Slot Allocation Planning for an Alliance Service

Asia Pacific Management Review 15(3) (2010) 325-339

www.apmr.management.ncku.edu.tw

Slot Allocation Planning for an Alliance Service with Ship Fleet Sharing Hua-An Lua,*, Ching-Wu Chua, Pei-Yu Cheb a

Department of Shipping and Transportation Management, National Taiwan Ocean University, Taiwan b Intra Asia Export Consolidation Section, Sea freight Department, Kuehne + Nagel Ltd., Taiwan Accepted 18 March 2009

Abstract This paper addresses a slot allocation planning problem for an alliance service operated by a liner carrier and its partners. In practice, co-operative carriers share ship’s capacities according to the respective ratio of their contributed ships for the service, but they can trade the surplus or shortage slots. For each participated carrier, this essential decision relies on its appropriate slot allocation planning to match the expected level of carrying demand for various kinds of containers. From a participating carrier’s viewpoint, this research formulates a model to maximize potential profits in a round trip voyage by optimizing slot allocation and contributed ships. We apply our model to assess a short sea alliance service of the studied company and to conduct the post-analysis for some parameters. The solution results can provide a detailed allocation with a higher slot utilization rate. Furthermore, the influences of slot sale price and ship operating cost are also helpful to the studied company. Keywords: Slot allocation, alliance service, fleet sharing, short sea service 1. Introduction* Alliance co-operation has become a main and popular stream of managing strategies in the contemporary liner shipping industry. No matter large or small carriers, they often keep cooperative relationships with their partners on certain loops to extend their service scopes and to share the investment costs. Many concrete collaborative patterns can be adopted in practice, such as fleet sharing, slot charter, slot purchase, and slot exchange. Co-operation is a popular tool for a liner company because the essential aim in managing the available slot resources to procure potentially maximal revenues or profits is never changed. Before formally introducing a service to the markets, the liner company has to assess a suitable input level for its possible turnover. This issue must be solved along with the slot allocation planning, which means how to sufficiently allot various kinds of containers with different sizes, potential unit revenue or profit and origin-destination ports to the allowable ship capacities. Various alliance contents may bring more inherent restraints than the self-operated service. This paper explores how to manage the optimal slot allocation on an alliance service with fleet sharing from the main operator’s perspective. Shipping alliance is a prevalent issue in the contemporary liner service. Several studies have been devoted on the strategic alliances from different perspectives. According to an observation of Midoro and Pitto (2000), organizational complexity and intra-alliance competition were the main driving factors to yield the high degree of instabilities in the beginning of strategic alliances. Ryan (2001) examined the evolution of container shipping networks over a ten-year span from 1989 to 1999 for the influence of alliances. Slack et al. (2002) investigated the development of strategic alliances from the transformation of services, *

Corresponding author. E-mail: [email protected]

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H.-A. Lu et al. / Asia Pacific Management Review 15(3) (2010) 325-339

the evolution of the fleet, and the adjustments of calling ports. The research of Kadar (1996) disclosed that the purposes of alliance members are to effectively reduce costs, to increase the freight revenues without investing any more capital, and to enjoy economies of scale by sharing resources with other partners. Ryoo and Thanopoulou (1999) made a survey for motivations and successful reasons of various co-operative ways to the major Koreanoperated carriers. Slot allocation management deals with the container delivery plan for each phase of shipping. Much research has focused on the topics of container movement control and of empty container repositioning by either seaborne distributions (Gao, 1994; Shen and Khoong, 1995; Cheung and Chen, 1998; Li et al., 2007) or land transports (Crainic et al., 1993; Lopez, 2003; Jula et al., 2006). However, the availability of seaborne container movement depends on the planning of enough slot capacities. A few studies treated the slot allocation with the concept of revenue management or yield management (Maragos, 1994; Ha, 1994), but this method fits the application of the short-term planning in each voyage. Recently, Ang et al. (2007) presented a yield maximization problem in considering cargos with various consigned periods from one origin port to multiple destination ports. They formulated this problem as a multi-dimensional multiple knapsack model subject to the available empty containers, volume capacities and weight capacities. It can only be applied to the planning of outbound cargos for one loading port. To the best of our current knowledge, there is no description and formulation for the planning of alliance slot allocation. Ting and Tzeng (2004) described the slot allocation problem of the self-operating service and proposed an integer programming model to obtain ideal allocated results of single directional traffic flows. This model can be applied to the cases with the characteristics of the traffic pattern like a deep ocean service. Song and Panayides (2002) suggested observing the operations of liner shipping strategic alliances from a co-operative game theory. They presented simple examples for assessing better coalition services in the cases of two players and more than two players. This conceptual introduction cannot provide liner carriers a concrete planning procedure or structure in practice yet. Several studies have been devoted to the issues regarding container management and shipping alliance from different perspectives. However, little research has been done on dealing with the overall slot allocation decision under alliance practice. The purpose of this paper is to examine the relative factors that influence seasonal slot allocation with fleet sharing alliance practice. Hence, this research formulates a model to maximize potential profits in a round trip voyage with optimizing slot allocation and contributed ships for one of operators. We apply this model to an analysis for a short sea service loop by courtesy of the studied company. In this research, various categories of containers for multiple trades are considered. Some efforts obtained from the post-analysis of varying crucial parameters are also presented. 2. Problem description Slot allocation defined in this paper is an inner operation of the shipping company to evaluate the utilization of ship capacities in every period. It can be regarded as a long-term planning issue relative to the slot arrangement of each voyage. Anticipated market information and operational properties of the service dominate the decision results of slot allocation. In the following subsections, we state the insights of planning contents and practical procedures of the studied company that can provide a comprehensive realization of the studied problem.

