# Time Reliability of the Maritime Transportation Network for China’s Crude Oil Imports

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Model for Transportation Time Reliability Evaluation

#### 3.1. Problem Statement

#### 3.2. Model Formulation

- (1)
- (2)
- The crude oil flow on node a for other countries is a known constant, which is denoted by o
_{a}. - (3)
- Suppose the variables are a daily amount, which means that the annual demand of China’s imported crude oil is averaged daily, and the unit is 100,000 tons.
- (4)
- The speed of vessels on different maritime transportation routes is the same.

R | R = (1,2,3,…r), set of origins for imported crude oil |

S | S = (1,2,3,…s), set of destinations for imported crude oil |

q_{rs} | Transportation volume of crude oil for OD pair rs |

p_{r} | Import price of crude oil for country r |

D | Daily demand for imported crude oil in China |

B_{r} | Largest possible import volume of crude oil from country r to China |

φ | Time value of imported crude oil |

x_{a} | Crude oil flow on node a for China (a = 1,2,…,A) |

o_{a} | Crude oil flow on node a for other countries (a = 1,2,…,A) |

C_{a} | Capacity of node a (a = 1,2,…,A) |

θ_{a} | Fraction of the capacity under normal operation for node a |

w_{a} | Total flow volume of all cargo types on node a (100,000 tons) |

x | Vector of flows across all nodes (a∈A) |

t_{a} | Time incurred on node a |

t_{a}^{0} | Free-flow transportation time for node a |

t_{a,a+1} | Transportation time of legs connecting two adjacent nodes |

T^{rs} | Transportation time for OD pair rs |

f_{k}^{rs} | Flow on path k of OD pair rs |

δ^{rs}_{a,k} | Indicator variable, which is equal to 1 if path k traverses node a, 0 otherwise |

η_{a} | Proportion of crude oil flow to the total flow volume on node a |

k_{a} | Asymmetry factor that reflects the interaction among different cargo flows on node a |

α, β | Parameters to be calibrated |

R_{e} | Transportation time reliability of the maritime transportation network for China’s imported crude oil |

w_{rs} | Weight of OD pair rs, which is calculated by its share of imported crude oil |

_{a}= 0. Equation (10) is the expression for the total traffic volume of all cargo types on node a.

#### 3.3. Solution Algorithm

_{m}.

_{rs}in the upper model, which is the transportation demand for the OD pair rs.

_{a}and the transportation time t

_{a}.

_{m}.

#### 3.4. Reliability Evaluation Procedure

- (1)
- Set sample number n = 1 and parameter count = 0.
- (2)
- Generate the capacity value according to the distribution properties for a specified node, {x
_{an}}, (a = 1,2,…,A), and the capacities for other nodes under normal conditions. - (3)
- Perform the bi-level model with the node capacity and solve the model using the above algorithm.
- (4)
- Collect statistics such as the transportation time of each OD pair and calculate the network transportation time T
_{n}.$${T}_{n}={\displaystyle \sum _{r}{\displaystyle \sum _{s}{T}^{rs}{w}_{rs}}}.$$If T_{n}is within the specified threshold, then count = count + 1. - (5)
- If sample number n is less than the required sample size N, the increment sample number is n = n + 1 and return to Step (2). Otherwise, go to Step (6).
- (6)
- Calculate the transportation time reliability of the network.$${R}_{e}=count/N.$$
- (7)
- Repeat Steps (1)–(6) above to calculate the transportation time reliability of the entire network under random capacity variations in each node.

## 4. Case Study

#### 4.1. Problem Setting

_{1},v

_{2},…,v

_{n}), and the cardinality of the node set is 33, where |V| = 33. We distributed the imported crude oil traffic over 13 OD pairs. The nodes in each OD pair, the transportation routes, the import price, and the largest possible import volume of crude oil from country r are shown in Table 1.

_{r}is determined by the volume of crude oil production for each country and the recent export volume to China. According to the forecast of China’s crude oil imports, the total crude oil demand from the above countries is 800,000 tons per day. The parameter φ relates to the consumption of crude oil per gross domestic product (GDP). By referring to the China Statistical Yearbook, we set φ to be 1.4 $/h.

