# Using a Hybrid Model on Joint Scheduling of Berths and Quay Cranes—From a Sustainable Perspective

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Problem Description and Assumptions

_{0}is the actual time in port for ship a, t

_{1}is the waiting time, t

_{2}is the remaining unloading time of the previous vessel before ship a, ${t}_{2}^{\prime}$ is the unloading time, t

_{3}is the stay time mainly for loading, and t

_{4}is the total loading and unloading time of the system. Formula (1) represents the required time for ship a to wait for the loading/unloading of the previous ship (remaining unloading and stay time). Formulas (2) and (3) are the unloading times of the ship. Formula (4) represents the required time to load and unload cargo (unloading and stay time) of ship a. Formula (5) is the actual formula for the calculation of ship a in port.

## 4. Construction of Joint Scheduling Model of the Port and Quay Cranes

#### 4.1. Model Building

#### 4.2. Algorithm Flow and Steps for Problem-Solving

## 5. Case Study

_{1}+ f

_{2}+ f

_{3}. The result is shown in Figure 8.

_{1}is concerned, the statistical data and results show that there are 17 times of the improved NSGA-II method converge to 2720 ± 20, and the other three times are in the range of 2720 ± 50, which proves that the solution performance of our method is stable.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Kang, D.; Kim, S. Conceptual model development of sustainability practices: The case of port operations for collaboration and governance. Sustainability
**2017**, 9, 2333. [Google Scholar] [CrossRef] - Han, X.L.; Gong, X.; Jo, J. A new continuous berth allocation and quay crane assignment model in container terminal. Comput. Ind. Eng.
**2015**, 89, 15–22. [Google Scholar] [CrossRef] - Hu, Q.M.; Hu, Z.H.; Du, Y. Berth and quay-crane allocation problem considering fuel consumption and emissions from vessels. Comput. Ind. Eng.
**2014**, 70, 1–10. [Google Scholar] [CrossRef] - Di Vaio, A.; Varriale, L. Management innovation for environmental sustainability in seaports: Managerial accounting instruments and training for competitive green ports beyond the regulations. Sustainability
**2018**, 10, 783. [Google Scholar] [CrossRef] - Papaefthimiou, S.; Maragkogianni, A.; Andriosopoulos, K. Evaluation of cruise ships emissions in the Mediterranean basin: The case of Greek ports. Int. J. Sustain. Transp.
**2016**, 10, 985–994. [Google Scholar] [CrossRef] - Chen, Z.; Pak, M. A Delphi analysis on green performance evaluation indices for ports in China. Marit. Policy Manag.
**2017**, 44, 537–550. [Google Scholar] [CrossRef] - Schipper, C.A.; Vreugdenhil, H.; de Jong, M.P.C. A sustainability assessment of ports and port-city plans: Comparing ambitions with achievements. Transp. Res. Part D-Transp. Environ.
**2017**, 57, 84–111. [Google Scholar] [CrossRef] - Asgari, N.; Hassani, A.; Jones, D.; Nguye, H.H. Sustainability ranking of the UK major ports: Methodology and case study. Transp. Res. Part E-Logist. Transp. Rev.
**2015**, 78, 19–39. [Google Scholar] [CrossRef] [Green Version] - Frojan, P.; Correcher, J.F.; Alvarez-Valdes, R.; Koulouris, G.; Tamarit, J.M. The continuous berth allocation problem in a container terminal with multiple quays. Expert Syst. Appl.
**2015**, 42, 7356–7366. [Google Scholar] [CrossRef] - Lun, Y.V.; Lai, K.H.; Wong, C.W.; Cheng, T.C. Environmental governance mechanisms in shipping firms and their environmental performance. Transp. Res. Part E-Logist. Transp. Rev.
**2015**, 78, 82–92. [Google Scholar] - Rodrigues, V.S.; Pettit, S.; Harris, I.; Beresford, A.; Piecyk, M.; Yang, Z.; Ng, A. UK supply chain carbon mitigation strategies using alternative ports and multimodal freight transport operations. Transp. Res. Part E-Logist. Transp. Rev.
**2015**, 78, 40–56. [Google Scholar] [CrossRef] [Green Version] - Yang, L.; Cai, Y.; Zhong, X.; Shi, Y.; Zhang, Z. A carbon emission evaluation for an integrated logistics system—A case study of the port of Shenzhen. Sustainability
**2017**, 9, 462. [Google Scholar] [CrossRef] - Tang, M.; Gong, D.; Liu, S.; Zhang, H. Applying multi-phase particle swarm optimization to solve bulk cargo port scheduling problem. Adv. Prod. Eng. Manag.
**2016**, 11, 299. [Google Scholar] [CrossRef] - Li, Q.; Huang, J.; Wang, C.; Lin, H.; Zhang, J.; Jiang, J.; Wang, B. Land development suitability evaluation of Pingtan island based on scenario analysis and landscape ecological quality evaluation. Sustainability
**2017**, 9, 1292. [Google Scholar] [CrossRef] - Baiocchi, V.; Lelo, K.; Polettini, A.; Pomi, R. Land suitability for waste disposal in metropolitan areas. Waste Manag. Res.
