This paper constructs a berth-quay crane capacity planning model with the lowest average daily cost in the container terminal, and analyzes the influence of the number of berths and quay cranes on the terminal operation. The object of berth-quay crane capacity planning is to optimize the number of berths and quay cranes to maximize the benefits of the container terminal. A steady state probability transfer model based on Markov chain for container terminal is constructed by the historical time series of the queuing process. The current minimum time operation principle (MTOP) strategy is proposed to correct the state transition probability of the Markov chain due to the characteristics of the quay crane movement to change the service capacity of a single berth. The solution error is reduced from 7.03% to 0.65% compared to the queuing theory without considering the quay crane movement, which provides a basis for the accurate solution of the berth-quay crane capacity planning model. The proposed berth-quay crane capacity planning model is validated by two container terminal examples, and the results show that the model can greatly guide the container terminal berth-quay crane planning.
Dragu V, Dinu O, Rusca A, Burciu S, Roman EA. Queuing theory models used for port equipment sizing. In: Kifor C, Naito M, Carausu C, et al. (eds.) 5th International Conference on Modern Technologies in Industrial Engineering (ModTech), 14-17 June 2017, Sibiu, Romania. Bristol, England: IOP Publishing Ltd; 2017.
Dragu V, Rosca E, Rusca F, Rusca A, Roman EA. Solutions for the port facilities development. In: Oanta E, Naito M, Carausu C, et al. (eds.) 6th International Conference on Modern Technologies in Industrial Engineering (ModTech), 13-16 June 2017, Sibiu, Romania. Bristol, England: IOP Publishing Ltd; 2018.
Jurjevic M, Hess S. The operational planning model of transhipment processes in the port. Promet – Traffic&Transportation. 2016;28(2): 81-89.
Rodriguez Garcia T, Gonzalez Cancelas N, Soler-Flores F. Setting the port planning parameters in container terminals through bayesian networks. Promet – Traffic&Transportation. 2015;27(5): 395-403.
Soriguera F, Robuste F, Juanola R, Lopez-Pita A. Optimization of handling equipment in the container terminal of the port of Barcelona, Spain. In: Inland Waterways, Ports, And Shipping. 85th Annual Meeting of the Transportation-Research-Board, JAN 22-26, 2006, Washington, USA; 2006. p. 44-51.
Zenzerovic Z, Vilke S, Jurjevic M. Queuing theory in function of planning the capacity of the container terminal in port of Rijeka. Pomorstvo - Scientific Journal of Maritime Research. 2011;25(1): 45-69. Available from: http://www.scopus.com/inward/record.url?eid=2-s2.0-79960526390&partnerID=40&md5=e86abdcafed8cb835adb5811db10af60 [Accessed 26th April 2020].
Zrnic DN, Dragovic BM, Radmilovic ZR. Anchorage-ship-berth link as multiple server queuing system. Journal of Waterway Port coastal and Ocean Engineering. 1999;125(5): 232-240.
Munisamy S. Timber terminal capacity planning through queuing theory. Maritime Economics & Logistics. 2010;12(2): 147-161.
Li L, Meng Q, Bei W. Based on queuing theory to solve the optimization number of berth. 2010 3rd International Symposium on Knowledge Acquisition and Modeling (KAM 2010), 20-21 October 2010, Wuhan, China. IEEE; 2010. p. 424-427.
Zhang M, Ji S, Zhou K. Modelling and Application on the Extension Scale of Port Based on Queuing Theory. In: Guo Q, Guo Y. (eds.) 9th International Symposium on Distributed Computing and Applications to Business, Engineering and Science (DCABES 2010), 10-12 August 2010, Hong Kong,China. IEEE Computer Soc; 2010. p. 663-666.
Bierwirth C, Meisel F. A follow-up survey of berth allocation and quay crane scheduling problems in container terminals. European Journal of Operational Research. 2015;244(3): 675-689.
Bierwirth C, Meisel F. A survey of berth allocation and quay crane scheduling problems in container terminals. European Journal of Operational Research. 2010;202(3): 615-627.
Correcher JF, Alvarez-Valdes R, Tamarit JM. New exact methods for the time-invariant berth allocation and quay crane assignment problem. European Journal of Operational Research. 2019;275(1): 80-92.
Turkogullari YB, Taskin ZC, Aras N, Altinel IK. Optimal berth allocation, time-variant quay crane assignment and scheduling with crane setups in container terminals. European Journal of Operational Research. 2016;254(3): 985-1001.
Zheng F, Li Y, Chu F, Liu M, Xu Y. Integrated berth allocation and quay crane assignment with maintenance activities. International Journal of Production Research. 2019;57(11): 3478-3503.
Sun D, Tang L, Baldacci R. A Benders decomposition-based framework for solving quay crane scheduling problems. European Journal of Operational Research. 2019;273(2): 504-515.
Liu D, Ge Y-E. Modeling assignment of quay cranes using queueing theory for minimizing CO2 emission at a container terminal. Transportation Research Part D-Transport and Environment. 2018;61(A, SI): 140-151.
Hubl A, Altendorfer K. State Probabilities For An M/M/1 Queuing System With Two Capacity Levels. 2015 Winter Simulation Conference (WSC), 06-09 December 2015, Huntington Beach, USA. IEEE; 2015. p. 2219-2226.
Liu Z, Song Y. The Mx/M/1 queue with working breakdown. RAIRO-Operations Research. 2014;48(3): 399-413.
Dhingra V, Roy D, de Koster RBM. A cooperative quay crane-based stochastic model to estimate vessel handling time. Flexible Services and Manufacturing Journal. 2017;29(1, SI): 97-124.
Ding D, Teo C-P. World container port throughput follows lognormal distribution. Maritime Policy & Management. 2010;37(4): 401-426.
Wood RM, Murch BJ. Modelling capacity along a patient pathway with delays to transfer and discharge. Journal of the Operational Research Society. 2019;70(5): 1-15.
Pang G, Gebka B. Forecasting container throughput using aggregate or terminal-specific data? The case of Tanjung Priok Port, Indonesia. International Journal of Production Research. 2017;55(9): 2454-2469.