DIRECT VERSUS TERMINAL ROUTING ON A MARITIME HUB-AND-SPOKE CONTAINER NETWORK

Transcription

1 Journal of Marine Science and Tecnology, Vol. 13, No. 3, pp (2005) 209 DIRECT VERSUS TERMINAL ROUTING ON A MARITIME HUB-AND-SPOKE CONTAINER NETWORK Caug-Ing Hsu* and Yu-Ping Hsie** Key words: routing decision, ub-and-spoe networs, multi-objective analysis. ABSTRACT Tis study formulates a two-objective model by individually minimizing sipping costs and inventory costs to decide weter to route a sipment troug a ub or directly to its destination. First, sipping and inventory cost functions are formulated for a multi-port calling route. Sipping costs include capital and operating cost, fuel cost and port carge, wile inventory costs include waiting time cost and sipping time cost. Ten, based on a trade-off between sipping costs and inventory costs for two types of sipping routes, Pareto optimal solutions of te two-objective model are determined, and a routing decision can be illustrated and made in objective value space. Te optimal routing, sip size and sailings frequency wit respect to eac level of inventory cost is sown. Te results sow tat te optimal decision tends to be direct sipping as container flow between origin and destination ports increases. INTRODUCTION Container carriers operate in an increasingly competitive and maret-driven environment. Most of tem continuously provide teir services using ub-and-spoe networs. Under a ub-and-spoe networ, economies of flow can be realized by consolidating freigt troug a ub and using large sips. However, routing all freigt troug a ub is not necessarily appropriate in any situations. Altoug te average sipping cost per TEU decreases on line-aul legs of ub-and-spoe networs, freigt originated in feeder ports must be transsipped troug a ub, and incur extra sipping distance, sipping time, port carges and stevedoring Paper Submitted 11/08/04, Accepted 04/22/05. Autor for Correspondence: Caug-Ing Hsu. cisu@cc.nctu.edu.tw. *Professor, corresponding autor, Department of Transportation Tecnology and Management, National Ciao Tung University, 1001 Ta Hsue Road, Hsincu, Taiwan 300, R.O.C. **P.D. Candidate, Department of Transportation Tecnology and Management, National Ciao Tung University; Associate Researcer, Center of Harbor & Marine Tecnology, Institute of Transportation, 2 Cung-Heng 10t Road, Wuci, Taicung, Taiwan 435, R.O.C. carges. Terefore, container carriers must decide weter to route a sipment troug a ub or directly to its destination. Tis study constructs an analytical model on exploring tis issue. Previous studies on maritime sipping service planning suc as sip routing, fleet deployment, and sip sceduling were focused largely on general networs (e.g., Rana and Vicson [15]; Co and Perais [3]; Powell and Perais [14]; Sambracos et al. [19]; Ronen [17, 18] etc.), wile studies about ub-and-spoe networs were few. However, as ub-and-spoe networs ave been used by more container carriers recently, more and more studies discuss about tese special networs (e.g., Robison [16]; Bendall and Stent [1]; Mourão et al. [13]; Hsie and Cang [9] etc.). Some of tem proposed employing constraints to deal wit te caracteristics of transsipment in ub-and-spoe networs, and some of tem introduced cost discount on main-line sipping to deal wit flow economies. However, differing from previous studies, tis study formulates flowdependent cost functions and constructs a two-objective model by individually minimizing sipping costs and inventory costs to analyze routing decision on providing sipping services in a ub-and-spoe networ. Container carriers concern bot sipping costs and inventory costs wen tey mae routing decisions, because tey not only aims at lowering teir sipping costs but also enancing teir services to attract more sippers. Inventory costs are considered to be crucial factors affecting te sippers demand. So bot inventory cost and sipping cost are regarded as decision factors. Inventory cost is commonly regarded as a major factor affecting sipping service decision in logistics literature. Tese studies usually determined te optimal sipping frequency by minimizing total sipping and inventory costs (e.g., Daganzo [5]; Hall [7] etc.). In maritime study, Jansson and Sneerson [11] also proposed an economic model to analyze sipping service decision by minimizing total sipping and inventory costs. However, in reality, altoug container carriers consider inventory cost as a decision factor, te weigt

