Analysis of liner shipping networks and transshipment flows of potential hub ports in sub-Saharan Africa

Transport Policy 69 (2018) 193–206

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Transport Policy journal homepage: www.elsevier.com/locate/tranpol

Analysis of liner shipping networks and transshipment flows of potential hub ports in sub-Saharan Africa

T

Hwa-Joong Kima, Jasmine Siu Lee Lamb, Paul Tae-Woo Leec,∗ a

Asia Pacific School of Logistics, Inha University, Republic of Korea School of Civil and Environmental Engineering, Nanyang Technological University, Singapore c Maritime Logistics and Free Trade Islands Research Center, Ocean College, Zhejiang University, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Sub-Saharan Africa Liner shipping network Transshipment Container hub port Maritime Silk Road Belt and Road Initiative

Owing to growing economic growth in tandem with regional economic developments on the route connecting Asia and sub-Saharan Africa (SSA), several countries in the SSA region such as South Africa have been developing container ports. This paper analyzes potential trunk line routes and transshipment flows that could be captured by potential hub ports in the SSA region. To this end, integer programing models are developed to represent liner shipping networks in the SSA region and a wide variety of numerical experiments based on realistic data are conducted for the SSA-Europe and SSA-Asia trade routes. This paper draws various meaningful policy and managerial implications through scenario analyses such as the effects of network evolution, different vessel sizes and speeds, carbon taxes and insights in association with the 21st Century Maritime Silk Road initiated by China.

1. Introduction Maritime connectivity among economic regions propels trade activities and economic development. A new initiative called the “Silk Road Economic Belt and the 21st-Century Maritime Silk Road”, in short “Belt and Road”, was proposed by China in late 2013. This initiative aims to strengthen the economic and maritime connectivity among Asia, Europe, and Africa. Furthermore, China has been very active in developing the China-Africa-South America (CASA) routes in recent years (Chen et al., 2013; Lee, 2015). Remarkably, South Africa is a growing economic region with much potential in maritime trade and logistics given these new developments in tandem with infrastructure development in her neighboring countries led by Chinese government (Lee, 2015; Ng et al., 2018). On the other hand, the route passing beside Cape Town could be a competitive alternative to the Suez Canal route, which is currently a major shipping route for vessels navigating on the Asia–Europe trade lane (Notteboom, 2011). This argument is supported by heightened security threats to piracy acts towards vessels on the Suez Canal route, the limited capacity of the Suez Canal route, and the expected economic growth in the future of the regions located on the Cape Town route such as sub-Saharan Africa (SSA) and South America (Lam and Dai, 2015; Lee and Lee, 2012; Notteboom, 2011). The SSA region is geographically the area of the African continent that lies south of the Sahara Desert. In

∗

Corresponding author. E-mail address: [email protected] (P.T.-W. Lee).

https://doi.org/10.1016/j.tranpol.2018.05.018 Received 10 January 2018; Received in revised form 29 May 2018; Accepted 30 May 2018

Available online 06 July 2018 0967-070X/ © 2018 Elsevier Ltd. All rights reserved.

order to make the Cape Town route more competitive, major hub ports need to be developed to serve the SSA region by mainline-feeder operations and to serve the trade between South America and Asia by interlining/relay operations (Fraser et al., 2016). To this end, South Africa announced a double hub port strategy in which the new port of Ngqura and the biggest port in SSA of Durban will be hub ports. As a result, the Port of Ngqura is being developed at a scale of five times its originally anticipated capacity (Notteboom, 2011). Under this maritime environment change in the SSA region, this paper aims to analyze liner shipping networks and transshipment (T/S) flows of potential hub ports in the region including the two ports in South Africa. Note that the geographical boundary of this research is only within the SSA region and hence the analyzed cargo flows are those towards/from ports in the SSA region. That is, the cargo flow comparison between the Cape Town route and the Suez Canal route is out of scope of this research. Specifically, this paper analyzes cargo flows, especially T/S volume at potential hub ports, truck line routes through potential hub ports, and the number of vessel calls per week for the trades of SSA-Europe and SSA-Asia. To this end, this paper develops integer programing models in order to draw meaningful policy and managerial implications. Although the issues tackled in this paper are strategic and policy-oriented that the maritime society would be interested in, we consider operational decision issues such as the route of liner vessels to draw useful insights for the SSA maritime transport

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H.-J. Kim et al.

Fig. 1. Illustration of the liner shipping network in SSA.

network, as in Wang and Cullinane (2014) and Yang and Chen (2016). The objective of the model is to minimize the transportation cost, including liner vessels’ port tariff, operating cost, vessel time cost, bunker cost, carbon tax, and feeder cost. In the perspective of modeling, the model in our study is an integrated model for shipping network design, vessel fleet deployment, and container cargo routing with T/S operations for liner vessels. The shipping network design problem is to determine a set of shipping routes, the fleet deployment problem is to assign a number of vessels over the shipping network, and container routing problem is to assign containers over the shipping network. A number of articles have reviewed these topics, e.g., Brouer et al. (2014), Christiansen et al. (2004, 2013), Lee and Song (2017), Meng et al. (2014), and Tran and Haasis (2015). Since these decision issues are very traditional issues in liner shipping firms as can be found in the survey papers, recent studies (e.g., Song and Dong (2013), Tran (2011), Wang and Meng (2012)) incorporate more detailed issues such as multiple T/S operations, container loading/unloading and new factors such as ship sailing speed, empty container repositioning. However, since the aim of our study is to analyze policy-oriented and strategic issues in SSA such as T/S volume at SSA hub ports, cargo flows along the SSA shipping network, not decision issues in a shipping firm considered in most of previous research, our study focuses on developing aggregated models by considering simplified operations such as single T/S operation between a liner route and feeder route, simple feeder route instead of detailed models developed in recent studies. Nevertheless, our study has meaningful contributions as follows:

•

This paper is organized as follows. Section 2 describes a potential liner shipping network in the SSA region and Section 3 illustrates the model formulation. Section 4 describes the data used in the numerical analysis and Section 5 the experimental results and their policy and managerial implications. The final section concludes by offering future research directions. 2. Potential liner shipping network in the SSA region As mentioned above, maritime trade flows increasingly link to Africa and evolve new shipping patterns. SSA is well positioned and South Africa sees the potential for developing a T/S center (Lee et al., 2009). A key concept of T/S is the shipping network (Lam, 2016). Thus, it is important to analyze the existing and potential shipping routes involved in SSA. This section illustrates a potential liner shipping network in the SSA region considered in this paper. Instead of using a detailed network, which is complex and hence almost impossible to formulate using a mathematical model, we use a simplified network consisting of major shipping routes in order to formulate it by mathematical models. Fig. 1 shows the ports selected for this analysis. Fourteen ports were selected in the SSA region based on cargo throughputs: Abidjan, Cape Town, Dakar, Dar es Salaam, Durban, Lagos, Luanda, Maputo, Mombasa, Ngqura/Port Elizabeth (NQ/PE), Port Louis, Walvis Bay, Tema, and Toamasina. Two ports were selected as representing ports for Europe and Asia: Las Palmas and Singapore, respectively. We considered six potential hub ports based on cargo throughputs and the advice of experts in the SSA maritime industry, which may compete against one another for capturing T/S cargoes in SSA; these are Dakar, Durban, NQ/PE, Maputo, Port Louis, and Walvis Bay, depicted as double circles in Fig. 1. Note that the models developed in this paper decide the hub ports out of the six potential hub ports and hence a potential hub port becomes a non-hub port if it is not selected as a hub port by the model. To represent real trade routes in the SSA region, the

