes the findings and povides soe suggestions fo the futue eseach. II. PROLEM DESCRIPTION Slot exchange pogas can be siple as conducting on a single loop of each caie o coplicated to involve ultiple lines fo each othe. siple case ay just exchange slots one by one, but a coplicated one ay contain any outes with diffeent sevice conditions. Ocean-going sevices ae aanged fo deliveing tansoceanic consignent. The sevice conditions on the aet, lie containe tansit tie between pot to pot, deployed vessel types and ain visiting pots, ae noally siila aong shipping lines. The slot exchange conditions ay be siple to eely swap fixed nube of slots fo each othe. On the othe hand, shot sea sevices see oe flexible in ound tip voyage, cycle tie, deployed vessel types and pot otation because thei sevice scopes tend to cove oe counties than tansoceanic outes. These diffeences lead slot exchange conditions aong shot sea sevices oe coplicated than the ocean-going sevices. In any case, the ost ipotant thing fo paticipants is to assess whethe slot allocation of vessels can satisfy the expected caying quantities within the scope of involved lines. The studied copany has been opeating global containe line sevices fo any yeas. This copany sustained coopeative elationships with its stategic alliance patnes though joint fleet and slot exchange. In ode to intensify Table 1. Sevice scopes and conditions fo involved outes in the contact. Line Route and pot otation 1 Japan/Taiwan/Hong Kong/Thailand JPTYO JPYOK JPNGO JPOS JPUK JPOIT TWKEL TWKHH HKHKG THLC THKK HKHKG TWKHH TWTXG TWKEL JPTYO 2 Japan/South Koea/Taiwan/Hong Kong/Singapoe/ Indonesia JPMOJ JPHKT KRPUS KRKWY TWKEL TWTXG TWKHH HKHKG SGSIN IDJKT IDSU HKHKG TWKHH TWTXG JPMOJ 3 Taiwan/Philippines TWKHH TWKEL PHMNS PHMNN TWKHH 4 Japan/Taiwan/Hong Kong/Thailand JPTYO JPYOK JPNGO JPOS JPUK TWKEL TWTXG TWKHH HKHKG THLC THKK THLC HKHKG TWKHH TWKEL JPTYO 5 China/Hong Kong/Philippines/Indonesia CNTO CHSH HKHKG PHMNN PHMNS IDJKT IDSU CNTO 6 Japan/South Koea/Taiwan/Hong Kong JPOS JPUK JPTYO JPMOJ KRPUS KRKWY TWKEL TWKHH HKHKG JPOS 7 China/Hong Kong/Philippines/Thailand CNNG CNSH HKHKG PHMNS THLC THKK CNNG 8 Japan/Taiwan/Hong Kong/Vietna JPNGO JPTYO JPYOK TWKEL TWKHH HKHKG VNSGN VNIHV HKHKG JPNGO Souce the studied copany Cycle tie (days) 28 inta sia sevices, the studied copany also had soe othe co-opeation with egional line copanies. This study focuses on a slot exchange contact between the studied copany and one of its long-te patnes, a local caie poviding soe line sevices within sia. Thei contact aintained a te of six onths peiod. The exchanged conditions wee eassessed fo enewal befoe expiation. The data in this contact is collected fo this eseach. The contact between the studied copany, denoted as, and its patne, denoted as, includes eight weely sevice loops. opeates thee of the and opeates the est. These outes cove 24 pots in nine ain counties within sia (shown in Table 1). lthough pats of the involved outes have sae pot otation, 1 and 4, two copanies enfoced thei sevice fequency in the indicated sevice scope though thei alliance contact. Without consideing the tanshipent of containes, this study focuses on diect tade aets (o pot pais) in each loop

3 H.-. Lu et al. Slot Exchange and Puchase Planning of Shot Sea Sevices fo Line Caies 711 Table 2. Deployed ships and shaed slots of involved outes in the contact. Main opeato Line Nube of deployed ships Contact slots of a ship (TEUs) Contibuted ships Shaed slots (TEUs) Souce the studied copany Thee ae 208 diect tades in total caied by. These diect tade aets excludes consignents between doestic pots in soe counties due to a cabotage liitation fo foeign caies to ship doestic cagoes. ccoding to the cycle tie of each line, vaious nubes of ships ae deployed on these lines fo fulfilling thei opeational equieent of fixed weely calls. It is noted that both copanies have adopted joint fleet ode on thee lines of aleady, unde anothe contact. s shown in Table 2, the slot shae of each copany coesponding to each line is calculated by ultiplying contact slots of a ship by the atio of