_{a}for the impedance function of port nodes are from the port authority website. For strait and canal nodes, the values of C

_{a}are represented by the volumes transported through the nodes and are from the U.S. Energy Information Administration. The parameter values of o

_{a}are calculated according to the values of C

_{a}and the import volume of China. In addition, the units for C

_{a}and o

_{a}are 100,000 tons/day. The values of η

_{a}, k

_{a}, α

_{a}, and β

_{a}are determined by referencing the study of Meng and Wang [38]. For port nodes, η

_{a}= 1 and k

_{a}= 0. For strait and canal nodes, η

_{a}= 0.6 and k

_{a}= 0.5. For all nodes, α

_{a}= 2.5 and β

_{a}= 2.

_{a}for port nodes are calculated using the port handling efficiency. In terms of strait or canal nodes, t

_{a}values are calculated using the distance between the strait or canal entrance and exit as well as the tanker speeds. We assume the tanker speed is 15 kn. The parameter t

_{a,a}

_{+1}refers to the transportation time of the legs between two adjacent nodes. Selecting different nodes implies varied transportation distances between the connected legs and thus different transportation times. For example, for the transportation routes of the OD pair from Saudi Arabia to Ningbo, the t

_{a,a}

_{+1}of the Strait of Malacca is the sum of the transportation time from the Strait of Malacca to the Strait of Hormuz and from the Strait of Malacca to the Taiwan Strait. According to the transportation distances and speed of tankers, the parameter t

_{a,a}

_{+1}is calculated, as shown in Table 2.

#### 4.2. Transportation Time Reliability Results

_{a}= 0, which is the lower bound of the capacity for each node. A Monte Carlo simulation was applied to generate random node capacities between the lower and upper bounds of the uniform distribution for each node, in order to illustrate the effects of extreme events on the node capacity. The estimated mean and standard deviation values resulting from 10,000 Monte Carlo simulations were close to those of the theoretical values. For example, the theoretical mean and standard deviation of the capacities for the Strait of Hormuz were found to be 11.5 and 6.64, respectively, whereas the estimated values were 11.49 and 6.62, respectively.