**2014**, 32, 707–716. [Google Scholar] [CrossRef] [PubMed] - Hamzeh, S.; Mokarram, M.; Haratian, A.; Bartholomeus, H.; Ligtenberg, A.; Bregt, A.K. Feature selection as a time and cost-saving approach for land suitability classification (case study of Shavur Plain, Iran). Agriculture
**2016**, 6, 52. [Google Scholar] [CrossRef] - Azadnia, A.H.; Saman, M.Z.M.; Wong, K.Y. Sustainable supplier selection and order lot-sizing: An integrated multi-objective decision-making process. Int. J. Prod. Res.
**2015**, 53, 383–408. [Google Scholar] [CrossRef] - Bai, C.; Fahimnia, B.; Sarkis, J. Sustainable transport fleet appraisal using a hybrid multi-objective decision making approach. Ann. Oper. Res.
**2017**, 250, 309–340. [Google Scholar] [CrossRef] - Golias, M.; Portal, I.; Konur, D.; Kaisar, E.; Kolomvos, G. Robust berth scheduling at marine container terminals via hierarchical optimization. Comput. Oper. Res.
**2014**, 41, 412–422. [Google Scholar] [CrossRef] - Robenek, T.; Umang, N.; Bierlaire, M.; Ropke, S. A branch-and-price algorithm to solve the integrated berth allocation and yard assignment problem in bulk ports. Eur. J. Oper. Res.
**2014**, 235, 399–411. [Google Scholar] [CrossRef] [Green Version] - Xu, R.; Wu, W. Study on disruption management models of continuous berth allocation at Shipyard Jetties. J. Residuals Sci. Technol.
**2016**, 13. [Google Scholar] [CrossRef] - Legato, P.; Mazza, R.M.; Gullì, D. Integrating tactical and operational berth allocation decisions via Simulation–Optimization. Comput. Ind. Eng.
**2014**, 78, 84–94. [Google Scholar] [CrossRef] - Al-Dhaheri, N.; Jebali, A.; Diabat, A. A simulation-based Genetic Algorithm approach for the quay crane scheduling under uncertainty. Simul. Model. Pract. Theory
**2016**, 66, 122–138. [Google Scholar] [CrossRef] - Tsai, S.B.; Yu, J.; Ma, L.; Luo, F.; Zhou, J.; Chen, Q.; Xu, L. A study on solving the production process problems of the photovoltaic cell industry. Renew. Sustain. Energy Rev.
**2018**, 82, 3546–3553. [Google Scholar] [CrossRef] - Tsai, S.B.; Zhou, J.; Gao, Y.; Wang, J.; Li, G.; Zheng, Y.; Ren, P.; Xu, W. Combining FMEA with DEMATEL models to solve production process problems. PLoS ONE
**2017**. [Google Scholar] [CrossRef] [PubMed] - Liu, W.; Wei, Q.; Huang, S.Q.; Tsai, S.B. Doing good again? A multilevel institutional perspective on corporate environmental responsibility and philanthropic strategy. Int. J. Environ. Res. Public Health
**2017**, 14, 1283. [Google Scholar] [CrossRef] [PubMed] - Du, P.; Xu, L.; Chen, Q.; Tsai, S.B. Pricing competition on innovative product between innovator and entrant imitator facing strategic customers. Int. J. Prod. Res.
**2016**. [Google Scholar] [CrossRef] - Xu, Y.; Chen, Q.; Quan, X. Robust berth scheduling with uncertain vessel delay and handling time. Ann. Oper. Res.
**2012**, 192, 123–140. [Google Scholar] [CrossRef] - Zhen, L.; Lee, L.H.; Chew, E.P. A decision model for berth allocation under uncertainty. Eur. J. Oper. Res.
**2011**, 212, 54–68. [Google Scholar] [CrossRef] - Monaco, M.F.; Sammarra, M. The berth allocation problem: A strong formulation solved by a lagrangean approach. Trans. Sci.
**2007**, 41, 265–280. [Google Scholar] [CrossRef] - Lee, D.H.; Qiu Wang, H. Integrated discrete berth allocation and quay crane scheduling in port container terminals. Eng. Optim.
**2010**, 42, 747–761. [Google Scholar] [CrossRef] - Imai, A.; Nishimura, E.; Papadimitriou, S. The dynamic berth allocation problem for a container port. Transp. Res. Part B
**2005**, 39, 401–417. [Google Scholar] [CrossRef] - Han, X.; Lu, Z.; Xi, L. A proactive approach for simultaneous berth and quay crane scheduling problem with stochastic arrival and handling time. Eur. J. Oper. Res.
**2010**, 207, 1327–1340. [Google Scholar] [CrossRef] - Kim, K.H.; Moon, K.C. Berth scheduling by simulated annealing. Transp. Res. Part B
**2003**, 37, 541–560. [Google Scholar] [CrossRef] - Hsu, H.P. A HPSO for solving dynamic and discrete berth allocation problem and dynamic quay crane assignment problem simultaneously. Swarm Evol. Comput.
**2016**, 27, 156–168. [Google Scholar] [CrossRef] - Oliveira, R.D. Clustering search for the berth allocation problem. Expert Syst. Appl.
**2012**, 39, 5499–5505. [Google Scholar] [CrossRef] - Ting, C.J.; Wu, K.C.; Chou, H. Particle swarm optimization algorithm for the berth allocation problem. Expert Syst. Appl.
**2014**, 41, 1543–1550. [Google Scholar] [CrossRef] - Imai, A.; Sun, X.; Nishimura, E.; Papadimitriou, S. Berth allocation in a container port: Using a continuous location space approach. Transp. Res. Part B
**2008**, 39, 199–221. [Google Scholar] [CrossRef] - Umang, N.; Bierlaire, M.; Vacca, I. Exact and heuristic methods to solve the berth allocation problem in bulk ports. Transp. Res. Part E-Logist. Transp. Rev.
**2013**, 54, 14–31. [Google Scholar] [CrossRef] [Green Version]

