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Network assignment model of integrating maritime and hinterland container shipping: application to Central America

  • Original Article
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Maritime Economics & Logistics Aims and scope

Abstract

The authors develop a model to predict worldwide container movements including both maritime and land shipping network from the viewpoint of cargo owners, given the liner shipping network provided by shipping companies and the level of service in each port. The network assignment methodology is applied to both an intermodal shipping network and maritime shipping sub-network, by which the solution can be obtained in a huge, real-scale network including more than 150 worlds’ container ports as well as some hinterland network of the world. The developed model is applied to the Central American region, where the international maritime containers are often transported across national borders by land. It is confirmed that the model output agrees with the actual container movement in terms of the container cargo throughput for each port, land container flow, and maritime flow by shipping company in Central America. Also, the model sensitivity to key parameters included in the model is confirmed reasonable. Finally, it is also confirmed that the model can predict the volume of containers handled in the port of La Union, where no liner service had previously called and a new liner service calls.

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Source: authors based on information from the APL website

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Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ryuichi Shibasaki.

Appendices

Appendix 1: Cost Function of Maritime Shipping Submodel

As mentioned in the main body, in the cost functions of all the links of the maritime shipping submodel, only shipping time is considered. The network structure of maritime shipping submodel is shown in Figure 2.

Navigating Link

In the maritime shipping link connecting each port, maritime shipping time and congestion are considered.

$$ t_{n} \left( {x_{a} } \right) = \frac{{l_{a} }}{{v_{a} }} + TW_{{a^{\prime}}} \cdot b1\left( {\frac{{x_{a} }}{{cap_{a} \cdot freq_{a} }}} \right)^{b2}, $$
(A1)

where t n is the shipping time of the navigating link (hour); x a the container cargo flow of the link a (TEU/year); l a the distance of the link a (NM); v a the vessel speed of the link a (knot); a’ the loading link in the departure port of the navigating link a; TW a’ the expected waiting time for the loading of the loading link a’ (hour); cap a the average vessel capacity of the service (TEU/vessel); freq a the service frequency (vessels/year); and b1, b2 are the parameters related to the congestion. The first term of equation (A1) is the shipping time in case that no congestion is considered. The second term represents the delayed time due to the congestion. The delayed time is defined by multiplying the waiting time for the loading as shown in equation (A2) by the congestion function which may have some relationship with a load factor (x a/cap a/freq a):

$$ TW_{{a^{\prime}}} = \frac{1}{2} \cdot \frac{YH}{{freq_{a} }}, $$
(A2)

where YH is the constant for conversion from one year to hours (52 (weeks/year) × 7(days/week) × 24(hours/day) = 8736 (hours/year)). The term (YH/freq a) represents duration hours of each vessel of the service. The expected waiting time is assumed to be half of it.

Loading Link

The link cost t l (hour) of a loading link a is defined as the sum of the loading time and the expected waiting time for departure.

$$ t_{l} \left( {x_{a} } \right) = TL_{a} + TW_{a}, $$
(A3)

where t l is time of the loading link (hour).

Unloading, Anchoring, and Transhipment Link

The link cost of an unloading, anchoring, and transshipment link is, respectively, defined as follows:

$$ t_{u} \left( {x_{a} } \right) = TU_{a} $$
(A4)
$$ t_{a} \left( {x_{a} } \right) = TA_{a} $$
(A5)
$$ t_{r} \left( {x_{a} } \right) = TR_{a}, $$
(A6)

where t u is time of the unloading link (hour); t a the time of the anchoring link (hour); t r the time of the transhipment link (hour); TU a the unloading time of the unloading link a (hour); TA a the anchoring time of the anchoring link a (hour); and TR a is the transhipment time of the transhipment link a (hour).

Carrier Choosing Link

In this model, container shipping utilizing multiple carriers is not allowed. (In other words, each container should be transported by only one carrier.) Therefore, the cost of the carrier choosing link, t c (hour), has to be set at a sufficiently small number to avoid transshipment of the container between carriers.

$$ t_{c} \left( {x_{a} } \right) = SSN, $$
(A7)

where t c is the time of the carrier choosing link (hour) and SSN is the sufficient small number.

