# Shore Power Deployment Problem—A Case Study of a Chinese Container Shipping Network

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model

#### Problem Description

**Sets and indices**- $\mathcal{P}$ the set of ports, indexed by i, $i=1,\dots \left|\mathcal{P}\right|$;
- $\mathcal{R}$ the set of routes, indexed by j, $j=1,\dots ,\left|\mathcal{R}\right|$;
- $\mathcal{N}$ the set of phases, indexed by n, $n=0,1,\dots ,\left|\mathcal{N}\right|$;
- ${\mathcal{P}}_{j}$ the set of ports, visited by route j, $\forall j\in \mathcal{R}$;
- ${\mathcal{R}}_{i}$ the set of routes, which visit port i, $\forall i\in \mathcal{P}$;
**Parameters**- ${\widehat{x}}_{i}$ binary parameter, equals 1 when port i is already equipped with SP facilities at the beginning of phase 0, 0 otherwise $\forall i\in \mathcal{P}$
- ${\widehat{y}}_{j}$ binary parameter, equals 1 when shipping route j is already equipped with SP facilities at the beginning of phase 0, 0 otherwise $\forall j\in \mathcal{R}$;
- ${F}_{ji}$ the annual fuel cost (USD) of route j for berthing at port i without using SP, $\forall i\in \mathcal{P},\forall j\in {\mathcal{R}}_{i}$;
- ${E}_{ji}$ the annual electricity cost (USD) of route j for berthing at port i using SP, $\forall i\in \mathcal{P},\forall j\in {\mathcal{R}}_{i}$;
- ${U}_{ji}$ the annual profit (USD) of port i selling SP to ships deployed on route j, $\forall i\in \mathcal{P},\forall j\in {\mathcal{R}}_{i}$;
- ${C}_{i}^{\mathcal{P}}$ the equivalent annual cost (USD/year) of onshore SP facilities at port i, $\forall i\in \mathcal{P}$;
- ${C}_{j}^{\mathcal{R}}$ the equivalent annual cost (USD/year) of onboard SP facilities for route j, $\forall j\in \mathcal{R}$;
**Variables**- ${x}_{i}$ binary variable, equal to 1 if port i receives government subsidy, 0 otherwise, $\forall i\in \mathcal{P}$;
- ${y}_{j}$ binary variable, equal to 1 if route j receives government subsidy, 0 otherwise, $\forall j\in \mathcal{R}$;
- ${\widehat{\mathcal{P}}}_{n}$ the set of ports that decide to construct onshore SP facilities at or before phase n, $\forall n\in \mathcal{N}$;
- ${\widehat{\mathcal{R}}}_{n}$ the set of routes that decide to retrofit the ships deployed and construct onboard SP facilities at or before phase n, $\forall n\in \mathcal{N}$;
- ${\alpha}_{i}\left(\widehat{\mathcal{R}}\right)$ binary variable, equal to 1 if port i will benefit from constructing onshore SP facilities, 0 otherwise, given a set of routes with onboard facilities, which is denoted by $\widehat{\mathcal{R}}$,

- ${\beta}_{i}\left(\widehat{\mathcal{R}}\right)$ binary variable, equal to 1 if route i will benefit from constructing onboard SP facilities, 0 otherwise, given a set of ports with onboard facilities, which is denoted by $\widehat{\mathcal{P}}$,

## 3. Solution Method

**Set**- $\Psi $ the set of all ports and shipping routes considered, $\Psi :=\mathcal{P}\cup \mathcal{R}$;
**Parameters**- ${\overline{C}}_{i}$ binary variable, equal to 1 if port i receives government subsidy, 0 otherwise, $\forall i\in \mathcal{P}$;
- ${y}_{j}$ binary variable, equal to 1 if route j receives government subsidy, 0 otherwise, $\forall j\in \mathcal{R}$;
- ${\widehat{\mathcal{P}}}_{n}$ the set of ports that decide to construct onshore SP facilities at or before phase n, $\forall n\in \mathcal{N}$;
- ${\widehat{\mathcal{R}}}_{n}$ the set of routes that decide to retrofit the ships deployed and construct onboard SP facilities at or before phase n, $\forall n\in \mathcal{N}$.

**Proposition**

**1.**

**Proposition**

**2.**

**Proposition**

**3.**

## 4. Numerical Experiment

#### 4.1. Parameter Settings

#### 4.2. Results and Discussions

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

UNCTAD | United Nations Conference on Trade and Development |

IMO | International Maritime Organization |

GHG | greenhouse gas |

SP | shore power |

${\mathrm{CO}}_{2}$ | carbon dioxide |

${\mathrm{SO}}_{2}$ | sulfur dioxide |

${\mathrm{NO}}_{\mathrm{X}}$ | nitrogen oxides |

${\mathrm{PM}}_{2.5}$ | fine particulate matter |

## Appendix A. Ports and Routes Considered in This Case Study

#### Appendix A.1. Ports Considered in This Case Study

No. | Port Name | Shore Power | No. | Port Name | Shore Power |
---|---|---|---|---|---|

