A heuristic algorithm for equipment scheduling at an automated container terminal with multi-size containers





automated container terminal, multi-size containers, yard cranes, energy consumption


With the increasing volume of shipping containers, container multimodal transport and port scheduling have attracted much attention. The allocation and dispatching of handling equipment to minimize completion time and energy consumption have always been a focus of research. This paper considers a scheduling problem at an automated land-maritime multimodal container terminal with multi-size containers, in which operating facilities and equipment such as quay cranes, vehicles, yard cranes, and external container trucks are involved. Moreover, the diversity of container sizes and the location of handshake areas in yards are concerned. A mixed integer programming model is established to schedule all operating facilities and equipment. To solve the mathematical model is a NP-hard problem, which is difficult to be solved by conventional methods. Then we propose a heuristic algorithm which merges multiple targets into one and designs an improved genetic algorithm based on the heuristic combination strategy in which 20-ft containers are paired-up to the same yard before allocation. After that, some experiments are designed to prove the effectiveness of the model and the algorithm. The effect of configurations on efficiency and energy consumption under different conditions is discussed, and the influences of different parameters and the proportion of 20-ft containers are also compared. Furthermore, the influence of locations of handshake area with different yard quantities are compared. To conclude, there is an optimal number of equipment to be allocated. If few equipment is used, the operation time will be prolonged; if too many, the energy consumption will be increased. When the yard operation is the bottleneck, the handover location should be in the centre, otherwise other locations might be feasible. When the proportion of 20-ft containers that can be combined is large, the method proposed in this paper has advantages over traditional methods. The proposed algorithm has made a breakthrough in improving efficiency and reducing energy consumption.


Ai, L., Han, X., (2018). Coordinated scheduling of handling equipments at automated terminals considering energy consumption. Journal of Shanghai Maritime University, 39(04), Article 04.

Assadipour, G., Ke, G. Y., Verma, M., (2014). An analytical framework for integrated mari-time terminal scheduling problems with time windows. Expert Systems with Applications, 41(16), 7415-7424. DOI: 10.1016/j.eswa. 2014.05.040.

Blazewicz, J., Cheng, T. C. E., Machowiak, M., Oguz, C., (2011). Berth and quay crane allocation: A moldable task scheduling model. Journal of the Operational Research Society, 62(7), 1189-1197. DOI: 10.1057/jors.2010.54.

Chen, L., Langevin, A., Lu, Z., (2013). Integrated scheduling of crane handling and truck transportation in a maritime container terminal. European Journal of Operational Research, 225(1), 142-152. DOI: 10.1016/j.ejor.2012 .09.019.

Du, Y., Chen, Q., Quan, X., Long, L., Fung, R. Y. K., (2011). Berth allocation considering fuel consumption and vessel emissions. Transportation Research Part E: Logistics and Transportation Review, 47(6), 1021-1037. DOI: 10.1016/j.tre.2011.05.011.

Dulebenets, M. A., Moses, R., Ozguven, E. E., Vanli, A., (2017). Minimizing Carbon Dioxide Emissions Due to Container Handling at Marine Container Terminals via Hybrid Evolutionary Algorithms. IEEE Access, 5, 8131-8147. DOI: 10.1109/ACCESS.2017.2693030.

Elaziz, M. A., Li, L., Jayasena, K. P. N., Xiong, S., (2019). Multiobjective big data optimization based on a hybrid salp swarm algorithm and differential evolution. Applied Mathematical Modelling. DOI: 10.1016/j.apm.2019.10.069.

Elwany, M. H., Ali, I., Abouelseoud, Y., (2013). A heuristics-based solution to the continuous berth allocation and crane assignment problem. Alexandria Engineering Journal, 52(4), 671-677. DOI: 10.1016/j.aej.2013. 09.001.

Frojan, P., Correcher, J. F., Alvarez-Valdes, R., Koulouris, G., Tamarit, J. M., (2015). The continuous Berth Allocation Problem in a container terminal with multiple quays. Expert Systems with Applications, 42(21), 7356-7366. DOI: 10.1016/j.eswa.2015.05.018.

Gharehgozli, A. H., Vernooij, F. G., Zaerpour, N., (2017). A simulation study of the performance of twin automated stacking cranes at a seaport container terminal. European Journal of Operational Research, 261(1), Article 1. DOI: 10.1016/j.ejor.2017.01.037.

Golias, M., Portal, I., Konur, D., Kaisar, E., Kolomvos, G., (2014). Robust berth scheduling at marine container terminals via hierarchical optimization. Computers Operations Research, 41, 412-422. DOI: 10.1016/j.cor.2013.07.018.

Han, X., Wang, Q., Huang, J., (2019). Scheduling cooperative twin automated stacking cranes in automated container terminals. Computers Industrial Engineering, 128, 553-558. DOI: 10.1016/j.cie.2018.12.039.

He, J., Huang, Y., Yan, W., Wang, S., (2015a). Integrated internal truck, yard crane and quay crane scheduling in a container terminal considering energy consumption. Expert Systems with Applications, 42(5), 2464-2487. DOI: 10.1016/j.eswa.2014.11.016.