2 210 Journal of Marine Science and Tecnology, Vol. 13, No. 3 (2005) placed on inventory cost is usually not equal to tat on sipping cost. Terefore, te model proposed erein regards sipping costs and inventory costs as two separate objectives. Te optimal routing wit respect to eac level of inventory cost and sipping cost can be determined using te proposed model. In addition, te proposed two-objective model not only provides flexibility for container carriers in routing decision-maing, but also provides a tool to analyze te trade-off between sipping cost and inventory cost. Furtermore, singleobjective decision-maing by minimizing total sipping and inventory costs or merely minimizing sipping cost could be regarded as a special case of te twoobjective decision. In tis study, a ub-and-spoe maritime networ is considered to provide freigt sipping services between two continents or regions separated by a major ocean. In eac region, one or several ports are selected as ub ports based on location and freigt sipping demands. Ten, large moter sips are used to provide services among ub ports in different regions, and small feeder sips are used to provide services between ub port and its spoe (or feeder) ports in te same region. A fundamental ub-and-spoe maritime networ considered in tis study is sown in Figure 1. Tis study explores route decision-maing on weter freigt between feeder ports on one feeder line at origin region (e. g., ports p1 and p2) and ub ports at destination region (e.g., ports p5 and p6) sould be sipped directly (i.e., sipped by te direct line, d: p1, p2, p5, p6, p5, p1) or sipped troug te local ub port at origin region (i.e., sipped via ub port, p3, by routing te feeder line, s: p1, p2, p3, p1, and ten te main line, : p3, p4, p5, p6, p5, p4, p3). Te remainder of tis study is organized as follows. In Section 2, sipping and inventory cost functions are formulated by analyzing sipping process for a containersip serving a multi-port calling route. Section 3 determines Pareto optimal solutions of te two-objective model based on a trade-off between sipping costs and inventory costs. Section 4 presents an example tat p3 Feeder line, s p2 Origin region p4 p1 Main line, Direct line, d p5 p6 Destination region Fig. 1. Te fundamental ub-and-spoe maritime networ. Hub port Spoe port Main line Direct line Feeder line demonstrates te usefulness of te proposed model. Concluding remars are finally made in Section 5. COST FUNCTIONS Consider a multi-port calling route, m, calls at n m ports, were n m N. Te route starts from port 1, and follows by port 2, port 3... and port n m, and ten returns bac to port 1. Te ports of call on te route may be different or some of tem are routed again on te returning route as sown by Figures 2(a) and 2(b), respectively. On te route, ocean carrier operates f sailings frequency per season using sip type t. Sips in tis study are containersips wit dry cargo containers, and te unit of containers is TEU, i.e. twenty-foot equivalent unit. Te cost function erein follows te formulation of Hsu and Hsie [8]. Tis section summarizes te cost function proposed by Hsu and Hsie [8]. Suppose flow from one port to anoter port on te route is given. Let Q m ij denote flow from port i to port j on route m per season, were i, j = 1, 2... n m m and Q ij = 0 for i = j. Ten te loading and unloading volumes in any port i per round voyage are 1 f Σ m Q ij and 1 m j f ΣQ ij, j respectively. Sipping costs can be divided into tree main