Symbol | Meaning |
---|---|

i | Berth number |

j | The jth ship is served at a berth |

m | Number of berths |

f_{a} | The ath ship’s departure time |

s_{a} | The ath ship’s arrivals time |

L_{a} | The length of ath ship (m) |

l_{a} | The migration distance of ath ship |

c_{1} | The cost coefficient of ship migration (yuan/m) |

c_{2} | Berth labor service cost coefficient (yuan/one) |

c_{3} | Cost coefficient of each berth bridge used (yuan/one) |

Q_{i} | Service cost of the ith berth (yuan/day) |

${u}_{ai}$ | Decision variables: if the ship at berth i, the value is 1, or 0 |

${v}_{\alpha \beta}$ | Decision variables: only when berth α and berth β are selected at the same time, the value is 1; otherwise, 0. |

$\alpha ,\beta $ | Indicates any two berths |

p_{i} | The cost of the ith berth bridge (yuan/one) |

r_{i} | The number of shore bridges required by each ship at the ith berth (one) |

L | Total length of port (m) |

n_{i} | The total number of berths allocated by the ith berth (one) |

w_{i} | The total amount of ship loading and unloading at the ith berth (t) |

$\overline{u}$ | The maximum number of quarries allowed for each berth |

$\underset{\xaf}{u}$ | The minimum number of quarries to be allocated to each berth |

LB_{i} | The length of the ith berth (m) |

v | The loading and unloading speed of shore bridge (t/min) |

Ship Number | Arrival Time | Departure Time | Hull Length/m | Freight Capacity/t |
---|---|---|---|---|

1 | 00:19 | 05:30 | 100 | 11,531 |

2 | 02:17 | 04:30 | 62 | 17,390 |

3 | 02:43 | 03:30 | 45 | 18,158 |

4 | 03:10 | 04:30 | 46 | 7650 |

5 | 06:39 | 09:00 | 72 | 8500 |

6 | 07:45 | 11:15 | 83 | 20,400 |

7 | 08:05 | 11:00 | 99 | 29,172 |

8 | 08:37 | 11:30 | 100 | 25,616 |

9 | 09:10 | 10:30 | 53 | 11,320 |

10 | 10:26 | 18:00 | 164 | 16,092 |

11 | 10:41 | 12:30 | 81 | 17,843 |

12 | 11:07 | 12:00 | 57 | 13,015 |

13 | 11:31 | 16:00 | 97 | 19,800 |

14 | 12:06 | 16:00 | 130 | 21,825 |

15 | 13:13 | 19:00 | 125 | 26,338 |

Berth Length/m | Minimum Number of Quay Crane | Maximum Number of Quay Crane | |
---|---|---|---|