## 5. Discussion

#### 5.1. Transportation Time Reliability under Each Node’s Capacity Variations

#### 5.2. Causes of Transportation Time Reliability Variations

#### 5.3. Vulnerability Analysis

## 6. Conclusions and Policy Implications

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Clarksons Research. China Intelligence Monthly; Clarkson Research Services Limited: London, UK, 2018; Volume 13, pp. 7–8. Available online: https://www.clarksons.net (accessed on 24 May 2018).
- Chen, A.; Yang, H.; Lo, H.K.; Tang, W.H. Capacity reliability of a road network: An assessment methodology and numerical results. Transp. Res. Part B
**2002**, 36, 225–252. [Google Scholar] [CrossRef] - Wardrop, J.G. Some theoretical aspects of road traffic research. In Proceedings of the Institution of Civil Engineers, Part II; Operational Research Society: Birmingham, UK, 1952; Volume 1, pp. 325–378. [Google Scholar] [CrossRef]
- Frank, M.; Wolfe, P. An algorithm for quadratic programming. Nav. Res. Logist.
**1956**, 3, 95–110. [Google Scholar] [CrossRef] - Clark, S.; Watling, D. Modelling network travel time reliability under stochastic demand. Transp. Res. Part B
**2005**, 39, 119–140. [Google Scholar] [CrossRef] [Green Version] - Szeto, W.Y.; O’Brien, L.; O’Mahony, M. Risk-averse traffic assignment with elastic demands: NCP formulation and solution method for assessing performance reliability. Netw. Spat. Econ.
**2006**, 6, 313–332. [Google Scholar] [CrossRef] - Szeto, W.Y. Cooperative game approaches to measuring network reliability considering paradoxes. Transp. Res. Part C
**2011**, 19, 229–241. [Google Scholar] [CrossRef] [Green Version] - Ng, M.W.; Waller, S.T. A computationally efficient methodology to characterize travel time reliability using the fast Fourier transform. Transp. Res. Part B
**2010**, 37, 1202–1219. [Google Scholar] [CrossRef] - Kim, J.; Mahmassani, H.S.; Vovsha, P.; Stogios, Y.; Dong, J. Scenario-based approach to analysis of travel time reliability with traffic simulation models. Transp. Res. Rec.
**2013**, 2391, 56–68. [Google Scholar] [CrossRef] [Green Version] - Mine, H.; Kawai, H. Mathematics for Reliability Analysis; Asakurashoten: Tokyo, Japan, 1982. [Google Scholar]
- Asakura, Y.; Kashiwadani, M. Road Network Reliability Caused by Daily Fluctuation of Traffic Flow. In Proceedings of the 19th PTRC Summer Annual Meeting, Brighton, UK, July 1991; pp. 73–84. Available online: https://trid.trb.org/view/1173049 (accessed on 25 December 2019).
- Chen, A.; Yang, H.; Lo, H.K.; Tang, W.H. A capacity related reliability for transportation networks. J. Adv. Transp.
**1999**, 33, 183–200. [Google Scholar] [CrossRef] - Bell, M.G.H.; Cassir, C.; Iida, Y.; Lam, W.H.K. A Sensitivity-Based Approach to Network Reliability Assessment. In Proceedings of the 14th International Symposium on Transportation and Traffic Theory, Jerusalem, Israel, 20–23 July 1999; pp. 283–300. [Google Scholar]
- Asakura, Y. Reliability Measures of an Origin and Destination Pair in a Deteriorated Road Network with Variable Flow. In Proceedings of the Transportation Networks: Recent Methodological Advances, Selected Proceedings of the 4th EURO Transportation Meeting, Newcastle, UK, 9–11 September 1996; pp. 273–287. [Google Scholar]
- Zheng, F.F.; Liu, X.B.; Zuylen, H.V.; Li, J.; Lu, C. Travel Time Reliability for Urban Networks: Modelling and Empirics. J. Adv. Transp.
**2017**, 2017, 9147356. [Google Scholar] [CrossRef] [Green Version] - Chen, X.Q.; Chen, X.W.; Zheng, H.Y.; Chen, C.Q. Understanding network travel time reliability with on-demand ride service data. Front. Eng. Manag.