• The fleet size (number of vessel calls per week) of a liner vessel is

• •

size-based cost) have not been considered in a model in the literature to the best of our knowledge. Most importantly, we have found no studies exploring the liner shipping network of SSA or South Africa except for Notteboom (2011), who applied multi-criteria analysis to the location of the hub port in South Africa, and Notteboom (2012), who compared the Cape route and the Suez Canal route using transit time and cost analyses. This study, therefore, intends to fill a gap in the literature.

determined using a round-trip time of the vessel in most of related studies. To our analysis, the fleet size should be determined using both a round-trip time of the vessel and the container demand because considering only one of them results in model infeasibilities in terms of vessel capacity or a weekly-shipping service. However, our study determines the fleet size using only container demand because the container shipping network in our study is a simplified one focusing on the trade between SSA and Asia or Europe. Our study considers the fleet size-based cost in the model objective function instead of the volume-based cost considered in most of related studies. The fleet size-based cost is computed as the number of deployed vessels multiplied by the unit variable cost, while the transport volume-based cost as the transport volume. The two aspects (container demand based-fleet size and the fleet 194

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by mega-vessels or any port in SSA calling at by conventional vessels and the feeder port is a port not calling at by mega-vessels or conventional vessels. Based on this assumption, the total feeder cost is calculated by the feeder cost per TEU and the T/S container amount. Feeder cost per TEU is calculated by assuming that the cost is proportional to the size of a feeder, e.g., bunker cost per TEU for the feeder, bcTEU , is f calculated by dividing bunker cost per TEU for the feeder by the car= bcf /(pc⋅cf ) . Using the same rying capacity of the feeder, i.e., bcTEU f idea, the other costs and times per TEU for the feeder with superscript TEU in the below equations are calculated as follows.

region was divided into two sub-regions according to Drewry Maritime Research (2012): West-SSA and South-East SSA. Ports in West-SSA are Abidjan, Dakar, Lagos, Luanda, Tema, and Walvis Bay. Ports in SouthEast SSA are Cape Town, Dar es Salaam, Durban, Maputo, Mombasa, NQ/PE, Port Louis, and Toamasina. We assume that the container cargoes are transported by four types of vessel: a mega-vessel, two types of the conventional liner vessel, and a feeder vessel. The conventional vessel is the liner vessel with the conventional size currently navigating on SSA trade routes. According to the current routes and sizes of vessels summarized in Drewry Maritime Research (2012), we assume that the conventional vessels with different sizes navigate in the two SSA sub-regions, i.e., one calls at ports in West-SSA and the other at ports in South-East SSA. Sample routes of the vessels on the SSA-Asia trade are depicted in Fig. 1. In the figure, thick solid arrows represent the route of the mega-vessel, thin solid arrows the route of the conventional vessel, and dotted arrows the route of feeders. That is, the mega-vessel calls at multiple ports: Port Louis, Durban, and NQ/PE. The conventional vessel calls at ports of Port Louis, and Dar es Salaam. The feeder vessel heading for South-East SSA calls at ports of Maputo and Dar es Salaam, and the feeder heading for West-SSA calls at ports of Cape Town, Walvis Bay and Luanda.

dcTEU = f

dcf pc ⋅ cf

, ptiTEU =

pti , pc ⋅ cf

ct TEU = f

ct f pc ⋅ cf

, mcifTEU =

mcif pc ⋅ cf

where dcTEU is the daily operating cost and charter rate per TEU for the f feeder, ptiTEU is the port time per TEU at port i, ct TEU is the daily carbon f tax per TEU for the feeder, and mciv is the marine charge of a vessel of type v at port i. Then, the total feeder cost per TEU is calculated by

∑

) fcij = (bcTEU + dcTEU + ct TEU f f f

k ∈ Pi → j

lk , k n + dcTEU f 24spf

∑

ptkTEU

k ∈ Pi → j

+ mcifTEU + mcTEU + 2hci jf wherePi → j is the set of all ports from port i to j calling at by the feeder, k n is the port which the feeder visits just after visiting port k, and 24 is the number of hours per day. In the equation, the first term implies the sum of the bunker cost, operating cost, charter rate, and carbon tax per TEU when the feeder sails from port i to j and the second term implies the operating cost and charter rate during the port time at all ports called at by the feeder. When a container is imported, it is transshipped at a T/S port from a conventional/mega vessel to a feeder vessel heading for its destination port, while vice versa when it is exported. That is, the container is transshipped once at the T/S port. It should be noted that the assumption of the single T/S operation is based on several previous studies (e.g., Aversa et al. (2005) and Gelareh and Pisinger (2011)). It is also assumed that the T/S of containers carried by a conventional vessel can occur at any port, while the T/S by a mega-vessel can only occur at a potential hub port. The T/S operation can be formulated by the following equations:

3. Model formulation The model developed in this paper is used to determine the amount of container cargoes transshipped or delivered directly, the number of vessel calls per week, and the routes of the mega-vessel and the conventional vessels. We assume that the mega-vessel can only call at the competing potential hub ports, e.g., Dakar, Walvis Bay, NQ/PE, Durban, Maputo, and Port Louis, whereas the conventional vessel and feeder vessel can call at all SSA ports. Note that the notations used in this section are summarized in Appendix A. The model in the current study is based on the carriers' perspective since the model is used to analyze how carriers will make routes and which ports carriers will select for T/S under various scenarios. Therefore, carriers choose vessel routes and T/S ports in an optimal way by minimizing their vessels’ port tariffs, operating costs, vessel time cost, bunker costs, and carbon taxes. Port tariff is represented by the marine charge and cargo handling charge (CHC) in the current study. Although many tariffs are charged to vessels such as vessel dues, towage, mooring, and pilotage, we aggregate them into a single term, a marine charge, for simplicity of analysis. Among the CHCs charged for cargo handling, the T/S CHC is only considered in the model since import and export CHCs charged to carriers are the same in any case, because the model does not consider land transportation. Vessel operating cost includes crew, repair and maintenance, insurance, stores and lubes, fuel for auxiliary power, and administration. Vessel time cost is considered in the model using the vessel charter rate, which is the rate of hiring a vessel. Bunker cost is the cost for bunker amount consumed during vessel navigation, which is represented by multiplying bunker prices and bunker consumption. Carbon tax is an environmental tax that is implemented by taxing the burning of bunker fuels consumed during vessel navigation. Although no carbon tax has yet been charged to ocean carriers, it is included for the purpose of a scenario analysis. For the purpose of modeling, we assume that import cargoes are carried by vessels coming to SSA and export cargoes are carried by vessels going out from SSA. The model is formulated independently for the trade between SSA and each of the other continents. As can be seen from Fig. 1, ports can be aligned in terms of geographical proximity to the representing port in the other continents, e.g., the alignment of SSA hubs in terms of proximity to Singapore is Port Louis, Maputo, Durban, NQ/PE, Walvis Bay, and Dakar. Therefore, the model in the current study uses the aligned ports when restricting liner routes. We also assume that feeders navigating between a T/S port and a feeder port call at all of ports located between the T/S port and the feeder port, where the T/S port can be any potential hub port calling at

∑j ∈ H Xsjim + ∑a ∈ R ∑j ∈ Pa Xsjiva = qiI ∀ i ∈ P ∑j ∈ H + Xijem + ∑a ∈ R ∑j ∈ P+ Xijeva = qi a

E

∀ i ∈ P+

(1) (2)

In equation (1), the first term implies that the import cargo at port i is transshipped at potential hub port j from a mega-vessel to a feeder visiting port i, and the second term implies that it is transshipped at a non-hub port from a conventional vessel to a feeder visiting port i. Note that they are directly delivered to port i via a mega-vessel or a conventional vessel only when port i = j. Equation (2) is for the export cargo. Assumptions made in the models above are summarized below for clarity of the model.