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2.1 Influential factors of slot allocation Shipping companies procure revenues by providing stowage slots of deployed ships to accommodate various kinds of containers with different origin-destination ports (we refer to them below as port pairs) for deliveries. Carriers estimate the possible quantities of shipments in various markets to allocate ship capacities according to the level of service conditions and properties of consigned freight. Due to market segments, various kinds of containers have their own market prices, which are nothing to do with their sizes. Carriers can select containers with higher potential profits to increase their income as much as possible in case of a boom in carrying demand. However, the actual volume of cargo that a ship may carry is limited by its cubic capacity and its weight capacity. In cubic measure, twenty-foot equivalent unit (TEU) in length is the standard scale of the container ship. Other containers with forty or forty-five feet lengths occupy double spaces of one TEU, and some higher boxes or out-ofgauge cargos may even require more slots. On the other hand, the sum of total loaded weight cannot exceed the maximal availabilities of the deployed ship, i.e. its deadweight tons. Sometimes, the allowable loaded weight of the ship will be reduced for the draft limitation. This situation, in particular, may take place during the period of falling tide at a visiting port. Nevertheless, it is difficult for the carrier to precisely estimate the mix of whole ship’s consignment at planning. To assume each type of containers with the same port pair has homogeneous volume, weight and price is an acceptable way for planning stage. Besides, empty containers are the necessary equipment to load shipment, but the trade gaps among countries result in the imbalance of import and export containers. This phenomenon also affects the available numbers of reused boxes for the carrier. Some ports with a surplus of empty containers have to pay more costs to arrange their storages. Those places having a shortage of empty ones, on the contrary, need to lease the adequate numbers of containers for export loads. These routine patterns will impact the level of profits if shipping companies do not proceed any repositioning of empty containers. However, it is difficult to evaluate the contribution of any repositioned container in competing with the laden one simultaneously, because containers circulate around all of carrying channels to be reused in the transport system. Although appropriate empty container repositioning can reduce expenditures to increase profits just as laden ones earn revenues, the latter still has a priority to be loaded from the practical aspect. Finally, shipping companies must consider the transshipment containers which may be relocated from or transfer to other services. In the peak season, these kinds of containers may produce longer storage durations in ports with extra expenses, and even damage the reputation of the company. If the amount of transshipment can be estimated, it can be treated as the demand of general laden containers. However, this study only treats with the single loop service. The requirement can just take into account the port pairs between lifting and transshipped ports or between transshipped and destination ports of the operating line. 2.2 Rotated services A liner service has a characteristic of fixed timetables during week days for every visiting port. For fulfilling this operational requirement, shipping companies must deploy enough ships and arrange the sequential round trip voyages for every ship. Thus, each deployed ship executes a fixed and cyclical port rotation according to its own schedule. Intuitively, the carrier should allocate slots to those containers with higher potential revenue as many as possible for attaining the maximal revenues. However, the operational property drives the carrier to stand on the overall planning perspective because the loaded containers may occupy the finite ship capacities more than one sailing leg. This fact also means that some slots may have been occupied before loading up at port by those transit containers. If achieving the 327