espective nube of contibuted ships to total nube of deployed ships. oth copanies can use contollable capacities as a counte in the planning of slot exchanges. ll of involved outes have a vaiety of sevice contents with cycle ties, scopes, and ship types and quantities. These dissiilaities iply that deploying capital and opeating costs of each line could be diffeent. Hence, it could hadly show the exact woth of slots on each line if the total nube of exchanged slots was eployed in the contact as an exchanged te. Fo this concen, both copanies ageed to exploit a paticula unit, naely TEU-day (TEU is twenty-foot equivalent unit of a standad containe size), as the exchanged conditions, athe than using the total nube of exchanged slots diectly. The exchanged TEU-days fo an alliance oute ae calculated by the poduct of the nube of slots exchanged to patne and the cycle tie in days of this sevice oute. It is noted that the su of exchanged TEU-days fo all involved lines should be, theefoe, equal fo each copany. lthough the cycle tie of a oute cannot sufficiently epesent the whole value of input esouces, it is a siple way and also one of the ipotant factos affecting the deploying costs of a sevice oute. ccoding to the te of cuent slot exchange contact, both copanies exchanged 19,250 TEU-days each othe. In total, swapped slots of 755 TEUs fo its opeating thee lines fo 875 TEUs of s five opeating lines. The total nube of TEU-days is even fo both copanies as Main opeato Table 3. Slot exchanges in the cuent contact. Line Cycle tie (Days) Slots exchanged to patne (TEUs) TEU-days Cuent contolled slot (TEUs) , , Total TEUs & TEU-days , , , , , , Total TEUs & TEU-days ,250 Souce the studied copany shown in Table 3. The final two coluns in this Table pesent contolled slots of both copanies afte exchange. esides the oiginal shaed capacities fo the join fleet contact, obtained oe slots to be used on outes 4, 5 and 8 by the exchange contact. III. MODEL FORMULTION pope slot exchange plan fo a caie ais to eet estiated deand levels and line opeational popeties though effective slot allocation. Fo an individual copany s standpoint, this pape poposes odels fo slot exchange planning and cobining it with slot puchase. Without consideing tanshipent, this study focuses on diect tade aets (i.e. pot pais that can be finished seabone caiage on a sevice oute) in each loop as the concens of the studied caie. It is assued that the ange of deand quantities in each diect tade aet is nown and epesented by lowe and uppe bounds. Moeove, we assue that the uppe bounds of patne s available exchanges and possible shotages on each oute ae nown in odelling. These paaetes can be futhe exploed thei influences against the optial decision with sensitivity analysis. efoe intoducing the foulated odels, the fist subsection descibes a vital concept elative to the epesentation of the elationships between diect tade aets and sailing legs of each oute. 1. Route-Maet-Leg Relationships t the planning peiod, the caie is hadly to estiate the cago ix fo thei consignent. To siplify cago types by containes sizes, lie 20-foot and 40-foot boxes, and/o special inds of containes, such as eefe and out-of-gauge ones, becoes a popula way to estiate elative paaetes. This altenative eans each size of containes on the sae aet has hoogeneous volue, weight and pice in a long-te

4 712 Jounal of Maine Science and Technology, Vol. 18, No. 5 (2010) pot 2 pot pot pot 2 pot Fig. 1. Containes shipped on boad fo the illustated exaple. 