categories: Capital and operating cost, fuel cost and port carge. Capital and operating cost represents te total expenses paid for using te sip eac day, including te cost of owning te sip, crew wages and meals, sip repair and maintenance, insurances, materiel and supplies, diesel oil consumption, and so on. Capital and operating cost increases wit sip size, operating time and sailings frequency. Te total sipping time per round voyage for a sip includes line-aul time at sea and dwelling time in port. Te port dwelling time include te cargo loading and unloading time and te arrival and departure process time tat a sip spends at ports. Te cargo loading and unloading time can be estimated by container loading/unloading volume and te andling rate. Let denote te average gross andling rate, TEU per day, in port i, ten te cargo loading and unloading 1 time in any port i is f Σ(Q m ij + Q m ji j ). Te arrival and 2 2, n m 1 1 n m 1 Fig (a) n m Sipping routes: (a) all ports of call are different; (b) some of ports are repeated. 1 (b)

3 C.I. Hsu & Y.P. Hsie: Direct Versus Terminal Routing on a Maritime Hub-and-Spoe Container Networ 211 departure process time includes not only time a sip moving into or out from te port but also time a sip waiting for entering or leaving a port. Te lengt of time can be estimated by te average sip waiting time and te average sip sailing time in a port. Let W i denote port arrival and departure process time in any port i, and te unit of time is day. Ten, time a sip spending in any port i is W i + 1 f (Q ij m + Q ji m ). Moreover, te total time tat a sip spends on all ports per round voyage is te sum of te dwelling time of n m ports, i.e. W i + 1 f Q m m ij + Q ji. Let D m i denote sipping distance between any consecutive port i and port i + 1 on route m, and V t denote average service speed for sip type t. Ten, sipping time at sea per round voyage is V 1 m t ΣD i, and i te total sipping time per round voyage is te sum of time spent in all ports and at sea, i.e. Σ (W i + D m i ) i V t + 1 f Q ij m + Q ji m. Furtermore, let S t denote average daily capital and operating cost for sip type t. Ten, te total capital and operating cost for a season wit f sailings frequency is fs t (W i + D m i V t )+S t Q ij m + Q ji m. (1) Fuel cost is te expense of fuel consumption by a sip sailing at sea and dwelling in port. Fuel cost increases wit sip size eiter at sea or in port. Moreover, fuel cost at sea is proportional to te sipping distance, since a sip normally cruises at constant speed at sea. Fuel cost in port is different from fuel cost at sea, for a sip must decelerate or accelerate wen entering or leaving a port, wile it also depends on distance a sip moving in port. If a port area is larger, te relative moving distance may be longer and te fuel cost in port is iger. Terefore, fuel costs for te same sip in various ports are different. Sometimes fuel cost in port can be ignored due to it is relatively small. Let F t denote fuel cost at sea per nautical mile by sip type t, and B it denote fuel cost in port i by sip type t. Ten, te fuel cost per round voyage on route m by sip type t is Σ(F t D m i + B it ), and te total fuel cost for a season wit i f sailings frequency is f (F t D i m + B it ). (2) Port carge is paid for a sip dwelling in port and can be divided into carge on sip and stevedoring carge. Te former is paid for servicing te sip, including pilotage, towage, line andling fee, and bert occupancy carge, etc. Te latter is paid for cargo andling, including container loading and unloading carges, equipment carge, and rent of container yard, etc. Te level and structure of port carge in various ports are different. In usual, port carge of a sip depends on gross tonnage or capacity of a sip and also depends on bert occupancy time, so port carge of a sip increases wit sip size and bert occupancy time. However, pilotage, towage, and line andling fee are independent of bert occupancy time, wile bert