maximal utilization of slots is expected, the ship must be fully loaded at every leg. In practice, it is almost impossible to control shipment as the carrier’s expectation. For obtaining a high utilization of slots, it is necessary to track delivery passages of containers for calculating loaded situation on each sailing leg. The relationships between port pairs of delivered containers and rotated service are illustrated by means of a round trip voyage with a port rotation of 1-2-3-4-2-1 as shown in Figure 1. This example has five sailing legs for five calls, and serves 12 port pairs because of visiting 4 different ports. Various categories of containers occupy the capacities of possibly passed legs according to their own shortest transit passages. This also implies that containers on board in each leg may come from various port pairs. If the service is an alliance one, the containers on board may belong to the different companies, such as partners A and B in Figure 1. Ship operator is in charge of making suitable stowage plan according to the contents of the alliance agreement. The decision of slot allocation must maintain the exact relationships between sailing legs and port pairs.

Figure 1. Containers allocated on board for the alliance example. 2.3 Practical slot planning in alliances The studied company planned a seasonal allocation depending on the planners’ experience and the market information provided from local agents. Besides considering the marginal contribution of outbound cargos, this company estimated the possible carrying demand with their sensitivities to the markets. A basic slot allocation table (BSA table) was made according to the country basis to display respective quotas of local agents for their freight 328


solicitation. This manner gives salesmen a few flexibilities in assembling various container categories to meet their shares, but the planning results evidently ignored the above mentioned factors regarding the slot allocation. In the fleet sharing alliance service, co-operative companies handle respective slot capacities in each voyage according to the ratio of their contributed numbers of ships. For example, an alliance weekly service with 28 days cycle time deploys 4 container ships with total contracted slots of 1,000 TEUs. Two companies contribute 1 and 3 ships, respectively. The first one will share 250 TEUs and release 750 TEUs to its partner on every leg. Each company will be able to allot their own controllable capacities, but the ship operator has to prepare the detailed stowage plan for all voyages of its served vessels. Although carriers follow the alliance coalition to share the slots of each deployed ship, they can further manage their slots flexibly through slot charter and/or slot purchase to/from their partners or even to the carriers outside the contract. The aim of these steps is to seek more profit besides satisfying their expected carrying demand. Before a new alliance loop being launched or an existing self-operated service being transformed, the shipping company has to draw up a well program for negotiating with its partners. This decision includes the desired number of contributed ships and the expected trades of slots. Slot allocation plan is a basic blueprint to guarantee the success of co-operation. 3. Model formulation The issue of managing slot resources for a carrier is to maximize the profits created from the available capacities shared from the contributed number of ships. The detail of allotment has to follow the basic characteristics of shipment carriage and the market values of slots. We assume that the carrier has sufficiently realized the related market information and the demand level for each category of containers on all of served port pairs, i.e. the given demand level is enough to reflect the market situation faced by the carrier. No matter laden and/or empty containers, each category has homogeneous conditions, such as prices, handling costs, weights and so forth, on the same port pair. Thus, the empty and laden containers with same size can be considered as the different categories. In addition, since liner carriers must plan the transshipment ways for this kind of containers on each line prior to practical operation, we assume the demand quantities from the origin port to the transshipped port or from the transshipped port to the destination port have been included in the estimated delivery quantities of which port pair. The notation used in the formulated model is listed as follows. Sets C E H R Ak

Set of index for all container categories. Set of category index for empty containers. Set of category index for laden containers. Set of category index for laden reefer containers. Set of port index for those required to reposition out empty containers of category k, k ∈ E. Lk Set of port index for those required to reposition in empty containers of category k, k ∈ E. Decision variables k xod

Allocated numbers for category k containers delivered from port o to port d.