4-3 Table 4. Route-aet-leg elation atix (α s ) fo the illustated exaple. Tade aets Route 1 ( = 1) Sailing legs (s) Route 2 ( = 2) Sailing legs (s) () (1, 2) (1, 3) (1, 4) (2, 1) (2, 3) (2, 4) (3, 1) (3, 2) (3, 4) (4, 1) (4, 2) (4, 3) planning level. line can cay containes fo all of tade aets aong calling pots in a sevice oute. Howeve, its pot otation is unliely able to povide non-stop deliveies fo all pot pai tades. Containes should be ept on boad when the ship calls at othe non-destination pots. This pactice iplies that soe slots of the vessel ay have been occupied by those tansit feights loaded at pevious pot calls. Ideally, the vessel should be fully loaded at evey sailing leg to achieve axial utilization of slot capacities, but shipping copany is unliely to contol shipents to eet such expectation in pactice. ccoding to the pot otation of a loop, the caied passages of consignents fo evey diect tade aet can be acquied a pioi fo the load planning. These paths ae noally aanged as the shotest one with inial tansit tie due to aet copetition. t the case with only one oute, a aet-leg elation paaete, α s, with value of 1 o 0 defined as whethe the delivey passage of consignents of diect tade aet passing the sailing leg s o not, 1 stands fo yes and 0 othewise. ound tip voyage with a pot otation is illustated hee to depict the slot occupied elationships between tade aets and sailing legs as shown in Fig. 1. This exaple has 5 sailing legs fo 5 calls and seves 12 pot pais because of visiting 4 diffeent pots. It is clea that the caied containes of tade fo pot 2 to pot 4, fo exaple, have to occupy the slots of legs 2-3 and 3-4. The value of coesponding aet-leg elation paaetes, α (2,4),(2,3) and α (2,4),(3,4), will be 1, and othes ae 0. The elationships fo othe aets and legs can be easily found. Extending aet-leg elationships to ultiple outes, the oute-aet-leg elation paaete could be edefined as α s by adding an index of oute. It epesents whethe the consignents of diect tade aet can be shipped by oute and pass leg s o not, 1 fo yes and 0 othewise. esides the fist oute, anothe loop with otation is appended to conside. The value of all paaetes elative to the pot 3 in the second oute will be 0 because it is not visited in this loop. The aet of pot 2 to pot 4 is a non-stop delivey, so the 2 value of coesponding paaete, α (2,4),(2,4), is 1 and 0 fo othes. The whole oute-aet-leg elationships fo the exaple can be found in Table Slot Exchange Model s noted, the caie of using odels is designated as, while its patne is. Fo ease of desciption, the following explanation will eploy thei oles. esides, containe types ae categoized as containe sizes and the nube of types can follow the classification of. The unit of slots is counted in tes of TEU in the odels. Othe sybols fo vaiables and paaetes used in the foulated odels ae intoduced and intepeted as follows. Vaiables x = nube of distibuting slots in TEUs fo type containe in aet equied on oute. q = slots in TEUs to be exchanged to on oute. n = slots in TEUs to be exchanged fo on oute. π = a switch vaiable to epesent exchanged slots fo o to on oute, 1 denotes fo the patne and 0 othewise. Q = expected TEU-days to be exchanged in the contact. y = puchased slots in TEUs fo the whole voyage on oute. Paaetes S = the set of sailing legs fo oute. α s = the oute-aet-leg elation paaete to epesent whethe the consignents of diect tade aet

5 H.-. Lu et al. Slot Exchange and Puchase Planning of Shot Sea Sevices fo Line Caies 713 can be shipped by oute and pass leg s o not, 1 fo yes and 0 othewise. p = possible evenue eceived pe type containe to be deliveed in aet. c = equied costs pe type containe to be deliveed in aet. w = equied slots in TEUs fo loading type containe, such as a 20 feet containe occupies 1 TEU and a 40 feet containe occupies 2 TEUs etc. U = slots contolled by on oute in TEUs. b = axial slots that can be eleased on oute in TEUs. z = s possibly axial shotage of slots on oute in TEUs. t = the cycle tie of oute in days. u = estiated uppe bound of caying quantities fo type containe in aet. l = estiated lowe bound of caying quantities fo type containe in aet. e = puchased pice pe TEU fo whole voyage on oute. s the discussion above fo slot distibution, it is noted that the caie has to allocate suitable slots to vaious types of containes fo each tade aet along with possibly caied paths. Intuitively the capacities of a ship should be eseved with highe pioities fo those containes with highe contibutions to pofit geneation. Howeve, too any ovelaps of the caied paths within vaious aets incease the coplexity of optial allocation of slots, especially to tae the slot exchange plan of ultiple lines into account. In