• The model in the current study is based on the carriers' perspective. • Container cargoes are transported by four types of vessel: a megavessel, two types of the conventional vessel, and a feeder vessel. • The T/S of cargoes carried by the conventional vessel can occur at • • • 195

all ports, while the T/S by the mega-vessel can occur only at potential hub ports. A container can be transshipped only once, i.e., single T/S operation. Container cargoes transshipped are transported by a feeder from a feeder port to a T/S port if the cargo is exported and from a T/S port to a feeder port if the cargo is imported. Container cargoes transshipped are transported by a mega-vessel or conventional vessel from a T/S port to Asia or Europe if the cargo is

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• • • • •

exported and from Asia or Europe to a T/S port if the cargo is imported. Import cargoes are carried by vessels coming to SSA and export cargoes are carried by vessels going out from SSA. Conventional vessels with different sizes navigate in the two SSA sub-regions, i.e., one call at ports in West-SSA and the other at ports in South-East SSA. Mega-vessels can only call at potential hub ports, whereas conventional and feeder vessels can call at all ports in SSA. Feeders navigating between a T/S port and a feeder port call at all of ports between the T/S port and the feeder port. Vessel speed is given in advance, i.e., a parameter not a decision variable, because our study deals with strategic issues in SSA, not operational issues in a shipping liner.

Yijva ∈ {0, 1}, Zijva ≥ 0 and integer

(18)

Zm, Z va ≥ 0 and integers ∀ a ∈ R

∑

∑

i ∈ H ∪ H + j ∈ HSi

+ (bcm + dcm + ctm) +

∑ ∑

∑

a ∈ R i ∈ Pa ∪ Pa+ j ∈ PSai

+ ct va) +

52 ⎛⎜dcm pti + mcim ⎝

lij ⎞ ⎟ Zijm 24spm ⎠

4. Data collection To run the proposed model, we collected the following required data from various reliable sources: bunker costs, carbon tax, vessel size, import and export amount, marine charge, nautical distance, port time, slot utilization, vessel charter rate, vessel operating cost, vessel speed, and CHC. Since bunker consumption can be approximated by the following cubic function of vessel speed (Ronen, 1982, 2011), the bunker cost was calculated by

⎛ 52 ⎜dc va pti + mciva + (bc va + dc va ⎝

lij ⎞ Zijv + 24spva ⎟ a ⎠

∑ ∑ fcij Xsijm + ∑ ∑

fcij Xjiem

i ∈ H + j ∈ P+

i∈H j∈P

∑ ∑ ∑ fcij Xsijva + ∑ ∑ ∑ a ∈ R i ∈ Pa j ∈ P

(19)

and the other decision variables are non-negative. The objective function minimizes the sum of the annual vessel operating costs, charter rates, marine charges, bunker costs, carbon taxes, and total feeder costs, in which 52 is the number of weeks per year. Constraints (3) and (4) are for generating the route of the mega-vessel calling at potential hub ports commonly used in the model for a shortest path problem, while constraints (5) and (6) are for the route of the conventional vessel. Constraints (7)–(10) imply that the direct calling and T/S at a port must not occur if no vessel visits the port. Constraints (11)–(14) calculate the number of the vessel calls per week. Constraints (15) and (16) restrict that the per-week calls of a vessel on a shipping leg equals that of the vessel serving SSA if the vessel navigates on the leg and otherwise it is zero. The remaining constraints are restrictions on decision variables.

Based on the definitions of the problem and cost factors, the model is formulated as follows.

[P] Minimize

∀ a ∈ R, i ∈ Pa ∪ {s}, j ∈ PSai ∀ a ∈ R, i ∈ Pa+, j ∈ PSai

a ∈ R i ∈ Pa+ j ∈ P +

fcij Xjieva

subject to (1), (2), and

bc v = bp ·rv spv3

∑j ∈ H Ysjm = 1, ∑i ∈ H + Yiem = 1 ∑j ∈ HPi Yjim = ∑j ∈ HSi Yijm ∀ i ∈ H ∪

(3)

H+

wherebc v is the daily bunker cost of vessel type v, bp the bunker price, which was set at 484 US$ per ton, average bunker price in 2010 in Drewry Maritime Research (2012), rv the factor for the daily bunker consumption rate of vessel type v, rv = brv / gspv3 (Ronen, 1982, 2011), brv the daily bunker consumption rate of vessel type v, brv = 0.0392c v + 5.582 (Tran, 2011), gspv the given ship speed of vessel type v, gspv = 5.4178c v0.1746 (Tran, 2011), and spv the speed of a vessel of type v. The carbon tax is calculated by considering the amount of a carbon tax per unit of CO2 emissions and the bunker consumption.

(4)

∑j ∈ Pa Ysjva = 1, ∑i ∈ P+ Yieva = 1 ∀ a ∈ R a

(5)

∑j ∈ PPai Yjiva = ∑j ∈ PSai Yijva ∀ a ∈ R, i ∈ Pa

(6)

∑j ∈ P Xsijm ≤ M ∑j ∈ HPi Yjim ∀ i ∈ H

(7)

∑j ∈ P+ Xjiem ≤ M ∑j ∈ HSi Yijm ∀ i ∈ H+

(8)

ctv = tax·e ·rv spv3

∑j ∈ P Xsijva ≤ M ∑j ∈ PPai Yjiva ∀ a ∈ R, i ∈ Pa

(9)

wherectv is the daily carbon tax of vessel type v, tax the tax on CO2 emissions, ande CO2 emissions per ton of fuel consumption, which was set at 3.17 tCO2 per bunker ton following Corbett et al. (2009). Sizes of the mega-vessel and the feeder vessel were set at 10000 TEU and 800 TEU, respectively. According to Drewry Maritime Research (2012), sizes of the conventional vessel for the SSA-Europe trade were set at 2000 TEU on West-SSA and 4000 TEU on South-East SSA, while those for the SSA-Asia trade were set at 2000 TEU on West-SSA and 5000 TEU on South-East SSA. Import and export data were obtained using Global Trade Analysis Project (GTAP) version 7.0. The GTAP obtained the values of import and export products between countries and the values were containerized using the method in Lee et al. (2013). More details of the method for generating the import and export data are summarized in Appendix B. Table 1 summarizes the import and export data at each port in 2020. Import and export are terms from SSA's perspective. The marine charge was approximated using mciv = sli⋅c v + ici which is an equation of a simple linear regression of the real data at ports in SSA obtained from the ports authorities in the SSA region (Table 2). In the equation, mciv is the marine charge of vessel type v at port i, sli the slope of the regression equation for port i, and ici the intercept of the

∑j ∈ P+ Xjieva ≤ M ∑j ∈ PSai Yijva ∀ a ∈ R, i ∈ Pa+

(10)

∑j ∈ HSi∪ {i} ∑k ∈ P Xsjkm ≤ 52pc⋅cm Zm ∀ i ∈ H

(11)

∑j ∈ HPi ∪ {i} ∑k ∈ P+ Xkjem ≤ 52pc⋅cm Zm ∀ i ∈ H+

(12)

∑j ∈ PSai∪ {i} ∑k ∈ P Xsjkva ≤ 52pc⋅c va Z va ∀ a ∈ R, i ∈ Pa

(13)