329


q

Sold slots in TEU. n Purchased slots in TEU. v The number of contributed ships. a A conflicted variable to distinguish the decision from selling or purchasing slots, 1 for prohibiting from sale, and 0 for prohibiting from purchase. Parameters k p od

k cod

α ods tk k wod l odk k uod

bok mdk

U Z DWTs r

e

β N M

Estimated average unit price for category k containers delivered from port o to port d. Estimated average unit variable cost for handling category k containers delivered from port o to port d, which includes stevedoring charge, document fee etc. An incident parameter to represent if the delivery for the trade of port pair (o, d) passes leg s, 1 for yes, 0 otherwise. Capacities occupied in TEU per container of category k. Average weights in ton per container of category k carried for port pair (o, d). Estimated lower bound of carried category k containers delivered from port o to port d, k ∈ H. Estimated upper bound of carried category k containers delivered from port o to port d, k ∈ H. Maximal number of empty containers of category k could be repositioned out from port o on this service, k ∈ E. Maximal number of empty containers of category k required to be repositioned into port d on this service, k ∈ E. Nominal capacities in TEU of the deployed ship. Number of plugs on board for laden reefer containers. Maximum available deadweight in ton on leg s. It may be decreased for the draft limitation of the departure or arrival ports of the leg s. Possible revenue per TEU for sale on this loop. Possible cost per TEU to purchase from partners on this loop. Ship operating costs for one deployed ship in one round trip voyage, which include the capital, bunker, and port cost items relative to the ship’s expenses. Number of deployed ships for running the service. A big enough number.

The formulated model aims to maximize the predicated profits in a round trip voyage from a ship operator’s perspective. For assessing the economic number of contributed ships, the shipping company must take into account the operating costs of contributed ships which are shared by the ratio of the deployed numbers. The complete formulation is as follows. Max.

∑ ∑( p k∈C ( o , d )

k od

k k − cod ) xod + rq − en − β

v N

(1)

s.t.

∑ ∑α k∈C ( o , d )

k t xod ≤

s k od

v ×U − q + n N

∀s

330

(2)


∑ ∑α k∈C ( o , d )

s od

∑∑ α

k∈R ( o , d )

k k wod xod ≤

v q−n DWTs − DWTs N U

k xod ≤Z

∀s

s od

∀s

(3) (4)

v≤N

(5)

v ×U N v n ≤ (1 − ) × U N n ≤ Ma

(8)

q ≤ M (1 − a)

(9)

q≤

k k lodk ≤ xod ≤ u od

(6)

(7)

∀(o, d ) , k ∈ H

(10)

∑

k xod ≤ bok

∀k ∈ E , o ∈ Ak

(11)

∑

k x od ≤ mdk

∀k ∈ E , d ∈ L k

(12)

d ∈L k

o∈A k

k a ∈ {1, 0} ; xod , q , n , v ≥ 0 and integer

(13)

The objective function of Equation (1) maximizes the sum of estimated profits, including freights from various types of containers, the revenues from slots for sale, the costs of slot purchase, and the share of ship operating costs from the contributed ratio in a round trip voyage. Equation (2) enforces that the sum of loaded containers owned by this company cannot be over the available capacities on each sailing leg, as well as Equation (3) restricts the loaded weights. Laden reefer containers need electronic power to keep suitable temperature on the way, but the number of power plugs installed on board is limited. This constraint is expressed in Equation (4). Equation (5) ensures that the number of contributed ships cannot be more than the total required ships for deploying on this service. Equations (6) and (7) limit that the quantities of selling and purchasing slots cannot be over the maximal amounts on this service, respectively. Equations (8) and (9) produce a switch decision either selling or buying. Only one of the two situations can occur, but never both. Equation (10) indicates the lower and upper bounds of allocated slots for laden containers of various categories and port pairs. Equations (11) and (12) ensure that possible carriage of empty containers cannot exceed the maximum number of empty containers that can be repositioned from port o or repositioned into port d, respectively. Equation (13) is the nonnegative and integer constraint of variables. This model is an integer programming (IP) problem. The number of variables is the product of the number of container categories and the number of port pairs. If the considered route with S legs visits N various ports, there are N × (N – 1) port pairs of shipments at most. While K categories of containers are involved, this problem will have K × N × (N – 1) + 4 variables. The number of constraints is 3S + 5 + K × N at most excluded the upper and lower bounds of variables. As we know, the length of a route has around 20 legs and 15 various ports at most in the studied company. The categories of containers are also finite. Thus, we estimate the number of variables is around 1,000, and the number of constraints is less than 200 for the practical cases. This scale of the IP problem might be solved within an acceptable CPU solution time by the traditional algorithm, such as the branch-and-bound method. If the 331


k scale of an instance is too large to solve within a reasonable time, we suggest relaxing xod into the real for rounding off the solution by cutting down the fraction. The integer variables are reduced to 4. This simple treatment can obtain a feasible solution because all of slot constraints are less than or equal to the right hand side except the lower bounds for variables.