this section, a atheatical odel is constucted to decide the optial aount of slot exchange with to axiize s pofits. The foulated odel [M1] is pesented as follows. [M1] s.t. Max. ( p ) c x (1) αsw x U q + n, s = 1,..., S (2) n b π (3) q z (1 π ) (4) tn = Q (5) tq = Q (6) S αs s= 1 x U,, (7) x u, (8) x l, (9) π {0,1}; x, q, n, Q 0 and intege (10) The objective function in (1) axiizes the su of estiated possible pofits of fo shipping vaious types of containes aong vaious tade aets. Since the contact of slot exchange o slot puchase is always discussed afte oute planning o sevice launch, the opeational costs elative to ship sailing has to be absobed by the caie as the deployed vessels type no atte the esult of coopeation. Slot allocation in consideing slot exchange and slot puchase only concens consignent evenues and containe handling costs. Theefoe, this pape taes into account the evenues that include aveage feight and any incoe fo shippes and the costs that ainly contain all containe handling chages occuing on loading and dischaging pots. Pot index fo handling costs occuing is sae as indexing by aet. Equation (2) enfoces that the su of distibuted slots on each sailing leg cannot exceed the available capacities, including the oiginally contollable slots plus the exchanged esults. Equations (3) and (4) estict each loop on exchanged slots eithe fo o to, and exchanged slots cannot exceed the axial nubes that could elease o its possible shotage on each oute. Equations (5) and (6) liit the nubes of exchanged TEU-days fo both sides ae consistent. The function of (7) is to ensue that the tade aets without on a specific oute should not be allocated any slots on this sevice. Equations (8) and (9) constain the allocated slots fo a specific categoy and tade aet falling into the ange between its lowe and uppe bounds. If the planne can ensue a pecisely nube fo the deand of a tade aet, he/she can set the sae value fo its uppe bound and lowe bound. Equation (10) epesents nonnegative and integal constaint of vaiables. This odel is an intege pogaing (IP) poble with seveal distibuted vaiables concened with the types of containes, involved outes and tade aets. s only diect tade aets on each line ae consideed, Eq. (7) will enfoce any distibuted vaiables to be 0 diectly if involved lines do not appea too any duplicated tade aets. The nube of othe intege vaiables is only aound thee ties of that of involved outes. 3. Model llowed Slot Puchase Slot puchase is anothe altenative adopted in an alliance ageeent, paticulaly in the situation whee has had excess supply of capacities while the is facing excess deand. In pactice, the decision of slot puchase noally follows the esult of slot exchange contact. Howeve, the caie can plan it siultaneously with the assessent

6 714 Jounal of Maine Science and Technology, Vol. 18, No. 5 (2010) of slot exchange when it holds enough infoation fo the patne. The equieent fo slot capacities is diven by the deand quantities. The caie can adopt the slot allocation with highe pofits in consideation both ethods if patne s situation is available. Model [M2] ais to povide the optial solution when patne s conditions and slot puchase pice ae given. Futheoe, slot puchase pice is just able to epesent the slot value in the whole context of the exchanged contact unde the cuent deand levels fo the copany. In this section, the possibility of slot puchase is consideed and anothe odel [M2] is constucted as follows. [M2] (11) Max. ( p c ) x e y s.t. αsw x U q + n + y, s = 1,..., S (12) (3) ~ (10) y + n b (13) y 0 and intege (14) The objective function of (11) axiizes the su of pofits fo the possible caied containes afte deducting the costs of slot puchase. Equation (12) eplaces (2) to append the available slots fo puchases. To the patne the available sold slots ust be the left ones fo the exchange contact. Equation (13) ae the su of patne s exchanged and sold slots on each line less than o equal to the axial that it can elease. Equation (14) is nonnegative and integal constaint fo slot puchase vaiables. The stuctue of [M2] is siila as [M1] but