1 | 200 | 2 | 5 |

2 | 200 | 2 | 5 |

3 | 300 | 1 | 5 |

4 | 260 | 2 | 5 |

Berth | 1 | 2 | 3 | 4 |
---|---|---|---|---|

1 | - | 700 | 970 | 1350 |

2 | 700 | - | 270 | 650 |

3 | 970 | 270 | - | 380 |

4 | 1350 | 650 | 380 | - |

Parameters | Related Data |
---|---|

${c}_{1}$ | 0.3 |

${c}_{2}$ | 0.55 |

${c}_{3}$ | 0.65 |

$L$ | 1500 m |

${Q}_{1}$ | 270 yuan/day |

${Q}_{2}$ | 220 yuan/day |

${Q}_{3}$ | 260 yuan/day |

${Q}_{4}$ | 210 yuan/day |

${P}_{1}$ | 200 yuan/one |

${P}_{2}$ | 240 yuan/ one |

${P}_{3}$ | 197 yuan/one |

${P}_{4}$ | 230 yuan/one |

Ship | Parking Berth (Matching Number of Quayside) | ||||
---|---|---|---|---|---|

1 | 1(5) | 2(5) | 2(5) | 3(4) | 1(5) |

2 | 1(5) | 2(5) | 2(5) | 3(4) | 1(5) |

3 | 2(5) | 1(5) | 1(5) | 3(4) | 2(4) |

4 | 1(5) | 2(5) | 3(4) | 1(5) | 1(5) |

5 | 1(5) | 1(5) | 3(4) | 1(5) | 1(5) |

6 | 2(5) | 2(5) | 2(5) | 1(5) | 1(5) |

7 | 3(4) | 3(4) | 1(5) | 2(5) | 3(4) |

8 | 3(4) | 2(5) | 2(5) | 2(5) | 2(4) |

9 | 1(5) | 1(5) | 3(4) | 1(5) | 1(5) |

10 | 2(5) | 1(5) | 1(5) | 1(5) | 1(5) |

11 | 1(5) | 2(5) | 3(4) | 3(4) | 2(4) |

12 | 1(5) | 3(4) | 1(5) | 1(5) | 1(5) |

13 | 1(5) | 1(5) | 1(5) | 1(5) | 1(5) |

14 | 2(5) | 3(4) | 2(5) | 1(5) | 3(4) |

15 | 2(5) | 1(5) | 3(4) | 2(5) | 1(5) |

Ship | Parking Berth (Matching Number of Quayside) | Ship | Parking Berth (Matching Number of Quayside) |
---|---|---|---|

1 | 1(5) | 9 | 1(5) |

2 | 1(5) | 10 | 2(5) |

3 | 1(5) | 11 | 1(5) |

4 | 2(5) | 12 | 2(5) |

5 | 1(5) | 13 | 2(5) |

6 | 2(5) | 14 | 1(5) |

7 | 2(5) | 15 | 1(5) |

8 | 2(5) |

© 2018 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**

Liu, A.; Liu, H.; Tsai, S.-B.; Lu, H.; Zhang, X.; Wang, J.
Using a Hybrid Model on Joint Scheduling of Berths and Quay Cranes—From a Sustainable Perspective. *Sustainability* **2018**, *10*, 1959.
https://doi.org/10.3390/su10061959

**AMA Style**

Liu A, Liu H, Tsai S-B, Lu H, Zhang X, Wang J.
Using a Hybrid Model on Joint Scheduling of Berths and Quay Cranes—From a Sustainable Perspective. *Sustainability*. 2018; 10(6):1959.
https://doi.org/10.3390/su10061959

**Chicago/Turabian Style**

Liu, Aijun, Haiyang Liu, Sang-Bing Tsai, Hui Lu, Xiao Zhang, and Jiangtao Wang.
2018. "Using a Hybrid Model on Joint Scheduling of Berths and Quay Cranes—From a Sustainable Perspective" *Sustainability* 10, no. 6: 1959.
https://doi.org/10.3390/su10061959