∑j ∈ PPai ∪ {i} ∑k ∈ P+ Xkjeva ≤ 52pc⋅c va Z va ∀ a ∈ R, i ∈ Pa+

(14)

Zm ≤ Zijm + M (1 − Yijm)

∀ i ∈ H , j ∈ HSi ∀ i ∈ H+, j ∈ HSi

(15)

Z va ≤ Zijva + M (1 − Yijva)

∀ a ∈ R, i ∈ Pa, j ∈ PSai ∀ a ∈ R, i ∈ Pa+, j ∈ PSai

(16)

Yijm ∈ {0, 1}, Zijm ≥ 0 and integer

∀ i ∈ H ∪ {s}, j ∈ HSi ∀ i ∈ H+, j ∈ HSi

(17) 196

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Table 1 Forecasted imports and exports in 2020 (unit: TEU). Port

Import

Abidjan Dakar Lagos Luanda Tema Walvis Bay Cape Town Dar es Salaam Durban Maputo Mombasa NQ/PE Port Louis Toamasina

Table 4 Port time (unit: day) and CHC (US$/TEU). Source: LMIU's Africa port calls in 2007 and 2008, Authorities of ports in the SSA region

Export

Europe

Asia

Europe

Asia

Port

Port time

CHC

180,800 154,433 672,398 98,142 170,268 46,055 242,895 158,720 862,961 62,004 175,709 121,865 39,490 36,451

339,236 313,816 1,154,591 251,670 319,483 121,283 404,849 419,425 1,657,255 182,028 389,185 203,120 81,316 82,319

307,701 268,073 1,041,531 251,450 289,786 92,304 200,627 228,871 615,497 269,142 185,351 100,658 153,882 39,665

83,777 68,157 188,545 106,650 78,899 38,959 148,225 123,721 436,670 54,729 85,638 74,367 13,706 4912

Abidjan Dakar Lagos Luanda Tema Walvis Bay Cape Town Dar es Salaam Durban Maputo Mombasa NQ/PE Port Louis Toamasina

1.83 2.55 3.92 5.62 3.90 2.82 3.01 5.06 2.30 3.50 6.58 1.61 4.50 4.50

114.71 228.46 114.71 130.81 114.71 214.77 67.52 85.70 76.86 106.00 114.71 58.17 48.00 83.58

Table 2 Regression equation for each port. Port

Slope

Intercept

R2

Abidjan Dakar Lagos Luanda Tema Walvis Bay Cape Town Dar es Salaam Durban Maputo Mombasa NQ/PE Port Louis Toamasina

4.0967 4.0967 4.0967 6.1366 4.0967 3.4380 4.0967 4.0203 4.5577 2.7349 4.0967 4.4074 3.5579 3.9208

5002.0441 5002.0441 5002.0441 7492.7509 5002.0441 3008.8480 5002.0441 4908.7644 7961.1041 4755.0000 5002.0441 5952.0947 1150.5300 4787.2603

0.9996 0.9996 0.9996 0.9996 0.9996 0.9999 0.9996 0.9996 0.9979 1.0000 0.9996 0.9982 1.0000 0.9996

dov=0.7748cv+4780.2642, which is an equation of a simple linear regression of the data in Gkonis and Psaraftis (2009) where do v is the daily operating cost of vessel type v. The speed of feeders was set by spv = 5.4178c v0.1746 obtained from Tran (2011) and that of the liner vessel was set at 17.05 knot by averaging the average speeds of vessels for Asia-North Europe trade in Drewry Maritime Research (2012). 5. Numerical analysis and implications This section summarizes the experimental results, which are results under current cost structure given above, various scenario analyses such as the effects of an evolution of the liner shipping network in SSA, different vessel sizes and speeds, carbon taxes, and insights in association with the 21st Century Maritime Silk Road. These analyses were independently performed for each of the trades of SSA-Asia and SSAEurope. In the experiment, the optimal solution of the model was obtained using CPLEX 11.2, which is a commercial integer program solver. Unlike many previous studies, we did not develop a heuristic since CPLEX generated the optimal solution within 400 s for all instances under the data setting given in Sections 2 and 4.

regression equation for port i. Table 3 shows the nautical distance between ports obtained from Netpas 2.9, a commercial software with port distance data base. Port time was adapted from LMIU's Africa port calls in 2007 and 2008, the port time at Toamasina was set at that of Port Louis due to its absence, and CHC was obtained from authorities of ports in the SSA region, which are summarized in Table 4. Slot utilization was set at 70% following Tran (2011). Vessel charter rate is calculated using crv = 108.05c v0.6257 obtained from Tran (2011), where crv is the daily charter rate of vessel type v. Vessel operating cost was calculated using

5.1. Experimental results under current cost structure This experiment aimed to analyze the liner route and T/S volume at hub ports under the cost structure described in Section 4. Fig. 2 summarizes the resulting route of vessels and potential T/S for Asia-SSA trade. The route of the mega-vessel was Asia → Durban →

Table 3 Nautical distance (unit: nautical mile). Source: Netpas 2.9

Abidjan Dakar Lagos Luanda Tema Walvis Bay Cape Town Dar es Salaam Durban Maputo Mombasa NQ/PE Port Louis Toamasina

Abid jan

Dakar

Lagos

Luanda

Tema

Walvis Bay

Cape Town

Dar es Salaam

Durban

Maputo

Mombasa

NQ/PE

Port Louis

Toam asina

Asia

Europe

0 1131 473 1336 267 2019 2674 5022 3456 3763 5158 3089 5035 4770

1131 0 1578 2370 1372 2953 3572 5918 4352 4649 6055 3986 5854 5667

476 1578 0 1087 215 1884 2565 5035 3350 3645 5052 2983 4917 4664

1428 2370 1088 0 1170 911 1610 4062 2395 2672 4097 2028 3943 3709

269 1372 211 1175 0 1917 2589 5067 3373 3678 5660 3007 4949 4688

2010 2953 1878 923 1908 0 732 3083 1517 1791 3219 1150 3063 2831

2674 3572 2565 1610 2589 732 0 2376 810 1106 2512 443 2312 2124

5153 5918 4916 3961 4939 3181 2376 0 1580 1475 180 1953 1353 1828

3456 4352 3350 2395 3373 1517 810 1580 0 311 1716 387 1558 1369

3753 4649 3646 2691 3670 1814 1106 1359 311 0 1495 684 1456 1266

5745 6055 5628 4654 5076 3773 2512 408 1716 2046 0 2089 1783 1964

3089 3986 2983 2028 3007 1150 443 1953 387 684 2089 0 1889 1701

4958 5854 4852 3897 4875 3019 2312 2017 1558 1447 2153 1889 0 506

4767 5667 4650 3675 4681 2795 2124 1072 1369 1235 1502 1701 475 0

8259 8529 8153 7198 8176 6320 5613 5354 4894 4793 5490 5214 3366 3775

1965 843 2403 3196 2197 3378 4397 6744 5178 5475 6880 4811 6680 6492

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Fig. 2. Vessel route and potential T/S for the Asia-SSA trade.