4. Application

We applied our formulation to a short sea service of the studied shipping company. The related data by courtesy of this company were keyed into the problem generator programmed with the Microsoft Visual C++ 6.0 and the model was solved by the commercial optimization package CPLEX 9.0. 4.1 Background of analyzed case The test route, JTC, was self-operated at its beginning, but the performance did not reach the expectation of the studied carrier. Therefore, it was gradually adjusted into an alliance service with selling some slots to other partners. This line visits 12 ports among Japan, Taiwan, Hong Kong, and Thailand with 16 sailing legs, and its port rotation is: Tokyo (TYO) – Yokohama (YOK) – Nagoya (NGO) – Osaka (OSA) – Kobe (UKB) – Oita (OIT) – Keelung (KEL) – Kaohsiung (KHH) – Hong Kong (HKG) – Laem Chabang (LCB) – Bangkok (BKK) – Laem Chabang – Hong Kong – Kaohsiung – Taichung (TXG) – Keelung – Tokyo. This loop as shown in Figure 2 can be divided into south and north bounds from the naturally geographical direction, but some legs are classified as both directions for the sake of its rotation. This service with a cycle time of 28 days is deployed 4 full-container vessels with 1,445 TEUs of nominal capacities operated by the studied company entirely for weekly service. However, this company used 1,100 TEUs to plan for its own loads and the partners’, and the left capacities are reserved for empty containers and extra flexibilities. The maximum available deadweight of this kind of fleet is 15,400 tons, and the number of reefer plugs is 100 for each ship. The studied company shares 675 TEUs from the total in each voyage. TYO

Japan UKB

OIT

YOK OSA

NGO

Hong Kong HKG

TXG

Thailand

KEL

Taiwan South bound KHH

BKK

North bound South and north bound

LCB

Figure 2. Port rotation of the JTC service of the studied company. Besides the general types of containers, the studied company also accepted few of 20-foot open top, flat rack, and tank containers. For the sake of simplicity, we combine these out-ofgauge ones into the category of special containers. The weights of loaded cargo in each type of containers are all different, so we use the average value for each involved category provided by the studied company. A container with higher cubic volume is counted as 2.25 332


Table 1. Data of weight and volume for all categories of containers. Category code

20’ D

40’ D

20’ R

40’ R

20’ E

40’ E

20’ special

4

40’ HQ 40’ higher cube 23

Container type

20’ dry

40’ dry

20’ reefer

40’ reefer

20’ 40’ empty empty

Weight (ton)

17

23

17

23

2

Volume (TEU)

1

2

1

2

1

20’ S

2

2.25

1

17

TEUs because this kind of containers normally occupies over a little of two slots. Table 1 shows the involved categories and their data on weights and volumes. Cost data are always confidential for any company. We made some assumptions based on the suggestion of the studied company, such as the unit handling costs of 40-foot dry and higher cube containers are 1.5 times of that of the 20-foot dry containers. The cost per empty container is 50% of that of the 20-foot dry container because empty boxes have no insurance, commission, and weighting fees. Although the cost of the reefer is slightly more than that of the dry container, we assume their costs are the same. But the cost of the special container is 50 US dollars more than that of the dry container for the requirement of the exclusive equipments in handling. For ease of calculating the contribution of empty containers, we use the extra rent at port with a shortage of containers as the price of repositioning one empty container into that port. The planned demand quantities of carrying containers were provided from the studied company. Deliveries of laden containers are not allowable among intra-country port pairs in Japan and Thailand due to the limitation of the cabotage right, but empty containers are excluded. In addition, port of Kaohsiung is a main load and repositioning center of the studied company. Thus, excess empty containers on the line are delivered to this port as many as possible in its empty equipment reposition policy. 4.2 Results and discussion This problem has 1,061 variables and 73 constraints, and it took 8.4 CPU seconds to be solved. The objective value is USD 201,551. Table 2 summaries the solving result and compares it with the current status of the studied company. The company can contribute 2 ships under such carried demand level if any partner intended to share other 2 ships. Therefore, controllable slots of this carrier are 722 TEUs, and 132 TEUs of which can sell to its partners based on the price per slot for sale. The studied company can still maintain 590 TEUs in a voyage for its own loads including empty containers. Apparently the company holds too many slots than the actual carried in current status. The reason for this is that it contributes all the service ships. On the other hand, its partners would prefer to purchase slots than to share fleet. Table 2. Comparisons of solving results and the current status. Current status Solving results Contributed ships 4 2 Shared ships 0 2 Price per TEU for sale and purchase $300 $300 Controllable slots (TEUs) a 1,100 722 Sold slots (TEUs) 425 132 Utilized slots (TEUs) b 675 590 a b