inceases the nube of involved lines of vaiables and constaints. These two odels can be solved by eploying any coecial softwae pacages fo atheatical pogaing available today. IV. COMPUTTIONL RESULTS ND NLYSIS This study used the coecial pacage of odelling language fo atheatical pogaing, ILOG OPL Studio 3.5, to geneate above foulations and to solve all instances by its ebedded banch-and-bound algoith. The elative data of this alliance wee pepaed fo ipleenting solution on the pesonnel copute with the CPU of Intel Pentiu 4, 2.4 GHz, and opeation syste of Micosoft Windows XP. 1. Solving Results ecause only too into account 20-foot and 40-foot laden containes in slot planning, this study excluded epty and special inds of containes. oth uppe bounds of Table 5. Copaisons of solving esults between two odels. Copaison ites Slot exchange only (Model [M1]) Slot exchange with 19,250 TEU-days (Model [M1]) Slot exchange and slot puchase (Model [M2]) Nube of vaiables 3,353 3,352 3,361 Nube of constaints 4,858 4,858 4,866 Objectives ($) 4,079,670 4,066,760 4,234,460 Solving tie (Sec.) Slot exchanged (TEU-day) 18,641 19,250 5,761 Slots puchased (TEU) available eleased slots fo (b ) and its possibly axial shotage of slots (z ) ae set as the cuent exchanged slots plus 10% oe on each involved line. This condition, heeafte, is called the default swap allowance fo distinguishing fo the te of the cuent exchanged slots. This teatent could eep the oiginal patten in the contact and give oe aet flexibilities fo obtaining possible optial decision. Moeove, the ost and least consigned nubes of containes of the studied copany fo evey tade aet ae collected to be the uppe and lowe bounds of caying quantities ( u and l ). The concened costs of each containe on each tade aet include handling chages at pots. The evenues include the feight and teinal handling chage (THC) collected fo the shippes. The puchase pice of a slot is set as USD 300 fo all of the outes accoding to s suggestion. This instance was solved with odel [M1] consideing slot exchange and futhe tested the instance at fixed exchanged TEU-days as the contact, i.e. 19,250 TEU-days. Model [M2] was also exploited to solve this instance incopoating slot puchase. s shown in Table 5, these cases can be obtained thei optial solutions within 5 CPU seconds. Futheoe, the esults eveal that the studied copany ay each the highest pofit when its patne is willing to sell out slots of 919 TEUs and to exchange 5,761 TEU-days. If is eluctant to sell the, then educing the exchanged condition to 18,641 TEU-days athe than 19,250 TEU-days will geneate a bette pofit. These esults iply the default slot puchase pice of USD 300 is lowe than the pofit that a unit slot ight ean. ccodingly, can puchase slots fo as any as possible to obtain the axial pofit unde the optial decision. In addition, the cuent exchanged slots in the contact indeed could not geneate the axial pofit fo because of eleasing too any slots fo exchange with., in fact, has the potential to stive fo oe consignents as long as is eady to elease capacities as s willingness. Fo the exchanged status of each line shown in Table 6, in eely consideation of slot exchange, is able to elease a few oe slots to its patne on lines 1 and 3 but to eseve oe to be used fo its own on line 2. Moeove, the copany can see oe exchanges than the cuent contact

7 H.-. Lu et al. Slot Exchange and Puchase Planning of Shot Sea Sevices fo Line Caies 715 Main opeato Line Table 6. Copaisons of cuent slot contol and esults of odel solution. Oiginal contol Cuent contact Model [M1] swap to swap to swap to swap to Model [M1] with 19,250 TEU-days swap to swap to Model [M2] swap to Unit TEUs swap to Table 7. llocated atios of slot allocation fo satisfying caying deands. Containe Nube and atio fo size allocation 20-foot 40-foot Meet with the lowe bound Meet with the uppe bound Fall between lowe and uppe bounds Meet with the lowe bound Meet with the uppe bound Fall between lowe and uppe bounds Model [M1] 33 (15.8%) 171 (82.2%) 4 (2.0%) 35 (16.8%) 169 (81.2%) 4 (2.0%) Model [M1] with 19,250 TEU-days 51 (24.5%) 