NQ/PE → Asia, i.e., the mega-vessel called at Durban and NQ/PE without calling at Dakar, Walvis Bay, Maputo, and Port Louis among competing SSA hub ports. This implies that the double hub strategy of South Africa can scarify competing hub ports just adjacent to the double ports, Walvis Bay and Maputo. The route of the conventional vessel for West-SSA was Asia → Lagos → Abidjan → Asia while that for SouthEast SSA was Asia → Dar es Salam → Mombasa → Dar es Salaam → Asia. Comparing with the current route of the conventional vessel in 2012, the number of calling ports of the conventional vessel decreases and the conventional vessel does not call potential hub ports. This result is because the mega vessel takes over potential hub ports of calls from the conventional vessel. Here, the current routes of the conventional vessel in 2012 are Asia → Walvis Bay → Tema → Asia for West-SSA and Asia → Port Louis → Durban → NQ/PE → Cape Town → Port Louis → Asia for South-East SSA, which were selected as representative routes among a number of routes in Drewry Maritime Research (2012). On the other hand, Durban and NQ/PE captured T/S cargoes of 0.3 and 1.5 million TEU, respectively, while the other competing hub ports did not capture T/S cargoes. As can be seen from Fig. 2, NQ/PE captured the Asia-SSA T/S cargoes up to Dakar on the West Coast and Durban up to Port Louis and Maputo on the East Coast. These results imply that NQ/ PE will function as a T/S hub port for cargoes on the West Coast of SSA for the SSA-Asia trade, and Durban will do so on the East Coast of SSA. Fig. 3 summarizes the market share of cargoes by T/S and direct

calling, and that of the mega-vessel and the conventional vessel for Asia-SSA trade. Out of 7.4 million TEU of Asia-SSA cargoes in 2020, the market shares of T/S and direct calling are 33.1% and 66.9%, respectively. This implies that T/S will be around 30% of Asia-SSA cargoes as long as the conventional vessel navigates in the SSA region. The market shares of the mega-vessel and the conventional vessels for West-SSA and South-East SSA are 55.5%, 29.2%, and 15.3%, respectively. This implies that the mega-vessel will capture more than half of Asia-SSA trade cargoes once liner companies deploy it. Finally, the number of vessel calls per week is 9 for the mega-vessel, 24 for the West-SSA conventional vessel, and 5 for the South-East SSA conventional vessel. The number of West-SSA conventional vessel calls is more than that of the others because the West-SSA 2000 TEU-sized conventional vessels are smaller than the 5000 TEU-sized South-East SSA conventional vessel and the 10000 TEU-sized the mega-vessel. Fig. 4 summarizes the resulting vessel routes and potential T/S for Europe-SSA trade. The route of the mega-vessel was Europe → NQ/PE → Durban → NQ/PE → Dakar → Europe. The route of the conventional vessel for West-SSA was Europe → Lagos → Tema → Abidjan → Europe, while that for South-East SSA was Europe → Dar es Salam → Mombasa → Dar es Salaam → Europe. The number of calling ports of the conventional vessel decreases and the conventional vessel does not call potential hub ports like results for Asia-SSA trade, comparing with the current routes of the conventional vessel in 2012, Europe →

Fig. 3. Market share of cargoes for the Asia-SSA trade. 198

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Fig. 4. Vessel route and potential T/S for the Europe-SSA trade.

Abidjan → Tema → Luanda → Tema → Europe for West-SSA for WestSSA and Europe → Cape Town → NQPE → Durban → NQ/PE → Cape Town → Europe for South-East SSA, which were selected as representative routes among a number of routes in Drewry Maritime Research (2012). On the other hand, NQ/PE and Durban captured T/S cargoes of 0.7 and 0.5 million TEU, respectively. NQ/PE captured the Europe-SSA T/S cargoes up to Luanda on the West Coast and Durban up to Port Louis and Maputo on the East Coast. This implies that NQ/PE will function as a T/S hub port for cargoes on the West Coast of SSA for the Europe-SSA trade. Fig. 5 summarizes the market share of cargoes by T/S and direct calling, and that of the mega-vessel and the conventional vessel for Europe-SSA trade. Out of 7.1 million TEU of Europe-SSA cargoes in 2020, the market share of T/S and direct calling was 28.8% and 71.2%, respectively. This implies that T/S will be around 30% of Europe-SSA cargoes as long as the conventional vessel navigates in the SSA region. The market shares of the mega-vessel and of the conventional vessels for West-SSA and South-East SSA are 44.8%, 43.8%, and 11.4%, respectively. This implies that the mega-vessel will capture almost half of Europe-SSA trade cargoes once liner companies deploy it. Finally, the number of vessel calls per week of the mega-vessel and of the conventional vessels for West-SSA and South-East SSA are 5, 25, and 3, respectively. Maputo, Port Louis, and Walvis Bay acted as feeder ports without any vessel calls.

5.2. Scenario analysis In these analyses, we attempt to analyze the effects of an evolution of the liner shipping network in SSA, different vessel sizes, vessel speeds, and carbon taxes. We focus on the experimental results for the SSA-Asia trade since a series of experiments for the SSA-Europe trade has shown similar results.

5.2.1. Effect of an evolution of the liner shipping network in the SSA region To examine the effect of an evolution of the liner shipping network in SSA, three models are analyzed: one with the conventional vessel; one with competition between the mega-vessel and the conventional vessel, i.e., model [P]; and one with the mega-vessel. The models with the conventional vessel and with the mega-vessel presented in Appendix C were developed by eliminating the corresponding constraints and variables from model [P]. The model with the conventional vessel assumes that the conventional vessel only navigates in the SSA sub-regions. This model is considered to represent the current liner shipping industry in SSA according to vessel routes in the SSA region in Drewry Maritime Research (2012). Second, due to the mega-vessel trend, vessels larger than 10000 TEU-size may be deployed to SSA in the near future, which may introduce competition between the conventional vessel and the mega-vessel. The analysis on this competition is performed using model [P]. Finally, we analyze the effect resulting

Fig. 5. Market share of cargoes for the Europe-SSA trade. 199

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Table 5 Effect of an evolution of the SSA liner shipping network. Model

Conventional vessel

Competition

Mega-vessel

Vessel type

CV for West-SSA CV for South-East SSA Mega vessel CV for West-SSA CV for South-East SSA Mega vessel

Vessel route

Market share

Lagos→Tema→Abidjan

Total cost (US$)

T/S

Per vessel type

46.3%

34.1%

Durban

4.8 × 109

65.9%

Durban→NQ/PE→Durban

33.1%

55.5%

Lagos→Abidjan

29.2%

Dar es Salam→Mombasa →Dar es Salaam Durban→NQ/PE

15.3% 73.9%

100%

3.7 × 109

5.3 × 109

Note: CV is the conventional vessel. Table 6 Effect of different sizes of the mega-vessel. Mega-vessel size (TEU)

6000

10,000

14,000

18,000

Vessel type

Mega vessel CV for West-SSA CV for South-East SSA Mega vessel CV for West-SSA CV for South-East SSA Mega vessel CV for West-SSA CV for South-East SSA Mega vessel CV for West-SSA CV for South-East SSA

Vessel route

Market share

Durban→NQ/PE→Durban Lagos→Abidjan Dar es Salam→Mombasa →Dar es Salaam Durban→NQ/PE→Durban Lagos→Abidjan Dar es Salam→Mombasa →Dar es Salaam Durban→NQ/PE→Durban Lagos→Abidjan Dar es Salam→Mombasa →Dar es Salaam Durban→NQ/PE→Durban Lagos→Abidjan Dar es Salam→Mombasa →Dar es Salaam

Total cost (US$)

T/S

Per vessel type

33.1%

52.6% 32.1% 15.3%

3.9 × 109

33.1%

55.5% 29.2% 15.3%

3.7 × 109

33.1%

52.6% 32.1% 15.3%

3.6 × 109

33.1%

55.5% 29.2% 15.3%

3.6 × 109

Note: CV is the conventional vessel.