Appendix 2: Details for the Monetary Cost Function of the Navigating Link

Each cost item (fuel cost, capital cost, operation cost, and canal toll) in the monetary cost function of the navigating link described in equation (15) is defined as follows:

Fuel Cost

The fuel cost, FC a , is defined as

$$ FC_{a} = FP \cdot FR_{a} \cdot \frac{{cap_{a} }}{{Vcap_{a} }}, $$
(A8)

where FP is the fuel price (US$/ton; we set FP = 587.0 from average price in 2010); FR a the fuel consumption rate of container vessel (ton/day); and Vcap a is the ship size of container vessel (TEU/vessel). Note that cap a is defined as the capacity of each shipping company; therefore, it is different from Vcap a in case that the capacity of the vessel is shared (co-operated or slot-chartered) by multiple companies. The fuel consumption rate, FR a , is commonly defined in marine engineering as follows:

$$ FR_{a} = \frac{{6.49*DWT_{a}^{{\frac{2}{3}}} \cdot v_{a}^{3} }}{{10^{6} }}, $$
(A9)

where DWT a is the dead weight tonnage of the vessel defined as

$$ DWT_{a} = 11.89 \cdot Vcap_{a} + 4414.0. $$
(A10)

Capital Cost

The capital cost of a container vessel, CC a , is defined as follows:

$$ CC_{a} = SP_{a} \cdot \frac{ir}{{\left\{ {1 - \left( {1 + ir} \right)^{ - PP} } \right\}}} \cdot \frac{1}{365 \cdot ODR} \cdot \frac{{cap_{a} }}{{Vcap_{a} }}, $$
(A11)

where SP a is the ship price of a container vessel (US$/vessel); ir the interest rate (we set ir = 0.02); PP the project period (year; we set PP = 15); and ODR is the operation day rate (we set ODR = 0.9, i.e. 365 * 0.9 = 329 days in operation per year). The term ir/{1 − (1 + ir)pp} represents the annual payment rate by compound interest calculation. The ship price of a container vessel, SP a , is estimated from Drewry Maritime Research (2011b) as follows:

$$ SP_{a} = \left( {0.0099 \cdot Vcap_{a} + 8.0} \right) \cdot 10^{6} . $$
(A12)

Operation Cost

The operation cost of a container vessel, CC a , including manning, insurance, stores, spares, lubricating oil, R&D, and administration cost is also estimated from Drewry Maritime Research (2011b) as follows:

$$ OC_{a} = \left( {0.7915 \cdot Vcap_{a} + 4276.0} \right) \cdot \frac{{cap_{a} }}{{Vcap_{a} }}. $$
(A13)

Canal Toll

The canal toll, CT a , is, respectively, defined as

$$ CT_{a} = 72.0 \cdot \frac{{x_{a} }}{{freq_{a} }} {\text{for the Panama Canal}},{\text{ and}} $$
(A14)
$$ CT_{a} = SDRrate \cdot (\beta_{1} \cdot scrnt_{a} + \beta_{2} )\quad {\text{for the Suez Canal}}, $$
(A15)

where SDRrate is the conversion rate from SDR (unit of account for Suez Canal) to US$ (we set SDRrate = 1.5 from the average in 2010); scrnt a the Suez Canal net tonnage of container vessel; and β 1 , β 2 are the coefficients established by the Suez Canal Authority. Note that a toll of the Panama Canal is set down by a container (i.e. 72.0 US$/TEU), while a toll of the Suez Canal is set down by a vessel so that a toll per TEU decreases as the size of a vessel increases. The Suez Canal net tonnage of container vessel, scrnt a , is defined as

$$ scrnt_{a} = 1 0. 9 2\cdot Vcap_{a} \, - { 1137} . 0. $$
(A16)

The coefficients β 1 and β 2 are set down by the Suez Canal net tonnage as shown in Table A1.

Table A1 Coefficient set down by the Suez Canal net tonnage (scrnt a ) in equation

Appendix 3: Ports Included in the Model and Their Throughput

No.

Port name

Country

Country/region in the WTS (as of 2013)

Annual throughput (‘000 teu, 2010)

Transshipped container (‘000 teu, 2010)

Transshipment rate (%)

Transshipment Time** TRr (hours)