154 (74.1%) 3 (1.4%) 80 (38.4%) 115 (55.4%) 13 (6.2%) Model [M2] 28 (13.4%) 176 (84.6%) 4 (2.0%) 25 (12.0%) 177 (85.1%) 6 (2.9%) on lines 4, 5, 6 and 7 if possible. Obviously, had less caying equieent on line 8, and should elease soe contolled capacities athe than to acquie oe. Fo this analysis, we conclude that lines 2 and 4 to 7 ae of lacing slots but lines 1, 3 and 8 wee of having exta ones to the studied copany. Cobining with the possibility of slot puchase, can obtain slots as any as possible in tes of this way at the cuent pice. Slot exchange can only tae lines 1, 3, 6 and 7 into account. ong the 208 O-D pais, solving esults show that can povide alost pot pais the ost slot atios eaching thei deand uppe bounds fo 20-foot and 40-foot containes. Using [M1] and [M2] odels can exceed 80%, but these atios decease to 74.1% and 55.4% espectively at fixing TUE-days with 19,250 fo solving Model [M1]. Only less than 7.0% of pot pai deands ae satisfied falling between lowe and uppe bounds in all solving cases. Othe pats ae those which can satisfy the lowe bounds at least. This analysis is displayed in Table 7. In the copaison of Tables 7 and 5, USD 4,100,000 4,095,000 4,090,000 4,085,000 4,080,000 4,075,000 4,070,000 4,065,000 4,060,000 4,055,000 4,050,000 Objective TEU-days exchanged -20% -10% 0% +10% +20% dded pecent fo swap allowances fo Copant 22,000 21,000 20,000 19,000 18,000 17,000 16,000 15,000 Fig. 2. Influences of swap allowances on objective and TEU-day. the oe the objective value, the highe the atios of eeting with the uppe bounds in slot allocation. It aes sense at the input-output veification fo the validity of ou poposed odels. 2. nalysis fo Swap llowance In this section we futhe exaine the influences of the swap allowances fo (i.e. b and z ) to the objective and exchanged TEU-days. The extension ange is fo 20% downwad to 20% upwad of the default swap allowance. Solving with the odel [M1], the axial pofit and the exchanged TEU-days ae positively associated with adjustents of the swap allowances as shown in Fig. 2. When the swap allowances incease, the axial pofit and the optial exchanged TEU-days will incease as well. Howeve, the inceased agin is lage at the swap allowance is lowe 10% than the default value, i.e. the cuent exchanged slots in the contact, and is salle at exceeding it. Note that it is infeasible when educing the swap allowance to 30% less than the default value because the least slot deands on soe tade aets of the copany can not be satisfied at such low allowance level. indeed needs slot exchanges to suppot its stong aet deand fo chasing oe benefits by coutesy of oe swap allowances fo. TEU-day

8 716 Jounal of Maine Science and Technology, Vol. 18, No. 5 (2010) USD Objective fo eeping default swap allowance inus 10% Objective fo eeping default swap allowance Objective fo eeping default swap allowance plus 10% oe 4,090,000 4,085,000 4,080,000 4,075,000 4,070,000 4,065,000 4,060,000 4,055,000 4,050,000 4,045,000 4,040,000 12,250 13,650 15,050 16,450 17,850 19,250 20,650 22,050 TEU-days exchanged Fig. 3. Fixed exchanged TEU-days analysis fo vaious swap allowances. USD 4,250,000 4,200,000 4,150,000 4,100,000 4,050,000 4,000,000 Objective TEU-days exchanged Unit pice of slot puchase (USD/TEU) Fig. 4. Sensitivity analysis of slot puchase pice. 20,000 15,000 10,000 5,000 0 TEU-day 3. Fixed TEU-Days nalysis In pactice, the bagain esults fo slot exchange with the patne ae noally diffeent fo the copany s initial plan because the patne s intention could not be pedicted pecisely in advance. This section ais to exploe the optial pofit levels fo with vaious fixed TEU-days. The nube of exchanged TEU-days is upwad and downwad fo 19,270 by a scale of 700 TEU-days at a tie. It is noted that the nube of TEU-days ust be the ultiples of 7 because of weely sevice on each line. Thee levels of swap allowance ae consideed, i.e. the default nube and 10% less and 10% oe of that. t the case of default swap allowance, the esults show that the pofits in odel [M1] ae alost the sae between 14,350 and 18,550 TEU-days (see Fig. 3). Howeve, the