1 | Anqing | N | 46 | Xiamen | Y |

2 | Changshu | N | 47 | Shantou | Y |

3 | Changzhou | N | 48 | Shanghai | Y |

4 | Dachanwan | N | 49 | Shekou | N |

5 | Dalian | Y | 50 | Shenzhen | Y |

6 | Dandong | N | 51 | Shunde | N |

7 | Deqing | N | 52 | Suqian | N |

8 | Dongguan | N | 53 | Taishan | N |

9 | Foshan | Y | 54 | Taizhong | Y |

10 | Fuzhou | Y | 55 | Taicang | N |

11 | Gaolan | N | 56 | Taizhou | N |

12 | Gaoming | N | 57 | Tangshan | Y |

13 | Gaoxiong | Y | 58 | Tianjin | Y |

14 | Guangxi | Y | 59 | Tongling | N |

15 | Haian | N | 60 | Waigaoqiao | N |

16 | Haikou | N | 61 | Wuchongkou | N |

17 | Humen | Y | 62 | Wuhu | Y |

18 | Huadong | N | 63 | Wuzhou | Y |

19 | Huanghua | N | 64 | Wuhan | Y |

20 | Huangpu | N | 65 | Xianggang | N |

21 | Huangshi | Y | 66 | Xinhui | N |

22 | Huizhou | Y | 67 | Xuzhou | N |

23 | Jilong | Y | 68 | Yantai | Y |

24 | Jiangmen | Y | 69 | Yantian | N |

25 | Jiangyin | N | 70 | Yangzhou | Y |

26 | Jinzhou | Y | 71 | Yangjiang | N |

27 | Jingzhou | N | 72 | Yangshan | N |

28 | Jiujiang | Y | 73 | Yichang | N |

29 | Lianyungang | Y | 74 | Yixing | N |

30 | Longtan | N | 75 | Yingkou | Y |

31 | Luzhou | N | 76 | Yueyang | N |

32 | Nanjing | Y | 77 | Yunfu | N |

33 | Nansha | N | 78 | Zhapu | N |

34 | Nantong | Y | 79 | Zhanjiang | N |

35 | Ningbo | Y | 80 | Zhangjiagang | N |

36 | Panjin | N | 81 | Zhaoqing | Y |

37 | Qiba | N | 82 | Zhenjiang | Y |

38 | Qinzhou | N | 83 | Zhongshan | Y |

39 | Qinhuangdao | N | 84 | Zhongqing | Y |

40 | Qingdao | Y | 85 | Zhuhai | Y |

41 | Qingyuan | N | |||

42 | Quanzhou | N | |||

43 | Rizhao | Y | |||

44 | Sanbu | N | |||

45 | Sanshui | N |

#### Appendix A.2. Routes Considered in This Case Study

No. | Route Type | Ports of Call | No. | Route Type | Ports of Call |
---|---|---|---|---|---|