As mentioned in context, the calculated bases of controlled slots are different for two cases. Empty containers are not involved in current status of the studied company.

333


The detailed allocation of the solution as shown in Table 3 reveals that some legs indeed reach full shared load limitation on volumes (590 TEUs) or weights (7,688 tons), such as legs 5, 8, 12 and 16. Dry cargos are the most important carrying sources on this service. The majority of slots are occupied by the 40-foot dry containers on legs between TYO to KHH (legs from 1 to 7) as well as between BKK to HKG (legs from 11 to 12). On the contrary, legs between KHH to BKK (legs from 8 to 10) and between HKG to TYO (legs from 13 to 16) should carry more 20-foot dry cargos than others. Moreover, slots distributed to 40-foot higher cube containers share a major part but legs between BKK to KHH are excluded. The leg LCB-HKG requires 78 slots for the 40-foot reefer containers, and other legs keep less for this category. There are no more than 13 TEUs assigned for 20-foot special and reefer Table 3. Slot occupied results for all sailing legs. Legs Container category

1 2 3 4 5 6 TYO ~ YOK ~ NGO ~ OSA ~ UKB ~ OIT ~ YOK NGO OSA UKB OIT KEL 20’ D 75 71 57 68 82 86 40’ D 53 101 96 98 100 95 20’ R 5 4 3 1 0 0 Laden 40’ R 39 37 35 35 32 32 20’ S 3 0 8 8 8 12 40’ HQ 56 49 58 83 89 91 20’ E 15 15 15 15 15 8 Empty 40’ E 10 10 10 10 10 0 Total weights 4885 5646 5573 6347 6683 6696 (tons) Total boxes 256 287 282 318 336 324 Total TEUs 428 497 496 565 590 565 Legs Container 9 10 11 12 13 14 category HKG ~ LCB ~ BKK ~ LCB ~ HKG ~ KHH ~ LCB BKK LCB HKG KHH TXG 20’ D 160 132 41 122 117 149 40’ D 95 78 84 155 102 70 20’ R 1 1 0 0 0 10 Laden 40’ R 10 6 8 78 26 17 20’ S 2 1 2 2 2 2 40’ HQ 70 55 0 0 0 31 20’ E 0 0 0 0 150 0 Empty 40’ E 0 0 0 0 0 0 Total weights 6796 5475 2847 7467 5267 5451 (tons) Total boxes 338 273 135 357 397 279 Total TEUs 531 426 227 590 525 405

334

7 8 KEL ~ KHH ~ KHH HKG 57 144 64 117 0 0 16 0 5 2 88 93 0 0 0 0 4918

7312

230 420

356 590

15 16 TXG ~ KEL ~ KEL TYO 167 180 84 96 12 13 32 47 5 5 43 45 0 0 0 0 6785

7688

343 513

386 586


containers on each leg. As for the empty container repositioning, TYO can shift 7 20-foot boxes and 10 40-foot boxes to OIT, and 8 additional 20-foot boxes to KEL. Furthermore, the leg HKG-KHH can reserve 150 slots for the 20-foot empty containers. With reference to the slot distribution for various container categories between port pairs in detail, we collected the allocated results of south and north bounds for various countries as displaying in Tables 4 and 5. In comparison with the original BSA of the studied company, there are slightly differences in the allocated slots between countries. This company may reduce some capacities allocated to the trades from Japan to Hong Kong for shifting a few of capacities to the markets between Japan to Taiwan, and increase more slots for the markets between Taiwan to Hong Kong in the south bound carriage. In the north bound, the company can deduct slots of the export in Hong Kong to replace to the markets from Taiwan to Japan and the reposition of empty containers. Based on these comprehensively allocated results, the company can understand the real sources of profits and design its slot control policy under current demand level. Table 4. Comparisons of the south bound slot allocation. Unit: TEU