occupancy carge is proportional to bert occupancy time. Let α it denote portion of port carge of a sip tat is independent of bert occupancy time, and β it denote portion of port carge of a sip tat is proportional to bert occupancy time, were subscript i and t indicate port i and sip type t, respectively. Ten, te total port carge on sip serving a route for a season wit f (Q m ij + Q m ji ). Let sailings frequency is f α it + β it G i denote average andling carge per TEU in port i. Ten, te total stevedoring carge for a season is G i (Q ij m + Q ji m ). Te total port carge is te sum of te total port carge on sip and te total stevedoring carge. Tat is f α it + β it + G i (Q ij m + Q ji m ). (3) From Eqs. (1)-(3), total sipping cost for a season wit f sailings frequency on route m by sip type t, TC1 m, is te sum of te capital and operating cost, te fuel cost, and te port carge. Tat is TC 1 m = f α it + S t W i + B it + D i m S t V t + G i + β it + F t + S t (Q ij m + Q ji m ). (4) Inventory cost represents opportunity cost or loss of value tat cargo cannot be used or sold in te sipping process, and is positively correlated wit cargo volume, value of cargo, and lengt of storage time. In tis study, only inventory cost related to container sipping process are taen into account, involving te waiting time cost in te loading port and te sipping time cost tat containers are sipped on a sip. However, inventory

4 212 Journal of Marine Science and Tecnology, Vol. 13, No. 3 (2005) cost tat occurred in te destination unloading port is not taen into account because it is not directly related to decisions on te containersip sipping routing. Waiting time cost is te cost related to sailings frequency wic result in scedule delay for containers eiter waiting in te loading port or at te place of production or origin. Te iger te sailings frequency is, te lower te waiting cost is. Assuming tat te arrival process of containers at eac loading port follows a uniform distribution, ten te average waiting time per TEU in a loading port is one alf of a sipping time cycle. Let H denote te daily value of time per TEU, and suppose one season approximates to 13 wees or 91 days. Te total waiting time cost per season for containers sipped on route m is 91H 2f Q ij m. (5) Sipping time cost is related to time wile containers are sipped on a sip, and increases wit te sipping time. Let T ij m denote te sipping time of containers from port i to port j on route m. It includes time tat a sip spends on routing troug all lins and ports on te pat from port i to port j. Since time tat containers spend in unloading ports is not easy to estimate and not related to routing decisions, te time tat containers spend in loading and unloading ports is approximately estimated as time spent in loading ports only. Terefore, T ij m can be represented as Were δ m ij T m ij = Σδ m ij δ m ij = W + D m V t is defined as + 1 f Σ Σ l m δ ij R (Q m l + Q m l ). 1, if pat from port i to j containesa lin betweenport and +1; 0, oterwises. (6) Te total sipping time cost per season for containers sipped on route m is equal to H (Q ij m T ij m ), and can be expressed furter as: H ΣQ m ij δ m ij W + D m V t (7) + H Q Σ f i Σ Σ m m ij δ ij (Q m l R l Q m l ). (8) From Eqs. (5) and (8), te total inventory cost for a season for containers sipped on route m by sip type t, TC2 m, is te sum of te total waiting time cost and te total sipping time cost. Tat is: TC 2 m = 91H 2f ΣQ m ij + j H ΣQ m ij δ m ij + H Q Σ f i Σ Σ m m ij δ ij l R ROUTING DECISION W + D m V t (Q m l + Q m l ). (9) Tere is a trade-off between sipping cost and inventory cost sown as Eqs. (4) and (9), above. Tat is, in a iger sailings frequency route, te inventory cost is low and te sipping cost is ig, wile in a lower sailings frequency route, te sipping cost is low and te inventory cost is ig. However, a complete optimal solution does not exist wen one objective aimed at minimizing sipping cost wile te oter objective aimed at