1

Tokyo

Japan

Japan

4285

689*

16.1*

24

2

Yokohama

Japan

Japan

3281

528*

16.1*

24

3

Nagoya

Japan

Japan

2549

410*

16.1*

24

4

Osaka

Japan

Japan

1980

318*

16.1*

24

5

Kobe

Japan

Japan

2556

411*

16.1*

24

6

Hakata

Japan

Japan

749

120*

16.1*

24

7

Busan

South Korea

South Korea

14,194

6272

44.2

12

8

Gwangyang

South Korea

South Korea

2085

335*

16.1*

12

9

Incheon

South Korea

South Korea

1903

306*

16.1*

24

10

Dalian

China

China

5242

843*

16.1*

48

11

Yingkou

China

China

3338

537*

16.1*

48

12

Tianjin/Xingang

China

China

10,080

1621*

16.1*

48

13

Qingdao

China

China

12,012

1931*

16.1*

24

14

Lianyungang

China

China

3870

2728

70.5

24

15

Shanghai

China

China

29,069

6263

21.5

24

16

Ningbo

China

China

13,144

1830

13.9

24

17

Fuzhou

China

China

1223 (2009)

197*

16.1*

48

18

Quanzhou

China

China

1051

169*

16.1*

48

19

Xiamen

China

China

5820

936*

16.1*

24

20

Shenzhen (Yantian)

China

China

10,134

662

6.5

24

21

Shenzhen (Shekou, Chiwan, Dachan Bay)

China

China

12,376

5123

41.4

24

22

Guangzhou (Nansha, Huangpu)

China

China

12,550

6119

48.8

24

23

Hong Kong

Hong Kong

Hong Kong

23,699

5808

24.5

12

24

Keelung

Taiwan

Taiwan

1963

316*

16.1*

24

25

Taichung

Taiwan

China

1193

(2009)

192*

16.1*

24

26

Kaohsiung

Taiwan

Taiwan

9181

4866

53.0

24

27

Manila

Philippines

Philippines

3155

507*

16.1*

48

28

Davao

Philippines

Philippines

524

84*

16.1*

48

29

Haiphong

Vietnam

Vietnam

954

91*

9.6*

48

30

Ho Chi Minh

Vietnam

Vietnam

3856

369*

9.6*

48

31

Cai Mep/Vung Tau

Vietnam

Vietnam

512

49*

9.6*

24

32

Laem Chabang

Thailand

Thailand

5068

485*

9.6*

24

33

Bangkok

Thailand

Thailand

1453

139*

9.6*

24

34

Pasir Gudang

Malaysia

Malaysia

876

84*

9.6*

24

35

Tanjung Pelepas

Malaysia

Malaysia

6530

5988

91.7

12

36

Port Klang

Malaysia

Malaysia

8872

5437

61.3

24

37

Penang

Malaysia

Malaysia

1106

106*

9.6*

24

38

Singapore/Jurong

Singapore

Singapore

29,179

24,631

84.4

12

39

Tanjung Perak (Surabaya)

Indonesia

Indonesia

2427

232*

9.6*

48

40

Tanjung Priok (Jakarta)

Indonesia

Indonesia

4613

441*

9.6*

48

41

Chittagong

Bangladesh

Other Indian Subcontinent

1329

374*

28.2*

48

42

Kolkata

India

India

526

148*

28.2*

48

43

Chennai/Madras

India

India

1520

428*

28.2*

48

44

Jawaharlal Nehru (JNPT)/Nhava Sheva

India

India

4752

1339*

28.2*

48

45

Mundra

India

India

1149

324*

28.2*

48

46

Colombo

Sri Lanka

Other Indian Subcontinent

4137

3078

74.4

24

47

Port Muhammad Bin Qasim

Pakistan

Pakistan

779

219*

28.2*

48

48

Karachi

Pakistan

Pakistan

1370

386*

28.2*

48

49

St Petersburg

Russia

Russia

1931

232

12.0

48

50

Vancouver BC

Canada

Canada

2514

141*

5.6*

24

51

Seattle

USA

United States

2134

119*

5.6*

24

52

Tacoma

USA

United States

1455

81*

5.6*

24

53

Oakland

USA

United States

2330

130*

5.6*

24

54

Los Angeles

USA

United States

7832

438*

5.6*

24

55

Long Beach

USA

United States

6263

351*

5.6*

24

56

Honolulu

USA

United States

939

53*

5.6*

24

57

Manzanillo (Mexico)