Original country Japan Current plan

Solving result

Destination Country Hong Taiwan Thailand Kong 305 290 80

Taiwan

60

Hong Kong

Loads

Empty

Total used

675

675

245

305

305

224

224

150

374

Sum

305

350

549

1204

150

1354

Japan

332

169

57

558

8 + 34a

600

135

229

364

364

248

248

248

534

1170

Taiwan Hong Kong Sum

332

304

42

1212

a

34 TEUs for empty containers are repositioned from Tokyo to Oita, and another 8 TEUs are moved from Tokyo to Keelung.

Table 5. Comparisons of the north bound slot allocation. Unit: TEU

Original country Thailand Current plan

Solving result

Destination Country Hong Taiwan Japan Kong 250 265 60

Hong Kong

100

Taiwan

Loads 575

150

250

365

365

Sum

250

365

575

1190

Thailand

262

269

59

590

2

45

47

482

482

586

1119

Hong Kong Taiwan Sum

262

271 335

Empty

Total used 575

35

285 365

35

1225 590

150

197 482

150

1269


The satisfying level of allocated results against demand bounds of port pairs for each category of containers, as shown in Table 6, can be used to assess the application of ship capacities. We find that each port pair is allotted either reaching the top or touching the bottom of demands for all of port pairs, and all of categories are satisfied above 90% to have highest allowances. Reefer and 20-foot special containers even attain 100% of upper bound distribution. These results imply that the most container categories at various markets can bring profits but a few port pairs just require satisfying their lowest demand. To reduce some loads at few segments instead of selling capacities to the partners will bring more income for the company. Meanwhile, it also discloses that the optimal results can not be obtained just with distributing slots to the container categories of the higher unit profit sequentially without considering the operational properties from the port rotation of this service. Otherwise, the allocated slots of the categories with higher unit profit like 40-foot dry and higher cube containers are supposed to be entirely allocated with their upper bounds of demands on all of markets. Table 6. Allocated ratios of satisfying carrying demands for laden containers. Container category Number of allocated port pairs Number (ratio) of allocating to the lower bound Number (ratio) of allocating to the upper bound

20’ D

40’ D

20’ R

40’ R

40’ HQ

20’ S

54

49

7

24

32

6

4 (7.4%)

1 (2.0%)

0

0

2 (6.3%)

0

50 48 7 (92.6%) (98.0%) (100%)

24 30 6 (100%) (93.7%) (100%)

4.3 Slot sale price analysis The above results reflect that the decision of contributing two ships is sufficient enough to satisfy the current carrying demands and have some additional slots for sale. An interesting issue of how much the sale price per TEU in the market can change the decision is further analyzed. We add 50 US dollars per time to solve the model, while other parameters remain

280,000 270,000 260,000 250,000 240,000 230,000 220,000 210,000 200,000 190,000 180,000

Sold slots 272,249 926 245,611 236,759 228,859

221,843 215,021 208,271 201,551

135

135

137

144

162

191

132

300

350

400

450

500

550

600

650

Slot price for sale ($ per TEU)

Figure 3. Influences of changing slot price for sale. 336

1,000 900 800 700 600 500 400 300 200 100 0

Slots (TEU)

Objective ($)

Objective


the same as the original problem. As shown in Figure 3, the objective value increases gradually with around 3.5% until selling price of slot is changed to $600. More of this price, the objective has a great jump for the next increment. However, the number of sold slots only has a bit of increasing at the slot price below $450, and then the growing tendency is obvious as the consecutive increments larger than it. As well as the objective, the sold slots have a great expansion when the selling price of slot is increased to $650. The reason comes from the number of contributed ships is increased to 4, the whole of the deployed fleet. The company can own all of the ship’s capacity to sell more to its partners. As displayed in Table 7, by varying the selling price of slot from $600 to $650, we find that the critical price changing the number of contributed ships is $627. This price exactly equals to the result of dividing ship operating costs of one ship by its total capacity, i.e. β / U . Intuitively, the carrier would like to contribute more ships when the income from selling slots can cover the operating costs of ships. Under the assumption of sufficient purchasing requirement for slots in this paper, the decision of directly increasing the number of contributed ships to 4 at the selling price of slot higher than the critical one is without doubt for selling more slots as many as possible. Table 7. Analysis for the critical slot price for sale. Slot price for sale ($) 600 610 620 627 630