minimizing inventory cost due to tey conflict wit eac oter. Instead of a complete optimal solution, te Pareto optimality concept is introduced erein. Te Pareto optimality is te solution were no objective can be reaced witout simultaneously worsening at lease one of te remaining objectives. (Coon [4]) Te feasible solutions tat minimize two objectives for eac type of sip are determined using tradeoff relationsip and te constraint of sip capacity. And te Pareto optimal solution can be furter determined by comparing te feasible solutions of all types of sips. Moreover, te optimal sip size and sailings frequency yielding te minimum sipping cost wit respect to eac level of inventory cost can be determined at te same time. In te meantime, te Pareto optimal solutions for decisions on eiter routing a sipment troug a ub or directly to its destination can be determined furter in a similar way. Suppose routing decisions are made by two objectives, i.e. individually minimizing total sipping costs and minimizing total inventory costs of a ub-andspoe networ system. Wen comparing Pareto optimal solutions for routing a sipment troug a ub wit routing directly to its destination, since te Pareto optimal solutions for containers sipped from spoe ports on one feeder line in origin region to a ub in destination region won t be affected by all oter feeder lines, it is not necessary to calculate sipping and inventory costs of all routes in te system. As sown in Figure 1, only costs on tree lines, i.e. lines s,, and d, are considered wen routing a sipment directly to its destination, wile costs on two lines s and are considered wen routing a sipment troug a ub. Since a ub as te advantage of cargoconsolidation, it is assumed cargo flow in a main line is very large. Ten, te main line can be serviced wit te

5 C.I. Hsu & Y.P. Hsie: Direct Versus Terminal Routing on a Maritime Hub-and-Spoe Container Networ 213 minimum sipping cost, no matter ow large te inventory cost is. Let TC 1t denote te minimum sipping * cost in main line, and TC 2 denote te respective t * inventory cost. Ten, te minimum sipping cost results from te optimal sailings frequency wic equals to te maximum lin flow, Max Σδ ij Q ij j, divided by Σδ ij Q ij j Max te capacity of sips, U t*. Tat is f =. U t * Substituting it for f in Eqs. (4) and (9), respectively. TC 1 and t * TC 2 can be furter expressed as: t * Max TC 1 t * = TC 1 t * = Σδ ij Q ij j U t * S * + D t * i + F V t * t * + G i + β it * + S t * 2Max 91HU t * Σδ Σ ij Q i ΣQ ij j ij j + H ΣQ ij δ ij + Max HU t * Σδ ij Q ij j α it * + S t *W i + B it * (Q ij + Q ji ), (10) W + D V t * Q Σ Σ ij δ ij l R (Q l + Q l ). (11) Furtermore, TC1 m (Q m ) and TC2 m (Q m ) represent, respectively, te sipping cost and inventory cost on route m, wic depend on te total flow Q m. As sown in Figure 3, q d denote te total flow between te spoe port at origin region and ub at destination region, and q denote te total flow on te main line between ub at origin and ub at destination region and q s denote te total flow on te feeder line between spoe port at origin region and ub at origin region. Ten, wen tere is total flow q d sipped directly to its destination, total flows on direct line, main line and feeder line will be q d, q q d, and q s q d, respectively, as sown in Figure 3(a). Let TTC1 t and TTC2 t denote te total sipping costs and te total inventory costs of feeder line and main line for sipping flow q d troug a ub, respectively. If te main line is serviced wit te minimum sipping costs, ten TTC1 t and TTC2 t can be expressed as TTC1 t = TC 1 t *(q ) + TC 1 s (q s ), (12) TTC2 t = TC 2 t *(q ) + TC 2 s (q s ). (13) Were TC1 s (q s ) and TC2 s (q s ) in Eqs. (12) and (13) are te sipping and inventory costs for te feeder line. Moreover, te Pareto optimal solutions for te feeder line can be determined by sipping and inventory cost functions formulated and trade-off relationsip between tem. Te Pareto optimal sipping cost for sipping troug a ub