Mexico

Mexico

1509

460*

30.5*

24

58

Lazaro Cardenas

Mexico

Mexico

796

242*

30.5*

24

58-1

Puerto Quetzal

Guatemala

Central America

265#

32

11.9#

48

58-1

Acajutla

El Salvador

Central America

147#

0

0.0#

48

58-3

La Union

El Salvador

Central America

0

0

0.0

48

58-4

Corinto

Nicaragua

Central America

65#

1

1.9#

48

58-5

Caldera

Costa Rica

Central America

155#

0

0.0#

48

59

Balboa

Panama

Central America

2759 #

2561

92.8 #

24

60

Manzanillo (Panama)/Cristobal/Colon

Panama

Central America

2803 #

2205

78.7 #

24

61

Puerto Limon

Costa Rica

Central America

881#

22

2.5#

48

62

Puerto Cortes/Puerto Castilla

Honduras

Central America

613#

0

0.0#

48

62-1

Santo Tomas De Castilla/Puerto Barrios

Guatemala

Central America

732#

109

15.0#

48

63

Veracruz

Mexico

Mexico

663

202*

30.5*

24

64

San Juan

USA (Puerto Rico)

Caribbean Basin

1526

465*

30.5*

48

65

Caucedo

Dominican Rep

Caribbean Basin

1005

306*

30.5*

48

66

Kingston

Jamaica

Caribbean Basin

1892

1627

86.0

48

67

Freeport

Bahamas

Caribbean Basin

1125

1114

99.0

48

68

Houston

USA

United States

1812

101*

5.6*

24

68-1

New Orleans/Freeport

USA

United States

635

36*

5.6*

24

69

Miami

USA

United States

847

47*

5.6*

24

70

Port Everglades

USA

United States

793

44*

5.6*

24

71

Jacksonville

USA

United States

857

48*

5.6*

24

72

Savannah

USA

United States

2825

158*

5.6*

24

73

Charleston

USA

United States

1384

77*

5.6*

24

74

Virginia

USA

United States

1895

106*

5.6*

24

75

Baltimore

USA

United States

611

34*

5.6*

24

76

New York/New Jersey

USA

United States

5292

296*

5.6*

24

77

Montreal

Canada

Canada

1331

75*

5.6*

24

78

Buenaventura

Colombia

Colombia

663

68*

10.2*

48

79

Guayaquil

Ecuador

Ecuador

1093

112*

10.2*

48

80

Callao

Peru

Peru

1346

137*

10.2*

48

81

Valparaiso

Chile

Chile

879

90*

10.2*

48

82

San Antonio

Chile

Chile

871

89*

10.2*

48

83

Cartagena

Colombia

Colombia

1433

146*

10.2*

48

84

Puerto Cabello

Venezuela

Venezuela

630

64*

10.2*

48

85

Santos

Brazil

Brazil

2722

278*

10.2*

48

86

Paranagua

Brazil

Brazil

672

69*

10.2*

48

87

Navegantes

Brazil

Brazil

568

58*

10.2*

48

88

Itajai

Brazil

Brazil

957

98*

10.2*

48

89

Rio Grande

Brazil

Brazil

647

66*

10.2*

48

90

Montevideo

Uruguay

Other East Coast of South America

672

69*

10.2*

48

91

Buenos Aires

Argentina

Argentina

1731

177*

10.2*

48

92

Shahid Rajaee (Bandar Abbas)

Iran

Arabian Gulf

2593

249*

9.6*

48

93

Dammam

Saudi Arabia

Arabian Gulf

1333

128*

9.6*

48

94

Mina Zayed (Abu Dhabi)

UAE

Arabian Gulf

530

51*

9.6*

48

95

Dubai/Jebel Ali

UAE

Arabian Gulf

11,600

5498

47.4

24

96

Khor Fakkan/Sharjah Combined

UAE

Arabian Gulf

3023

2315

76.6

24

97

Salalah

Oman

Arabian Gulf

3485

3405

97.7

24

98

Jeddah

Saudi Arabia

Arabian Gulf

3831

1683

43.9

24

99

Aqaba

Jordan

Other Mediterranean

619

59*

9.6*

48

100

El Sokhna

Egypt

Egypt

607

171

28.2

48

101

Port Said

Egypt

Egypt

3475

2477

71.3

24

102

Damietta

Egypt

Egypt

1096

187*

17.0*

48

103

Alexandria El Dekheila

Egypt

Egypt

1496

255*

17.0*

48

104

Tangier/Tangier Med

Morocco

W. Med

2058

1980

96.2

24

105

Las Palmas De Gran Canaria

Spain (Canary Is)