pofit geneated by the cuent contacted exchanged TEU-days of 19,250 is lowe than that. Othe two cases show that the geate is the swap allowance the highe is the pofit. In addition, the change patten of pofits with vaious TEU-days in these two cases is sae as the fist one. Obviously, the ange of TEU-days with axial pofits becoes lage as the swap allowance inceases. When TEU-days fall below this ange, the pofit will gadually incease as it inceases. On the othe side, the pofits shaply decease when TEU-days incease and no feasible solution exists at TEU-days lage than a cetain nube. The citical nubes in thee cases ae 19,250, 20,650 and 22,750 TEU-days, espectively. The cuves in Fig. 3 ae of eaningfulness fo the studied copany because involved lines ae all esticted within the shot sea sevices in sia. The diffeences of unit pofits fo the sae categoy of laden containes in vaious tade aets ae slight. This analysis suggests that could easily adjust the slot allocation to obtain the bette pofits fo a fixed nube of exchanged TEU-days. Cetainly, the inceental agin would be odeated when the enfoced exchanged TEU-days ae lowe than the citical one. Contaily, the pofit will apidly loose due to the slot esouces ae wasted to exchange with athe than to load the boxes with actual incoes. If the wastes ae speading oe, ship s slots cannot affod to satisfy the least caying deand finally. This analysis is valuable fo the to ealize the suitable levels of exchanged TEU-days and citical edge of slot esouces. 4. Pice nalysis fo Slot Puchase Model [M2] consides slot puchase in the slot exchange ageeent to eflect the value of unit slot esouce fo. It shows, in section of solving esults, that the suggested slot puchase pice of USD 300 is lowe than the opeating value of s own and can contibute to an incease in pofit fo it at a decease in exchanged TEU-days. This esult iplies that the studied copany should puchase slots as any as possible fo athe than executing slot exchange. Rationally, if ealized the aet value of unit slot to, it ight not sell any slot at this pice fo the eason of copetition unless this deal also benefits. ccodingly, we caied out a pice sensitivity analysis to find out the acceptable level of slot puchase pice fo. dditional USD 50 is added to the unit puchase pice at a tie fo analysis. s shown in Fig. 4, the pofits educe as the unit pice inceases because of exta expenses of puchasing, and the deceent is diinishing. On the othe hand, the nube of exchanged TEU-days inceases associated with an incease in unit puchase pice, but thee is an abupt lift of exchanged TEU-days at the pices between USD 550 and 600 following a sooth change path. When the puchase pice eaches USD 850, the solution does not appea any puchased slot. The citical pice locates at USD 841 though futhe tests. It is found that does not adopt slot puchase policy any oe when the unit puchased pice is ove it. This pice could be a efeence in picing slots sold to its patne o othe caies. If could sell the slot with the pice highe than this one, it athe did than opeated by self. Note that the citical pice of is not the sae as this pice because its deands on these lines ae diffeent. We futhe exploed the citical puchase pices fo in tes of five swap allowances fo. s shown in Table 8, the citical puchase pice ises as the swap allowance inceased, but the ange is nealy sall at the allowance enlaged oe than the default case. The pofits

9 H.-. Lu et al. Slot Exchange and Puchase Planning of Shot Sea Sevices fo Line Caies 717 Table 8. Citical puchase pices of the unit slot unde vaious swap allowances. Swap allowance Citical puchase pice (USD/TEU) Objective (USD) TEU-days exchanged (TEU-day) -20% 781 4,056,080 13,384-10% 800 4,069,910 17,150 Default 841 4,079,670 18, % 845 4,088,380 18, % 846 4,096,610 17,688 incease but with a diinishing tendency. Howeve, the exchanged TEU-days do not show an inceasing path when the swap allowance is lage than the default case. The citical puchase pice would be egaded as the value of unit slot fo the studied copany only executing slot exchange. Optial slot allocation