is te Pareto optimal sipping cost of te feeder line added by a constant value, TC 1 t *(q ), and te Pareto optimal inventory cost for sipping troug a ub is te Pareto optimal inventory cost of te feeder line added by a constant value, TC 2t *(q ). Let TTC1 d and TTC2 d denote, respectively, te total sipping costs and te total inventory costs of direct line, main line, and feeder line for sipping flow qd directly. Ten, if te main line is serviced wit te minimum sipping cost, ten TTC1 d and TTC2 d can be expressed as TTC1 d = TC 1 t *(q q d ) + TC 1 s (q s q d )+TC 1 d (q d ), (14) TTC2 d = TC 2 t *(q q d ) + TC 2 s (q s q d )+TC 2 d (q d ). (15) Were TC1 s (q s q d ) and TC2 s (q s q d ) are te sipping and inventory costs of te feeder line, respectively; TC1 d (q d ) and TC2 d (q d ) are te sipping and inventory costs of te direct line, respectively. Since tere are trade-offs between sipping cost and inventory cost, te Pareto optimal solutions for tese two lines can also be determined by te cost functions formulated. Consequently, te Pareto optimal solutions for direct sipping can be determined. Tey are te Pareto optimal sipping costs of bot te feeder line and Feeder line, q s q d Fig. 3. Hub Spoe Main line, q q d Direct line, q d (a) Hub Feeder line, q s Hub Spoe Main line, q Te total flow on eac line: (a) part wit direct sipment; (b) all wit transsipment. (b) Hub

6 214 Journal of Marine Science and Tecnology, Vol. 13, No. 3 (2005) te direct line added by a constant value, TC 1 t *(q q d ), and te Pareto optimal inventory costs of bot te feeder line and direct line added by a constant value, TC 2 t *(q q d ). EXAMPLE A Transpacific containersip service from Far East to U.S. west coast is considered erein to demonstrate te application of te proposed model. Te sipping service is operated by an ocean carrier wo provides services using ub-and-spoe networs. Te sipping route of main line starts at Kaosiung, passes Busan, Los Angeles, Busan, Hong Kong, and bacs to Kaosiung, as sown on solid lines of Figure 4. Te objective of te example attempts to apply te proposed model to mae analyses about routing decisions on weter sipping containers from Manila, a major port in Pilippines, to U.S. west coast troug ub port, Kaosiung, or directly to U.S. west coast, as sown in Figure 4(a) and 4(b), respectively. Suppose tere are five types of sips used by te ocean carrier, and let T i (i = ) denote te types of sips from i = 1, te smallest, to i = 5, te largest. Table 1 sows te capacity, service speed, capital and operating costs, and fuel cost for eac type of sip. In addition, port carge on sip (α it, β it ) and loading/ unloading carges in port, G i, are estimated using port carge of Kaosiung Harbor (Kaosiung Harbor Bureau. MOTC, ROC [12]). Two-way flows between Kaosiung and Manila are estimated from data publised by Department of Statistics, MOTC, ROC [6], wile te oters are estimated from te data provided by Institute of Transportation, MOTC, ROC [10]. Besides, te average gross andling rate,, and te port arrival and departure time, W i, are estimated from te vessel arrival/departure time data of Kaosiung Harbor. Wen containers between Manila and U.S. west coast are transsipped troug te ub, Kaosiung, te minimum sipping cost of te main line is Table 1. Capacity, service speed, daily capital and operating cost, and fuel cost for eac type of sip Type of sips a T1 T2 T3 T4 T5 Capacity, U t (TEU) 1,810 2,728 3,428 4,211 5,652 Service speed, V t (nautical miles per day) a Daily capital and operating cost, S t (U.S. dollars) b 21,940 22,865 23,571 24,360 25,813 Fuel cost per nautical mile, F t (U.S. dollars) b Fuel cost in port, B it (U.S. dollars) b a Source: Five types of sips are currently used by Evergreen Marine Corporation, ttp:// b Source: Wang [20]. Busan Los Angles Busan Los Angles Kaosiung Kaosiung Hong Kong Manila 543 Hong Kong Manila (a) (b) Source of sipping distance: Caney and Reynolds [2]. Fig. 4. Te marine networs: (a) direct sipment; (b) transsipment. (number represent lin distance in nautical miles)