1 | T1 | 75 - 33 | 46 | T2 | 25 - 80 - 55 - 72 |

2 | T1 | 75 - 57 - 58 - 4 | 47 | T2 | 55 - 72 |

3 | T1 | 58 - 33 | 48 | T2 | 74 - 55 - 48 |

4 | T1 | 40 - 43 - 29 - 50 - 11 | 49 | T2 | 67 - 52 - 55 |

5 | T1 | 39 - 68 - 33 | 50 | T2 | 15 - 55 |

6 | T1 | 5 - 26 - 46 - 33 | 51 | T3 | 48 - 23 - 54 - 13 |

7 | T1 | 19 - 33 | 52 | T3 | 48 - 13 - 54 - 23 |

8 | T1 | 75 - 58 - 79 - 38 | 53 | T3 | 5 - 58 - 40 - 29 - 54 - 35 |

9 | T1 | 26 - 57 - 43 - 38 | 54 | T4 | 33 - 11 - 51 |

10 | T1 | 68 - 40 - 46 | 55 | T4 | 33 - 11 - 45 |

11 | T1 | 75 - 58 - 42 - 46 | 56 | T4 | 33 - 11 - 12 |

12 | T1 | 75 - 58 - 46 - 47 | 57 | T4 | 33 - 11 - 9 |

13 | T1 | 42 - 46 - 16 | 58 | T4 | 33 - 4 - 20 |

14 | T1 | 75 - 68 - 48 | 59 | T4 | 33 - 4 - 18 |

15 | T1 | 26 - 48 | 60 | T4 | 33 - 17 |

16 | T1 | 6 - 48 | 61 | T4 | 33 - 11 - 66 |

17 | T1 | 48 - 78 - 61 | 62 | T4 | 33 - 11 - 53 - 44 |

18 | T1 | 55 - 50 - 17 - 11 | 63 | T4 | 33 - 11 - 63 |

19 | T1 | 48 - 42 - 46 | 64 | T4 | 33 - 11 - 14 |

20 | T1 | 5 - 75 - 36 - 34 | 65 | T4 | 33 - 11 - 81 |

21 | T1 | 58 - 34 | 66 | T4 | 33 - 11 - 77 - 7 |

22 | T1 | 40 - 29 - 48 | 67 | T4 | 33 - 4 - 8 |

23 | T2 | 31 - 64 | 68 | T4 | 33 - 4 - 22 |

24 | T2 | 84 - 64 - 1 | 69 | T4 | 33 - 11 - 83 |

25 | T2 | 84 - 1 - 55 - 48 | 70 | T4 | 33 - 85 |

26 | T2 | 84 - 64 | 71 | T4 | 33 - 4 - 41 |

27 | T2 | 73 - 27 - 76 | 72 | T4 | 33 - 11 - 71 |

28 | T2 | 73 - 27 - 64 | 73 | T4 | 20 - 65 - 20 |

29 | T2 | 76 - 48 | 74 | T4 | 65 - 18 |

30 | T2 | 64 - 21 - 28 - 55 - 48 | 75 | T4 | 65 - 17 |

31 | T2 | 1 - 60 | 76 | T4 | 33 - 65 |

32 | T2 | 1 - 59 - 55 - 48 | 77 | T4 | 51 - 9 - 12 - 33 |

33 | T2 | 1 - 48 | 78 | T4 | 20 - 33 |

34 | T2 | 62 - 32 - 48 | 79 | T4 | 24 - 33 |

35 | T2 | 32 - 48 | 80 | T4 | 49 - 65 |

36 | T2 | 37 - 30 - 55 - 48 | 81 | T4 | 51 - 49 |

37 | T2 | 70 - 82 - 56 - 55 - 48 | 82 | T4 | 9 - 12 - 49 |

38 | T2 | 3 - 25 - 55 - 48 | 83 | T4 | 51 - 65 |

39 | T2 | 80 - 34 - 48 | 84 | T4 | 69 - 65 |

40 | T2 | 80 - 34 - 55 - 48 | 85 | T4 | 79 - 65 |

41 | T2 | 2 - 55 - 48 | 86 | T4 | 16 - 65 |

42 | T2 | 55 - 48 | 87 | T4 | 38 - 65 |

43 | T2 | 64 - 72 | 88 | T4 | 47 - 65 |

44 | T2 | 21 - 28 - 62 - 72 | 89 | T4 | 10 - 65 |

45 | T2 | 32 - 70 - 72 | 90 | T4 | 46 - 65 |

91 | T4 | 65 - 42 |

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Content | Value |
---|---|

Original bunker (ton/year) | $5.28391\times {10}^{8}$ |

Final bunker (ton/year) | $2.72231\times {10}^{6}$ |

Environmental benefits (USD/year) | $6.94303\times {10}^{11}$ |

Subsidized ports | 67,69,77 |

Subsidized routes | 1,13,17,23,24.26,29,72,80 |

Ports that finally adopt SP | 1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35, 36,37,38,39,40,41,42,43,44,45,46,47,48,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66, 67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91 |

Routes that finally adopt SP | 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35, 36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,53,54,55,56,57,58,59,60,62,63,64,65,66,67, 68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85 |

Case | Budget Proportion | Final Bunker (ton/year) | Environmental Benefits (USD/year) | Subsidized Ports | Subsidized Routes |
---|---|---|---|---|---|

L-1 | 2.5% | $1.9588\times {10}^{7}$ | $6.72027\times {10}^{11}$ | 69,77 | 7,13,27 |

L-2 | 5% | $8.45733\times {10}^{6}$ | $6.87\times {10}^{11}$ | 69,77 | 1,13,27,72,80 |

L-3 | 7.5% | $5.36911\times {10}^{6}$ | $6.91\times {10}^{11}$ | 67,69,77 | 1,7,13,17,24,27,72,80 |

L-4 | 10% | $3.8822\times {10}^{6}$ | $6.93\times {10}^{11}$ | 67,69,77 | 1,7,13,17,24,26,27,72,80 |

L-5 | 12.5% | $1.01203\times {10}^{6}$ | $6.96562\times {10}^{11}$ | 67,69,77 | 1,7,13,17,23,24,26,29,72,80 |

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## Share and Cite

**MDPI and ACS Style**

Qi, J.; Wang, H.; Zheng, J.
Shore Power Deployment Problem—A Case Study of a Chinese Container Shipping Network. *Sustainability* **2022**, *14*, 6928.
https://doi.org/10.3390/su14116928

**AMA Style**

Qi J, Wang H, Zheng J.
Shore Power Deployment Problem—A Case Study of a Chinese Container Shipping Network. *Sustainability*. 2022; 14(11):6928.
https://doi.org/10.3390/su14116928

**Chicago/Turabian Style**

Qi, Jingwen, Hans Wang, and Jianfeng Zheng.
2022. "Shore Power Deployment Problem—A Case Study of a Chinese Container Shipping Network" *Sustainability* 14, no. 11: 6928.
https://doi.org/10.3390/su14116928