**2017**, 4, 388–398. [Google Scholar] [CrossRef] - Woodard, D.; Nogin, G.; Koch, P.; Racz, D.; Goldszmidt, M.; Horvitz, E. Predicting travel time reliability using mobile phone GPS data. Transp. Res. Part C
**2017**, 75, 30–44. [Google Scholar] [CrossRef] - Lo, H.K.; Tung, Y.K. Network with degradable links: Capacity analysis and design. Transp. Res. Part B
**2003**, 37, 345–363. [Google Scholar] [CrossRef] - Ng, M.W.; Waller, S.T.; Szeto, W.Y. Distribution-free travel time reliability assessment with probability inequalities. Transp. Res. Part B
**2011**, 45, 852–866. [Google Scholar] [CrossRef] [Green Version] - Bell, M.G.H. A game theory approach to measuring the performance reliability of transport networks. Transp. Res. Part B
**2000**, 34, 533–545. [Google Scholar] [CrossRef] - Bell, M.G.H.; Cassir, C. Risk-averse user equilibrium traffic assignment: An application of game theory. Transp. Res. Part B
**2002**, 36, 671–681. [Google Scholar] [CrossRef] - Liu, Y.H.; Li, J.L.; Chen, X.; Luo, X. Impact of Incident on Travel Time Reliability in Advanced Traveler Information Systems. J. Transp. Syst. Eng. Inf. Technol.
**2018**, 18, 36–41. [Google Scholar] - Ahmad, T.H.; Luis, F.; Simon, W.; Phil, C.; Ameneh, S. Modelling the impact of traffic incidents on travel time reliability. Transp. Res. Part C
**2016**, 70, 86–97. [Google Scholar] [CrossRef] - Chen, A.; Ji, Z.W.; Recker, W. Travel Time Reliability with Risk-Sensitive Travelers. Transp. Res. Rec.
**2002**, 1783, 27–33. [Google Scholar] [CrossRef] - Recker, W.; Chung, Y.S.; Park, J.Y.; Wang, L.; Chen, A.; Ji, Z.W.; Liu, H.X.; Horrocks, M.; Oh, J.S. Considering Risk-Taking Behavior in Travel Time Reliability; California Partners for Advanced Transit and Highways (PATH), Institute of Transportation Studies: Berkeley, CA, USA, 2005. [Google Scholar]
- Watling, D.P. A second order stochastic network equilibrium model. Transp. Sci.
**2002**, 36, 149–183. [Google Scholar] [CrossRef] - Yin, Y.; Lam, W.H.K.; Ieda, H. New technology and the modelling of risk taking behavior in congested road networks. Transp. Res. Part C
**2004**, 12, 171–192. [Google Scholar] [CrossRef] - Lo, H.K.; Luo, X.W.; Siu, B. Degradable transport network: Travel time budget of travelers with heterogeneous risk aversion. Transp. Res. Part B
**2006**, 40, 792–806. [Google Scholar] [CrossRef] - Siu, B.W.Y.; Lo, H.K. Doubly uncertain transportation network: Degradable capacity and stochastic demand. Eur. J. Oper. Res.
**2008**, 191, 166–181. [Google Scholar] [CrossRef] - Zhou, Z.; Chen, A. Comparative analysis of three user equilibrium models under stochastic demand. J. Adv. Transp.
**2008**, 42, 239–263. [Google Scholar] [CrossRef] - Lam, W.H.K.; Shao, H.; Sumalee, A. Modeling impacts of adverse weather conditions on a road network with uncertainties in demand and supply. Transp. Res. Part B
**2008**, 42, 810–890. [Google Scholar] [CrossRef] - Wang, J.Y.T.; Ehrgott, M.; Chen, A. A bi-objective user equilibrium model of travel time reliability in a road network. Transp. Res. Part B
**2014**, 66, 4–15. [Google Scholar] [CrossRef] [Green Version] - Xu, X.; Chen, A.; Cheng, L. Assessing the effects of stochastic perception error under travel time variability. Transportation
**2013**, 40, 525–548. [Google Scholar] [CrossRef] - Xu, X.; Chen, A.; Cheng, L.; Lo, H.K. Modeling distribution tail in network performance assessment: A mean-excess total travel time risk measure and analytical estimation method. Transp. Res. Part B
**2014**, 66, 32–49. [Google Scholar] [CrossRef] - Lam, J.S.L.; Yap, W.Y.; Cullinane, K. Structure, conduct and performance on the major liner shipping routes. Marit. Policy Manag.
**2007**, 34, 359–381. [Google Scholar] [CrossRef] - Sadovaya, E.; Tha, V.V. Impacts of Implementation of the Effective Maritime Security Management Model (EMSMM) on Organizational Performance of Shipping Companies. Asian J. Shipp. Logist.
**2015**, 31, 195–215. [Google Scholar] [CrossRef] [Green Version] - Bao, T.T.; Xie, X.L.; Long, P.Y. Shipping enterprise performance evaluation under uncertainty base on multiple-criteria evidential reasoning approach. Transp. Res. Procedia
**2017**, 25, 2761–2772. [Google Scholar] [CrossRef] - Meng, Q.; Wang, X.C. Intermodal hub-and-spoke network design: Incorporating multiple stakeholders and multi-type containers. Transp. Res. Part B
**2011**, 45, 724–742. [Google Scholar] [CrossRef] - Yu, S.N.; Yang, Z.Z.; Yu, B. Air express network design based on express path choices e Chinese case study. J. Air Transp. Manag.
**2017**, 61, 73–80. [Google Scholar] [CrossRef] - Clarksons Research. Word Tanker Ports Map. 2018. Available online: https://www.clarksons.net (accessed on 2 April 2018).