competition model minimized the least total cost, which implies that deploying a combination of big and small vessels is more beneficial from carriers’ perspective. In other words, container carriers should adopt a portfolio approach of having both conventional vessels and mega-vessels in order to save costs, i.e., container carriers should not deploy solely a mega-vessel into a shipping lane although the current trend is towards mega-vessels.

only if liner companies deploy only the mega-vessel without deploying the conventional vessel. We suppose that the SSA liner shipping network is most developed when the mega-vessel only navigates in the SSA region, while it is least developed when the conventional vessel only navigates. Table 5 summarizes the effect of an evolution of the SSA liner shipping network for the SSA-Europe trade. The table shows that more T/S cargoes were generated with the evolution of the system, with a dramatic increase to 73.9% in the mega-vessel model, although those in the competition model became slightly smaller than in the conventional model. This implies that T/S volume dramatically increases and hence the SSA ports will compete fiercely to capture the T/S cargoes if the mega-vessel only navigates in the SSA oceans in the future. The market share of South-East SSA conventional vessel sharply decreased as the system evolved, which may be because cargoes at ports in South-East SSA were more transshipped at Durban and NQ/PE by the mega-vessel. For example, the T/S cargoes at Durban and NQ/PE were 0.3 and 1.5 million TEU in the competition model, respectively, while those increased to 1.2 and 4.3 million TEU, respectively. This implies that the maritime transport industry in the SSA region will undergo winnertakes-all evolution if the mega-trend becomes prevalent in the SSA region, i.e., hub ports will handle the majority of container cargoes while the non-hub ports will do the remaining cargoes. The conventional vessel model resulted in no calls at NQ/PE, which was the largest T/S port in the other models. This result implies that NQ/PE should develop an aggressive marketing strategy to attract the mega-vessel. Finally, the

5.2.2. Scenario analyses of the other factors In these analyses, we attempted to analyze the effects of different sizes of mega-vessel, vessel speeds, and carbon taxes, which are hot trends in the global shipping industry. All experiments are based on the competition model with the conventional vessel and the mega-vessel, which is the most plausible model in the future among the three models investigated in subsection 5.2.1 since the competition model is the most economical from carriers’ perspective as discussed above. To enjoy economies of scale, container carriers are increasingly deploying mega-vessels larger than 8000 TEU-size, which is called the mega-ship trend. Experimental analyses of different sizes of mega-vessel should examine how the vessel route, market share, and the total cost are affected by the deployment by container carriers of bigger vessels. The experimental results for the effect of different sizes of the megavessel are summarized in Table 6. As known in the maritime transport society, the average cost decreased with increasing vessel size, which implies that container carriers can seek economies of scale by replacing their vessels with mega-vessels. However, the vessel route and market 200

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Table 7 Effect of different speeds of the mega-vessel. Mega-vessel speed (knot)

14

18

22

26

Vessel type

Mega vessel CV for West-SSA CV for South-East SSA Mega vessel CV for West-SSA CV for South-East SSA Mega vessel CV for West-SSA CV for South-East SSA Mega vessel CV for West-SSA CV for South-East SSA

Vessel route

Market share

Durban→NQ/PE→Durban Lagos→Abidjan Dar es Salam→Mombasa →Dar es Salaam Durban→NQ/PE→Durban Lagos→Abidjan Dar es Salam→Mombasa →Dar es Salaam Durban→NQ/PE→Durban Lagos→Abidjan Dar es Salam→Mombasa →Dar es Salaam Durban→NQ/PE→Durban Lagos→Tema→Abidjan Dar es Salam→Mombasa →Dar es Salaam

Total cost (US$)

T/S

Per vessel type

33.1%

55.5% 29.2% 15.3%

3.7 × 109

33.1%

55.5% 29.2% 15.3%

3.8 × 109

28.8%

50.6% 34.1% 15.3%

3.9 × 109

28.8%

50.6% 34.1% 15.3%

4.0 × 109

Note: CV is the conventional vessel.

Vessel size, speed, and carbon tax are key parameters in liner shipping design. The scenario analyses show that the model and results can assist container carriers and ports to make practical decisions in shipping and port operations. The analyses will be particularly helpful when liner companies venture into new markets like the SSA region.

share were not affected by the mega-vessel size, which implies that container cargo volume at each of the ports will not be affected and that container carriers will not change the vessel route greatly, even as they deploy even bigger vessels. That is, the more important thing from ports’ perspective is whether a port becomes a hub port or not, and a large cargo volume will be a blessing promised to the hub port that captures the mega-vessel. In recent years, container carriers have reduced their vessels' speed (slower steaming) to improve fuel efficiency and lower greenhouse gas (GHG) emissions. The experiment to analyze different vessel speeds aims to assess the effect when the vessel becomes faster or slower. Table 7 summarizes the experimental results on different speeds. The result reveals that the vessel speed does not greatly affect the vessel route, i.e., container carriers will not extensively change the vessel route, even as they differentiate their vessel speed. On the other hand, the market share and the total cost were affected by the vessel speed. The market share of the T/S cargoes increased as the vessel speed decreased. This result implies that the current slower steaming trend is a welcome novelty from the perspective of hub ports aiming to capture more T/S cargoes, but it is not from the perspective of non-hub ports. As expected, the total cost gradually increased as the vessel speed increased due to increased bunker costs. In summary, the experimental result implies that the current slower steaming trend is a welcome novelty from container carriers and giant ports’ perspective, but it is not from in the perspective of small ports. To lower GHG emissions in the maritime transport sector, the International Maritime Organization is considering some regulatory measures such as a carbon tax, which is a tax based on GHG emissions generated from bunker consumption. The experiment on different carbon taxes aims to analyze the effect of the tax charged to container carriers, which is summarized in Table 8. The table shows that container carriers will call at more ports to capture more cargoes to offset the cost increase owing to the carbon tax if the environmental regulation is realized. The market share of the mega-vessel decreased as the carbon tax increased. As expected, the total cost increased as the carbon tax increased. In fact, this analysis may have a limitation in a sense that the vessel speed and the carbon tax cannot be analyzed in a separate way because the carbon tax affects the bunker price, which further impacts shipping liner's slow steaming behavior (Sheng et al., 2017), i.e., the vessel speed decreases as the carbon tax increases. However, under the circumstance that a function representing the relationship between the carbon tax and the vessel speed is unavailable, we can conjecture from results in Tables 7 and 8 that the market share of the mega-vessel will not change significantly with carbon taxes.

5.3. Insights in association with the 21st century Maritime Silk Road All of the above test results indicated that the two ports in South Africa, i.e., NQ/PE and Durban, will be included in the shipping service route of the mega-vessel, and NQ/PE will function as a T/S hub port for cargoes on the West Coast of SSA and Durban will do so on the East Coast of SSA for the SSA-Asia trade. The reason for these results is that the two ports are located as vertices of SSA, shaped like an inverted triangle despite of geographical proximity of the two ports as 387 nautical miles. These results imply that the two ports in South Africa should become strategic economic regional footholds of the Belt and Road Initiative, and furthermore, they should be included in the relay service for the trade between Asia and South America and the CASA route directing South America, which are parts of the new Maritime Silk Road proposed by Lee et al. (2018). The maritime society should notice that a new maritime geography centered on the two ports in South Africa will be appeared in the near future in tandem with China's growing engagement in developing infrastructure for landlocked countries in Africa (Lee, 2015). 6. Concluding remarks This paper has analyzed potential liner routes and T/S flows for the trades of SSA-Europe and SSA-Asia that could be captured by the liner shipping network in the SSA region being developed by SSA countries such as South Africa. The analysis was done by an integer programing model formulated to represent the potential liner shipping network. The paper contributes by producing original results and implications that could shape the future developments of shipping networks linking Asia, Europe and Africa. The implications drawn from the experimental results can be summarized follows:

• NQ/PE and Durban will function as T/S hub ports for cargoes on the

West and East Coast, respectively, of SSA for the SSA-Europe trade. NQ/PE will also function as a T/S hub port for cargoes on the West Coast of SSA for the Asia-SSA trade. NQ/PE has a strong potential to be a T/S port and the recommendation is to proactively attract mega

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Table 8 Effect of different carbon taxes. Carbon tax (US$/tCO2)

0

Vessel type

Mega vessel CV for West-SSA CV for South-East SSA Mega vessel CV for West-SSA CV for South-East SSA Mega vessel CV for West-SSA CV for South-East SSA Mega vessel CV for West-SSA CV for South-East SSA

100

200

300

Vessel route

Market share

Durban→NQ/PE→Durban Lagos→Abidjan Dar es Salam→Mombasa →Dar es Salaam Durban→NQ/PE→Durban Lagos→Tema→Abidjan Dar es Salam→Mombasa →Dar es Salaam→Toamasina Durban→NQ/PE→Durban Lagos→Tema→Abidjan Dar es Salam→Mombasa →Dar es Salaam→Toamasina Durban→NQ/PE→Durban Lagos→Tema→Abidjan Port Louise→Dar es Salam→Mombasa →Dar es Salaam→Toamasina

Total cost (US$)

T/S

Per vessel type

33.1%

55.5% 29.2% 15.3%

3.7 × 109

28.6%

50.6% 34.1% 15.3%

4.0 × 109

28.6%

50.6% 34.1% 15.3%

4.3 × 109

28.6%

50.6% 34.1% 15.3%

4.5 × 109

Note: CV is the conventional vessel.

model is applicable for analyzing other shipping trade lanes, which is a meaningful future research topic. Importantly, in view of the growth potential of Africa highlighted by the Belt and Road initiative and the CASA route development, this study provides a practical reference to shipping companies and ports for better understanding the SSA market. The insights provided will be useful for ship deployment and port facility investment decisions. More research on Africa's maritime trade and logistics can be conducted in future studies. For example, the strategy for creating a vibrant maritime and logistics cluster and analysis on the impact of the Belt and Road Initiative on container liner shipping network developments in the SSA region with container cargo flow would be interesting topics. Future research should also extend the study to link the shipping routes to South America.

vessels rather than conventional vessels.

• T/S volume will dramatically increase and hence the SSA ports will • • • •

compete fiercely to capture the T/S cargoes if the mega-vessel only navigates in the SSA oceans in the future. Hub ports in the SSA region will handle the majority of container cargoes while the non-hub ports will do the remaining cargoes. Therefore, the SSA ports will compete fiercely to become the hub port as the mega-trend becomes more prevalent in the SSA region. Container carriers should deploy a combination of big and small vessels, i.e., container carriers should not deploy solely the megavessel in the SSA region although the current trend is towards the mega-vessel. Container cargo volume at each of the ports in the SSA region will not be affected and container carriers will not change the vessel route greatly, even as they deploy even bigger vessels. The current slower steaming trend will be welcomed from container carriers and giant ports' perspective, but not from the perspective of small ports in terms of container volume at ports and the total carriers' cost.

Acknowledgments This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF2017S1A2A2041812).

Although the present experiment is confined to the SSA region, the Appendix A

R H H+ HPi HSi

set of SSA sub-regions set of potential hub ports, which are aligned in terms of geographical proximity to the representing port of Asia or Europe, i.e., Singapore for the SSA-Asia trade set of potential hub ports with a sequence reverse to the sequence of hub ports in setH set of potential hub ports preceding hub port i in terms of the sequence, HPi ⊂ H ∪ H+ ∪ {s} , wheres is the first departure port, e.g., Singapore for the SSA-Asia trade set of potential hub ports succeeding hub port i in terms of the sequence, HSi ⊂ H ∪ H+ ∪ {e} , where e is the last arrival port (portss ande are physically same), e.g., Singapore for the SSA-Asia trade set of ports, which are aligned in terms of geographical proximity to the representing port of Asia or Europe set of ports with a route sequence reverse to the sequence of ports in setP set of the aligned ports in sub-region a set of ports in sub-region a with a sequence reverse to the sequence of ports in set Pa

P P+ Pa Pa+ PPai set of ports in sub-region a preceding port i in terms of the sequence, PPai ⊂ Pa ∪ Pa+ ∪ {s} PSai set of ports in sub-region a succeeding port i in terms of the sequence, PSai ⊂ Pa ∪ Pa+ ∪ {e} Parameters and indices index for the feeder f m index for the mega-vessel

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va a (i) bc v cv ctv dc v fcij hci i+ lij M mciv pc pti

conventional vessel that serves ports in SSA sub-region a SSA sub-region where port i is located daily bunker cost of vessel type v, v ∈ {f , m} size of a vessel of type v daily carbon tax of vessel type v daily operating cost and charter rate of a vessel of type v calculated by dc v = do v + crv wheredo v is the daily operating cost of vessel type v and crv is the daily charter rate of vessel type v total feeder cost per TEU between port i and j T/S cargo handling charge at port i replica port of port i in the reversely sequenced ports, i.e., i+ ∈ P + (ports i andi+ are physically same) nautical distance between ports i and j

qiI

arbitrarily large number marine charge of a vessel of type v at port i portion of the vessel size, i.e., slot utilization port time at port i import amount at port i (TEU)

qiE

export amount at port i (TEU)

spv

speed of a vessel of type v

Decision variables Xijkv number of containers transported from port i to k by being transshipped at port j (≠i) or called directly at port j (=i) by a vessel of type v Yijv = 1 if a vessel of type v navigates the shipping leg from ports i to j; 0 otherwise Zijv number of vessel calls of type v per week on the shipping leg from ports i to j number of vessel calls of type v per week serving SSA Zv

Appendix B The import and export data were obtained as follows: the imports and exports between SSA countries and the other continents were generated using the method in Lee et al. (2013), which is a method for converting trade value by GTAP ver. 7.0 into trade containers; and it was converted into those between SSA ports and the other continents using an allocation method. To run the GTAP, countries in the other continents were first aggregated to avoid a huge data requirement. In the case of African countries, we considered the following countries, some of which were aggregated: Botswana, Central Africa, Madagascar, Malawi, Mauritius, Mozambique, Nigeria, Rest of Eastern Africa, Rest of South African Customs, Rest of South Central Africa, Rest of Western Africa, Senegal, South Africa, Tanzania, Uganda, Zambia, and Zimbabwe. Table B1 Continental aggregation for running the GTAP Continents Comprising GTA countries/regions Europe

Asia

Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, United Kingdom, Switzerland, Norway, rest of Asian Free Trade Area, Albania, Bulgaria, Belarus, Croatia, Romania, Russian Federation, Ukraine, rest of Eastern Asia, rest of Asia, Kazakhstan, Kyrgyztan, rest of Former Soviet Union, Armenia, Azerbaijan, Georgia China, Hong Kong, Japan, Korea, Taiwan, rest of East Asia, Cambodia, Indonesia, Lao People's Democratic Republic, Myanmar, Malaysia, Philippines, Singapore, Thailand, Viet Nam, rest of Southeast Asia, Bangladesh, India, Pakistan, Sri Lanka, rest of South Asia, Iran Islamic Republic of, Turkey, rest of Western Asia