tends to shift slot esouces to the ost usage fo obtaining the axial pofit. Since the pofits ae gowing as the flexibility of exchange inceases, the slot value still gows. Exchanged TEU-days eflect the adjustents of slot allocation accoding to the slot availabilities of each line. When the swap allowance is enlaged to 10% oe than the default case, slot allocation has oe effective esults so that the nubes of TEU-days exchanged can be educed. V. CONCLUSIONS ND SUGGESTIONS Unde alliance co-opeation, caie s decision-aing in how to execute slot exchange with its patnes is an ipotant pat of its slot allocation plan, which lins to copany s pofitability. ased on an opeating slot exchange contact between two caies, this study has contibuted two odels aiing to assist caie distibuting slots in optial slot exchange and with consideation of slot puchase fo the involved lines. These odels could also geneate esults evealing which lines should elease capacities o swap slots accoding to the estiated deands of diect tade aets. Hence, they can be extendedly applied to a suvey egading which lines should be involved in the alliance contact. Ipotant findings of this study in espective of slot allocation in the slot exchange alliance ae concluded as follows. 1. In the shot sea sevices, the optial pofits fo vaious slot exchanges appeaed to be the sae within a ange of exchanged TEU-days. The inceent agin of pofits was odeated as exchanged TUE-days inceases and less than the ange. Howeve, the pofits apidly deceased as the exchanged TEU-days went beyond the citical ange until no way to satisfy the least caying deand because of slot esouces wasting on exchange conditions. 2. Swap allowance levels eleased fo the patne doinated the context of slot exchange. Given a stong caying deand, the pofits and exchanged TEU-days positively associated with the change of swap allowances. 3. Given that slot puchase was allowed and when the puchase pice was lowe than the pofit gained fo slot exchange without puchase, the studied copany would have a bette pofit by adopting a slot exchange and puchase stategy. 4. The citical slot puchase pice eflected the axial pofit that the unit slot could be eaned fo the studied caie s viewpoint. It could be a valuable efeence given to the studied copany when consideing selling in slots to its patne o othes. This pape dealt with a pactical case. The test cases only focused on the scale of the intoduction in Section II. No atte the epot in Table 5 o othe cases in sensitivity analysis, the coecial optiization pacage could solve the in efficiency. In theoy, futue studies can conside developing effective algoith that can handle the lage cases in ational tie. Slot allocation planning is a vital issue of slot anageent in line s pactical opeations. It becoes oe coplicated especially afte peeating alliance opeations as the diffeent chaacteistics of each ind. The slot exchange contact pesented in this eseach is only a specific case between the studied caie and its patne. Diffeent alliance ageeent and oe involved paties will lead to oe valuable study topics fo eseaches. Moeove, odels pesented in this eseach ae based on the standpoint of one paticipant. Soe data egading the patne ust be eady in hand. If line caie would apply to it, these paaetes could be collected in the pocess of bagaining and odified gadually. In the futue eseach, the win-win odels can be developed on the basis of utual ageeent. CKNOWLEDGMENTS This eseach was patially suppoted by a gant (NSC H ) fo the National Science Council of Taiwan. We also than M. Jacie Chen, anage of Yang Ming Maine Tanspot Copoation, fo poviding valuable nowledge and pactical viewpoint egading alliance co-opeation. REFERENCES 1. ng, S. K., Cao, C., and Ye, H. Q., Model and algoiths fo ultipeiod sea cago ix poble, Euopean Jounal of Opeational Reseach, Vol. 180, pp (2007). 2. Cheung, R. K. and Chen, C. Y., two-stage stochastic netwo odel and solution ethods fo the dynaic epty containe allocation poble, Tanspotation Science, Vol. 32, No. 2, pp (1998). 3. Cainic, T. 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