**Figure 3.**Schematic diagram of the maritime transportation network for China’s imported crude oil. Note: The solid arrows demonstrate the transportation stages between port nodes and strait or canal nodes. The dotted arrows demonstrate the transportation stages between strait and canal nodes.

**Figure 5.**Transportation time reliability of the entire network under random capacity variations in each node.

Region | Sources | Major Ports | Crude Oil Transportation Routes | Price of Crude Oil (ton/$) | B_{r} (100,000 tons) |
---|---|---|---|---|---|

Middle East | Saudi Arabia | Yanbu | Strait of Hormuz-Strait of Malacca/Sunda Strait/Lombok Strait-Taiwan Strait-Ningbo | 393.2 | 2.0 |

Ras Tanura | |||||

Juaymah | |||||

Iraq | Fao | 375.2 | 2.0 | ||

Al Basrah | |||||

Iran | Kharg Island | 382.9 | 2.0 | ||

Bandar Mahshahr | |||||

United Arab Emirates | Das Island | 409.2 | 2.0 | ||

Zirku | |||||

Fujairah | |||||

Kuwait | Mina Al Ahmadi | 388.2 | 2.0 | ||

Mina Saud | |||||

Oman | Mina Al Fahal | Strait of Malacca/Sunda Strait/Lombok Strait-Taiwan Strait-Ningbo | 399.1 | 1.2 | |

Africa | Angola | Cabinda | Cape of Good Hope-Strait of Malacca/Sunda Strait/Lombok Strait-Taiwan Strait-Ningbo | 399.1 | 2.0 |

Palanca | |||||

Congo | Djeno Terminal | 400.0 | 0.4 | ||

Sudan | Port Sudan | Bab el Mandeb-Strait of Malacca/Sunda Strait/Lombok Strait-Taiwan Strait-Ningbo | 406.4 | 0.2 | |

Libya | Es Sider | Suez Canal-Bab el Mandeb-Strait of Malacca/Sunda Strait/Lombok Strait-Taiwan Strait-Ningbo | 423.0 | 0.6 | |

Ras Lanuf | Strait of Gibraltar-Cape of Good Hope-Strait of Malacca/Sunda Strait/Lombok Strait-Taiwan Strait-Ningbo | ||||

Latin America | Venezuela | Puerto Jose | Panama Canal-Ningbo/Cape of Good Hope-Strait of Malacca/Sunda Strait/Lombok Strait-Taiwan Strait-Ningbo | 301.7 | 2.0 |