Table B2 summarizes the imports and exports between countries/regions in 2020 obtained by the method in Lee et al. (2013) converting trade value from the GTAP into containers. Note that the imports and exports were from the perspective of SSA countries. Table B2 Imports and exports between countries and continents by the GTAP (unit: TEU) Africa country

Botswana Central Africa Madagascar Malawi Mauritius

Import

Export

Europe

Asia

Europe

14887 309334 36451 12288 39490

22455 160692 82319 38015 81316

22306 70932 39665 33827 153882

203

Asia 919 17874 4912 5240 13706 (continued on next page)

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Table B2 (continued) Africa country

Import

Mozambique Nigeria Rest of Eastern Africa Rest of South African Customs Rest of South Central Africa Rest of Western Africa Senegal South Africa Tanzania Uganda Zambia Zimbabwe

Export

Europe

Asia

Europe

Asia

16910 459975 242970 17662 185235 588678 64013 1026599 40345 23505 12540 5225

49063 755962 726964 85492 548699 1505974 82499 1655046 149671 81615 33099 16060

212112 679947 289742 66903 22451 1437546 47266 795641 89431 79562 50682 15161

17724 90097 158545 15358 14664 392774 7827 621899 66543 24270 78428 8587

Source: Obtained from the method in Lee et al. (2013) converting trade value from the GTAP into containers.

Then, the imports and exports between SSA countries and the other continents were converted into those between SSA ports and the other continents using the adjacent port and the allocation ratio in Table B3. We assumed that the imports and exports of countries without a port are handled by adjacent ports while those of SSA countries with ports are handled by their own ports. For example, the imports and exports of Botswana were assumed to be handled at the adjacent ports of Durban, Maputo and Walvis Bay, since Botswana neighbors with South Africa, Mozambique, and Namibia. The port-by-port allocation was done by multiplying the allocation ratio and the imports and exports of a country. For example, imports and exports of Malawi were allocated into Maputo and Dar es Salaam by multiplying the corresponding allocation ratios. The allocation ratio of a port is the ratio of the throughput of the port over the sum of the adjacent ports’ throughputs obtained from the port authority of South Africa. Table B3 Allocation rule of the imports and exports SSA country

Adjacent port

Botswana

Durban Maputo Walvis Bay Abidjan Dar es Salaam Djibouti Lagos Mombasa Tema Toamasina Dar es Salaam Maputo Port Louis Maputo Lagos Dar es Salaam Djibouti Maputo Mombasa Cape Town Durban NQ/PE Durban Maputo Walvis Bay Abidjan Dakar Lagos Luanda Tema Walvis Bay Dakar Cape Town

Central Africa

Madagascar Malawi Mauritius Mozambique Nigeria Rest of Eastern Africa

Rest of South African Customs

Rest of South Central Africa

Rest of Western Africa

Senegal South Africa

204

Allocation ratio 0.8921 0.0530 0.0549 0.1955 0.1172 0.0860 0.2296 0.1876 0.1841 1.0000 0.6977 0.3023 1.0000 1.0000 1.0000 0.2655 0.1947 0.1150 0.4248 0.2326 0.6507 0.1167 0.8921 0.0530 0.0549 0.2044 0.1536 0.2402 0.1542 0.1925 0.0551 1.0000 0.2326 (continued on next page)

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Table B3 (continued) SSA country

Tanzania Uganda Zambia

Zimbabwe

Adjacent port

Allocation ratio

Durban NQ/PE Dar es Salaam Dar es Salaam Mombasa Luanda Maputo Walvis Bay Durban Maputo

0.6507 0.1167 1.0000 0.3846 0.6154 0.5876 0.2025 0.2099 0.9440 0.0560

Appendix C [Mega-vessel model] Minimize

∑

∑

i ∈ H ∪ H + j ∈ HSi

lij ⎞ 52 ⎛⎜dcm pti + mcim + (bcm + dcm + ctm) ⎟ Zijm + 24spm ⎠ ⎝

∑ ∑ fcij Xsijm + ∑ ∑

fcij Xjiem

i ∈ H + j ∈ P+

i∈H j∈P

subject to

∑j ∈ H Xsjim = qiI ∀ i ∈ P ∑j ∈ H + Xijem = qiE ∀ i ∈ P +

∑j ∈ H Ysjm = 1, ∑i ∈ H + Yiem = 1 ∑j ∈ HPi Yjim = ∑j ∈ HSi Yijm ∀ i ∈ H ∪ H+

∑j ∈ P Xsijm ≤ M ∑j ∈ HPi Yjim ∀ i ∈ H

∑j ∈ P+ Xjiem ≤ M ∑j ∈ HSi Yijm ∀ i ∈ H+ ∑j ∈ HSi∪ {i} ∑k ∈ P Xsjkm ≤ 52pc⋅cm Zm ∀ i ∈ H

∑j ∈ HPi ∪ {i} ∑k ∈ P+ Xkjem ≤ 52pc⋅cm Zm ∀ i ∈ H+

Zm ≤ Zijm + M (1 − Yijm)

∀ i ∈ H , j ∈ HSi ∀ i ∈ H+, j ∈ HSi

Yijm ∈ {0, 1}, Zijm ≥ 0 and integer

∀ i ∈ H ∪ {s}, j ∈ HSi ∀ i ∈ H+, j ∈ HSi

Zm ≥ 0 and integer and the other decision variables are non-negative. [Conventional ship model] Minimize

∑ a∈R

⎡ ⎢ ∑ + ⎣ i ∈ Pa∪ Pa

∑ j ∈ PSai

lij ⎞ ⎛ 52 ⎜dc va pti + mciva + (bc va + dc va + ct va) Zijv + 24spva ⎟ a ⎝ ⎠

∑ ∑ fcij Xsijva + ∑ ∑ i ∈ Pa j ∈ P

subject to

∑a ∈ R ∑j ∈ Pa Xsjiva = qiI ∀ i ∈ P ∑a ∈ R ∑j ∈ P+ Xijeva = qiE ∀ i ∈ P + a

∑j ∈ Pa Ysjva = 1, ∑i ∈ P+ Yieva = 1 ∀ a ∈ R a

205

i ∈ Pa+ j ∈ P +

⎤ fcij Xjieva ⎥ ⎥ ⎦

Transport Policy 69 (2018) 193–206

H.-J. Kim et al.

∑j ∈ PPai Yjiva = ∑j ∈ PSai Yijva ∀ a ∈ R, i ∈ Pa ∑j ∈ P Xsijva ≤ M ∑j ∈ PPai Yjiva ∀ a ∈ R, i ∈ Pa ∑j ∈ P+ Xjieva ≤ M ∑j ∈ PSai Yijva ∀ a ∈ R, i ∈ Pa+

∑j ∈ PSai∪ {i} ∑k ∈ P Xsjkva ≤ 52pc⋅c va Z va ∀ a ∈ R, i ∈ Pa

∑j ∈ PPai ∪ {i} ∑k ∈ P+ Xkjeva ≤ 52pc⋅c va Z va ∀ a ∈ R, i ∈ Pa+ Z va ≤ Zijva + M (1 − Yijva)

∀ a ∈ R, i ∈ Pa, j ∈ PSai ∀ a ∈ R, i ∈ Pa+, j ∈ PSai

Yijva ∈ {0, 1}, Zijva ≥ 0 and integer

∀ a ∈ R, i ∈ Pa ∪ {s}, j ∈ PSai ∀ a ∈ R, i ∈ Pa+, j ∈ PSai

Z va ≥ 0 and integer ∀ a ∈ R and the other decision variables are non-negative.

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