He, J., Huang, Y., Yan, W., Wang, S., (2015b). Integrated internal truck, yard crane and quay crane scheduling in a container terminal considering energy consumption. Expert Systems with Applications, 42(5), Article 5. DOI: 10.1016/j.eswa.2014.11.016.

Homayouni, S. M., Tang, S. H., Motlagh, O., (2014). A genetic algorithm for optimization of integrated scheduling of cranes, vehicles, and storage platforms at automated container terminals. Journal of Computational and Applied Mathematics, 270, 545-556. DOI: 10.1016/j.cam.2013.11.021.

Hu, H., Chen, X., Wang, T., Zhang, Y., (2019). A three-stage decomposition method for the joint vehicle dispatching and storage allocation problem in automated container terminals. Computers Industrial Engineering, 129, 90-101. DOI: 10.1016/j.cie.2019.01.023.

Hu, Q.-M., Hu, Z.-H., Du, Y., (2014). Berth and quay-crane allocation problem considering fuel consumption and emissions from vessels. Computers Industrial Engineering, 70, 1-10. DOI: 10.1016/j.cie.2014.01.003.

Jachimowski, R., (2017). Review of horizontal transport decision problems in the marine intermodal terminal. Archives of Transport, 44(4), 35-45. DOI: 10.5604/01.3001.0010.6160.

Ku, W.-Y., Beck, J. C., (2016). Mixed Integer Programming models for job shop scheduling: A computational analysis. Computers Operations Research, 73, 165-173. DOI: 10.1016/j.cor.2016.04.006.

Lee, K., Kim, B. S., Joo, C. M., (2012). Genetic algorithms for door-assigning and sequencing of trucks at distribution centers for the improvement of operational performance. Expert Systems with Applications, 39(17), 12975-12983. DOI: 10.1016/j.eswa.2012.05.057.

Lin, C.-M., Gen, M., (2008). Multi-criteria human resource allocation for solving multistage combinatorial optimization problems using multiobjective hybrid genetic algorithm. Expert Systems with Applications, 34(4), 2480-2490. DOI: 10.1016/j.eswa.2007.04.016.

Lin, J., Zhu, L., Gao, K., (2020). A genetic programming hyper-heuristic approach for the multi-skill resource constrained project scheduling problem. Expert Systems with Applications, 140, 112915. DOI: 10.1016/j.eswa.2019. 112915.

Lu, Y., Le, M., (2014). The integrated optimization of container terminal scheduling with uncertain factors. Computers Industrial Engineering, 75, 209-216. DOI: 10.1016/j.cie.2014.06.018.

Qiu, J., Ren, W., Tang, M., Ma, P., Zhang, Y., (2022). Determination of Truck Maintenance Allocation Scheme Based on SA-GA. Archives of Transport, 62(2), 59-71. DOI: 10.5604/01.3001.0015.9177.

Raa, B., Dullaert, W., Schaeren, R. V., (2011). An enriched model for the integrated berth allocation and quay crane assignment problem. Expert Systems with Applications, 38(11), 14136-14147. DOI: 10.1016/j.eswa.2011.04. 224.

Salido, M. A., Rodriguez-Molins, M., Barber, F., (2012). A decision support system for man-aging combinatorial problems in container terminals. Knowledge-Based Systems, 29, 63-74. DOI: 10.1016/j.knosys.2011.06.021.

Steenken, D., Voß, S., Stahlbock, R., (2004). Container terminal operation and operations research - A classification and literature review. OR Spectrum, 26(1), Article 1. DOI: 10.1007/s00291-003-0157-z.

Tan, C., Yan, W., Yue, J., (2021). Quay crane scheduling in automated container terminal for the trade-off between operation efficiency and energy consumption. Advanced Engineering Informatics, 48, 101285. DOI: 10.1016/ j.aei.2021.101285.

Tang, L., Zhao, J., Liu, J., (2014). Modeling and solution of the joint quay crane and truck scheduling problem. European Journal of Operational Research, 236(3), 978-990. DOI: 10.1016/j.ejor.2013.08.050.

Yang, Y., Zhong, M., Dessouky, Y., Postolache, O., (2018). An integrated scheduling method for AGV routing in automated container terminals. Computers Industrial Engineering, 126, 482-493. DOI: 10.1016/j.cie. 2018.10.007.

Zhen, L., Lee, L. H., Chew, E. P., (2011). A decision model for berth allocation under uncertainty. European Journal of Operational Research, 212(1), 54-68. DOI: 10.1016/j.ejor. 2011.01.021.






Original articles

How to Cite

Li, H. (2023). A heuristic algorithm for equipment scheduling at an automated container terminal with multi-size containers. Archives of Transport, 65(1), 67-86. https://doi.org/10.5604/01.3001.0016.2478


Most read articles by the same author(s)

1 2 3 4 5 6 7 8 9 10 > >> 

Similar Articles

1-10 of 72

You may also start an advanced similarity search for this article.