Puerto La Cruz | |||||

Colombia | Barranquilla | 360.3 | 1.4 | ||

Brazil | Sao Sebastiao | 397.4 | 2.0 | ||

Gebig |

Region | Sources | Nodes | t_{a} | t_{a,a}_{+1} |
---|---|---|---|---|

Middle East | Yanbu | 22.73 | 149.13 | |

Ras Tanura | 22.73 | 23.66 | ||

Juaymah | 22.73 | 24.12 | ||

Saudi Arabia, Iraq, Iran, United Arab Emirates, Kuwait | Fao | 25 | 33.74 | |

Al Basrah | 95.24 | 32.29 | ||

Kharg Island | 10 | 27.04 | ||

Bandar Mahshahr | 125 | 3.07 | ||

Das Island | 16.67 | 13.98 | ||

Zirku | 43.25 | 15.13 | ||

Fujairah | 25 | 5.26 | ||

Mina Al Ahmadi | 50 | 32.92 | ||

Mina Saud | 56.67 | 31.63 | ||

Strait of Hormuz | 5.40 | — | ||

Strait of Malacca | 38.88 | 334.21 | ||

Sunda Strait | 5.40 | 380.91 | ||

Lombok Strait | 2.90 | 405.90 | ||

Taiwan Strait | 13.32 | 34.93 | ||

Oman | Mina Al Fahal | 11.11 | — | |

Strait of Malacca | 38.88 | 323.61 | ||

Sunda Strait | 5.40 | 368.61 | ||

Lombok Strait | 2.90 | 393.60 | ||

Taiwan Strait | 13.32 | 34.93 | ||

Africa | Angola, Congo | Cabinda | 25 | 119.69 |

Palanca | 45 | 113.14 | ||

Djeno Terminal | 125 | 121.98 | ||

Strait of Malacca | 38.88 | 492.01 | ||

Sunda Strait | 5.40 | 483.90 | ||

Lombok Strait | 2.90 | 556.62 | ||

Taiwan Strait | 13.32 | 34.93 | ||

Sudan | Port Sudan | 100 | 36.58 | |

Bab el Mandeb | 1.80 | — | ||

Strait of Malacca | 38.88 | 360.32 | ||

Sunda Strait | 5.40 | 392 | ||

Lombok Strait | 2.90 | 476.18 | ||

Taiwan Strait | 13.32 | 34.93 | ||

Libya | Es Sider | 100 | 68.16/91.78 | |

Ras Lanuf | 78.67 | 68.21/92.59 | ||

Suez Canal | 6.84 | 83.04 | ||

Bab el Mandeb | 1.80 | — | ||

Strait of Gibraltar | 2.09 | 340.43 | ||

Strait of Malacca | 38.88 | 360.32/492.01 | ||

Sunda Strait | 5.40 | 392/483.90 | ||

Lombok Strait | 2.90 | 476.18/556.62 | ||

Taiwan Strait | 13.32 | 34.93 | ||

Latin America | Venezuela, Colombia, Brazil | Puerto Jose | 25 | 381.91/65.91 |

Puerto La Cruz | 33.67 | 381.69/66.57 | ||

Barranquilla | 125 | 422.52/24.87 | ||

Sao Sebastiao | 25 | 222.56/242.45 | ||

Gebig | 27.78 | 221.05/290.29 | ||

Strait of Malacca | 38.88 | 492.01 | ||

Sunda Strait | 5.40 | 483.90 | ||

Lombok Strait | 2.90 | 556.62 | ||

Taiwan Strait | 13.32 | 34.93 | ||

Panama Canal | 2.93 | 569.33 |

_{a}for port nodes refers to the required loading time of 100,000 tons of crude oil. The unit for both t

_{a}and t

_{a,a}

_{+1}is hours.

Region | Sources | Transportation Time | Import Volume | Transportation Time of the Network |
---|---|---|---|---|

Middle East | Saudi Arabia | 736.5 | 2 | 814.4 |

Iraq | 876.2 | 2 | ||

Iran | 721.9 | 1.34 | ||

United Arab Emirates | 822.8 | 1.73 | ||

Kuwait | 760.5 | 0.33 | ||

Oman | 662.5 | 0.6 | ||

Africa | Angola | 896.9 | 0.29 | |

Congo | 999.2 | 0.4 | ||

Sudan | 648.67 | 0.2 | ||

Libya | 1078.7 | 0.22 | ||

Latin America | Venezuela | 965.6 | 0.31 | |

Colombia | 1083.2 | 0.39 | ||

Brazil | 839.7 | 0.23 |

Region | Sources | Crude Oil Transportation Routes | Transportation Time (Hours) |
---|---|---|---|

Middle East | Saudi Arabia | Strait of Hormuz-Strait of Malacca-Taiwan Strait-Ningbo | 392.8 |

Africa | Congo | Cape of Good Hope-Strait of Malacca-Taiwan Strait-Ningbo | 648.9 |

Libya | Strait of Gibraltar-Cape of Good Hope-Strait of Malacca-Taiwan Strait-Ningbo/Suez Canal-Bab el Mandeb-Strait of Malacca-Taiwan Strait-Ningbo | 958.5/538.7 | |

Latin America | Brazil | Panama Canal-Ningbo/Cape of Good Hope-Strait of Malacca-Taiwan Strait-Ningbo | 811.7/749.5 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, S.; Lu, J.; Jiang, L.
Time Reliability of the Maritime Transportation Network for China’s Crude Oil Imports. *Sustainability* **2020**, *12*, 198.
https://doi.org/10.3390/su12010198

**AMA Style**

Wang S, Lu J, Jiang L.
Time Reliability of the Maritime Transportation Network for China’s Crude Oil Imports. *Sustainability*. 2020; 12(1):198.
https://doi.org/10.3390/su12010198

**Chicago/Turabian Style**

Wang, Shuang, Jing Lu, and Liping Jiang.
2020. "Time Reliability of the Maritime Transportation Network for China’s Crude Oil Imports" *Sustainability* 12, no. 1: 198.
https://doi.org/10.3390/su12010198