Western Africa

1187

334

28.2

24

106

Ashdod

Israel

Israel

1018

173*

17.0*

24

107

Haifa

Israel

Israel

1264

215*

17.0*

24

108

Beirut

Lebanon

Other Mediterranean

949

162*

17.0*

48

109

Latakia

Syria

Other Mediterranean

586

100*

17.0*

48

110

Mersin

Turkey

Turkey

1024

174*

17.0*

48

111

Izmir

Turkey

Turkey

728

124*

17.0*

48

112

Ambarli/Istanbul

Turkey

Turkey

2540

432*

17.0*

48

113

Constantza

Romania

Romania

557

95*

17.0*

48

114

Odessa/Illichivsk

Ukraine

Ukraine

653

111*

17.0*

48

115

Piraeus

Greece

C. Med

878

149*

17.0*

24

116

Marsaxlokk

Malta

Other Mediterranean

2371

2265

95.5

24

117

Cagliari

Italy

C. Med

553

94*

17.0*

24

118

Taranto

Italy

C. Med

582

99*

17.0*

24

119

Gioia Tauro

Italy

C. Med

2852

2676

93.8

24

120

Naples

Italy

C. Med

535

91*

17.0*

24

121

Leghorn (Livorno)

Italy

C. Med

628

107*

17.0*

24

122

La Spezia

Italy

C. Med

1285

219*

17.0*

24

123

Genoa

Italy

C. Med

1759

299*

17.0*

24

124

Marseilles/Fos

France

France

953

162*

17.0*

24

125

Barcelona

Spain

W. Med

1948

332*

17.0*

24

126

Valencia

Spain

W. Med

4207

2156

51.2

24

127

Algeciras

Spain

W. Med

2810

2626

93.4

24

128

Felixstowe

UK

United Kingdom

3400

408*

12.0*

24

129

London (Tilbury)/Thamesport

UK

United Kingdom

424**

51*

12.0*

24

130

Southampton

UK

United Kingdom

1540

185*

12.0*

24

131

Liverpool

UK

United Kingdom

681

82*

12.0*

24

132

Dublin

Eire

United Kingdom

554

67*

12.0*

24

133

Lisbon

Portugal

W. Med

513

87*

17.0*

24

134

Bilbao

Spain

W. Med

531

90*

17.0*

24

135

Bordeaux

France

France

632

76*

12.0*

24

136

Le Havre

France

France

2358

283*

12.0*

24

137

Zeebrugge

Belgium

N. Europe

2390

287*

12.0*

24

138

Antwerp

Belgium

N. Europe

8468

2286

27.0

24

139

Rotterdam

Netherlands

N. Europe

11,146

3344

30.0

24

140

Bremen/Bremerhaven

Germany

N. Europe

4871

2192

45.0

24

141

Hamburg

Germany

N. Europe

7900

2610

33.0

24

142

Gdansk

Poland

N. Europe

509

61*

12.0*

24

143

Gothenburg

Sweden

N. Europe

796

96*

12.0*

24

144

Abidjan

Ivory Coast

Western Africa

530

149*

28.2*

48

145

Tema

Ghana

Western Africa

590**

166*

28.2*

48

146

Lagos/Apapa/Tin Can Island

Nigeria

Western Africa

500**

141*

28.2*

48

147

Cape Town

South Africa

Southern Africa

697

196*

28.2*

24

148

Durban

South Africa

Southern Africa

2529

713*

28.2*

24

149

Mombasa

Kenya

Kenya

696

196*

28.2*

48

150

Djibouti

Djibouti

Other East Africa

600

169*

28.2*

48

151

Brisbane

Australia

Australia

929

62*

6.7*

24

152

Sydney

Australia

Australia

2020

135*

6.7*

24

153

Melbourne

Australia

Australia

2322

155*

6.7*

24

154

Fremantle

Australia

Australia

583

39*

6.7*

24

155

Auckland

New Zealand

New Zealand

894

60*

6.7*

24

156

Tauranga

New Zealand

New Zealand

591

39*

6.7*

24

  1. Source: authors’ estimation from CI-online database and Drewry Maritime Research (2011a).
  2. Bold: major transhipment ports shown in Drewry Maritime Research (2011a) which are utilized for parameter estimation of the maritime shipping submodel.
  3. * Estimated based on the average transhipment rate by region shown in Drewry Maritime Research (2011a).
  4. ** Authors’ estimation.
  5. # COCATRAM (Central American Commission of Maritime Transport).

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Shibasaki, R., Iijima, T., Kawakami, T. et al. Network assignment model of integrating maritime and hinterland container shipping: application to Central America. Marit Econ Logist 19, 234–273 (2017). https://doi.org/10.1057/s41278-016-0055-3

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