7 C.I. Hsu & Y.P. Hsie: Direct Versus Terminal Routing on a Maritime Hub-and-Spoe Container Networ U.S. dollars and te corresponding inventory cost of te main line is U.S. dollars. In addition, te Pareto optimal solutions of te feeder line are determined using Eqs. (4) and (9), and sown as: TC 1 s = TC 2 s 452,685 for 452,685 < TC 2s , TC 2 s 528,446 for < TC 2 s , TC 2 S 539,995 for TC 2 s , TC 2 s 452,685 for TC 2 s (16) Te Pareto optimal solutions for routing a sipment troug ub port, Kaosiung, are determined and sown in te objective value space in Figure 5. Te optimal sip size for feeder line associated wit eac Pareto optimal solution is also obtained. Tere exist tree types of sips in te Pareto optimal solutions. Te optimal sip size of feeder line is T4, T2 and T1, for tree cases tat te value of TTC2 t is witout constraint or constrained to be lower tan U.S. dollars; lower tan U.S. dollars; and lower tan U.S. dollars, respectively. On te oter and, wen containers between Manila and U.S. west coast are sipped directly, te minimum sipping cost of te main line is U.S. dollars, and te associated inventory cost of te main line is U.S. dollars. In addition, te Pareto optimal solutions of te feeder line and te direct line are determined using Eqs. (4) and (9), as follows: TC 1 s = 833, , , , TC 2 s 186,713 for 186,173 < TC 2s 515,127, TC 2 s 217,330 for 515,127 < TC 2s , TC 2 s 222,080 for TC 2 s , TC 2 s 186,173 for TC 2 s , (17) TC 1 d = TC 2 d for < TC 2 d , TC 2 d for TC 2 d (18) Te Pareto optimal solutions for routing a sipment directly to U.S. west coast are determined and sown in Figure 6. Te optimal sip size for bot feeder line and direct line are also obtained and furter sown in Table 2. Figure 7 sows bot Pareto optimal solutions for transsipment and direct sipping in one objective value space. For te range of inventory costs between and U.S. dollars, transsipment is preferred, wile for oters, direct sipping is preferred. Furtermore, te influences of flow on te optimal solution are analyzed. Suppose tat two-way flows between Manila and Los Angeles and between Manila and Busan are raised five times, wile te oters remain te same. Ten, te Pareto optimal solutions for bot routing a sipment troug Kaosiung and directly to Los Angeles are determined and sown in one objective value space (Figure 8). Figure 8 sows tat no matter

8 216 Journal of Marine Science and Tecnology, Vol. 13, No. 3 (2005) Te inventory costs for direct sipping Table 2. Te optimal sip size for direct sipping Optimal sip size TTC2 d Direct line Feeder line TTC2 d < T4 T < TTC2 d < T4 T < TTC2 d < T4 T < TTC2 d < T5 T < TTC2 d < T5 T < TTC2 d < T5 T4 Unit: U.S. dollars TTC1 t ($) T1 T2 T4 TTC1 ($) Direct sipping Transsipment TTC2 t ($) TTC2 ($) Fig. 5. Te Pareto optimal solutions for transsipment. Fig. 7. Comparing Pareto optimal solution between transsipment and direct sipping TTC1 d ($) (T4, T4) (T4, T1) wat te inventory costs are, te direct sipping is always te optimal routing decision. Te result sows tat te routing decision tends to sip sipment directly to its destination as container flow between origin and destination ports increases. CONCLUSION (T4, T2) (T5, T2) (T5, T4) (T5, T1) Fig. 6. Te Pareto optimal solutions for direct sipping. TTC2 d ($) Tis study developed a two-objective model by TTC1 ($) Direct sipping Fig. 8. Transsipment TTC2 ($) Pareto optimal solutions for transsipment and direct sipping as flow increases. individually minimizing sipping costs and inventory costs to decide weter to route a sipment troug a ub or directly to its destination. Te cost functions formulated erein are flow-dependent. Moreover, te sipping costs include capital and operating cost, fuel cost and port carge, wile te inventory costs include waiting time cost and sipping time cost. Based on a trade-off between sipping cost and

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