640

650

Objective ($) 245,611 247,507 249,549 250,995 253,729 262,989 272,249 Sold slots (TEU)

191

192

200

922

926

926

926

Contributed ships

2

2

2

4

4

4

4

4.4 Ship operating cost analysis Ship operating cost affects the number of contributed ships for it concerns whether the carrier can obtain the return of investment. This cost varies with different companies because they use the owned or chartered ships with a higher or lower performance in fuel consumption. We hence employed post-analysis to explore how ship operating cost influences the optimal

500,000 450,000 Objective ($)

400,000 350,000 300,000 250,000

Sold slots

476,411 426,551 8 52 401,551 376,551 351,551 326,551 301,551 276,551 251,551 226,551 201,551

200,000 1 32 1 32

1 32

1 32

1 32

1 32

1 32

1 32

1 32

900 800 700 600 500 400 300 200

1 32

150,000

100 0

50

100

150

200

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300

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450

Reduced amount for ship operating cost (thousand $)

Figure 4. Influences of changing ship operating costs. 337

500

Slots (TEU)

Objective


decision of slot allocation. We reduce ship operating costs with an amount of $50,000 per case and find that the objective has a linear increment caused from its effect directly when the number of contributed ships remains the same. The number of sold slots remains the same as shown in Figure 4. When the deducted amount reaches $500,000, 4 ships are commendable to enter this service. Additional analysis shows the number of contributed ships will become 3 when operating costs are reduced by $470,000. The operating cost item is not so significant to impact the decision at a given demand level. It is better for the carrier to arrange slot allocation well to satisfy the carrying demand in a suitable input level. Actually, different operating costs will also affect the willingness of other carriers to share ships for operation by themselves. It impacts the market prices of the possible revenue and cost for sale and purchase of unit slot (r and e) as well. The formulated model can obtain the optimal results by varying multiple parameters simultaneously although this analysis was not presented in this paper. In practical operation, it is known that carriers will take the risk management for controlling the stable fuel price. The formulated model proposed in this paper can help carriers to assess the confronted situation for each line. In particular, keeping a sustaining service without withdrawing at random is the main objective of most of carriers. More post-analysis can provide the carrier more insights of precise influence in finance. 5. Conclusions and suggestions

In the seasonal slot allocation planning, the shipping company has to decide the quotas for their local agents in consigning export cargos as well as to estimate the level of possible profits or revenues that the company might achieve. In this paper, we focused on an alliance route with fleet sharing and constructed a mathematical model for a main-operated carrier to plan the slot allocation and the number of contributed ships. The results can decide an optimal distributed outcome of the available capacities on a ship, which is even more detailed than that of the studied company, to meet the practical requirement on an alliance line. This model can be applied to plan a new launching alliance loop or to transform an existing self-operated service into a fleet sharing alliance. Ideally, the carrier can use it to examine each alliance route. From the perspective of long-term planning, our formulation can also assist a carrier to assess if the number and the size of the deployed ships satisfy the current level of carrying demands on a service. It will also be a fundamental to handle slot control decision in each voyage. From this research, some valuable observations in practice were found and summarized as follows. (a) The carrier is able to exploit the available slots for satisfying its own carrying demands as possible then to consider other slots else for sale in an alliance service. The categories of containers with high unit profits may have higher priorities for allotting sufficient capacities, but the operational properties from port rotation of the service can not be neglected. (b) The operating costs relative to the ship’s investment and handling is a key factor to decide the number of contributed ships. Unless the income from raising the selling price of slot can cover the operating costs, the carrier is not recommended to contribute more ships. (c) Ship operating costs will affect the carrier’s profits, but it is not significant to change the slot allocation, sold slots and the number of contributed ships. The market situation of the liner shipping industry is full of variation. The fluctuation of carrying demand is a crucial issue relative to the slot management of liner companies. Our model can be further applied to control some parameters, such as the estimation of sold slots 338


and various seasonal changes of carrying demand. Future works can be devoted to integrating the uncertain estimation into the slot allocation problem. Furthermore, different types of alliance patterns between liner carriers with more complexities of slot management provide researchers several valuably studied topics e.g. slot exchange and cross-slot charter. Finally, the globalization network of the liner company also needs more supports of slot management analysis, especially to the routing problem of transshipment containers. References

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