In this research we study the berth allocation problem (BAP) in real time as disruptions occur. In practice, the actual arrival times and handling times of the vessels deviate from their expected or estimated values, which can disrupt the original berthing plan and possibly make it infeasible. We consider a given baseline berthing schedule, and solve the BAP on a rolling planning horizon with the objective to minimize the total realized cost of the updated berthing schedule, as the actual arrival and handling time data is revealed in real time. The uncertainty in the data is modeled by making appropriate assumptions about the probability distributions of the uncertain parameters based on past data. We present an optimization-based recovery algorithm based on set partitioning and a smart greedy algorithm to reassign vessels in the event of disruption. Our research problem derives from the real-world issues faced by the Saqr port, Ras Al Khaimah, UAE, where the berthing plans are regularly disrupted owing to a high degree of uncertainty in information. A simulation study is carried out to assess the solution performance and efficiency of the proposed algorithms, in which the baseline schedule is the solution of the deterministic BAP without accounting for any uncertainty. Results indicate that the proposed reactive approaches can significantly reduce the total realized cost of berthing the vessels as compared to the ongoing practice at the port.
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Albers, S. (2003). Online algorithms: A survey, Mathematical Programming 97: 3–26. Invited paper at ISMP.
Ben-Tal, A., & Nemirovski, A. (1998). Robust convex optimization. Mathematics of Operations Research, 23(4),
Ben-Tal, A., & Nemirovski, A. (1999). Robust solutions of uncertain linear programs. OR Letters, 25, 1–13.
Ben-Tal, A., & Nemirovski, A. (2000). Robust solutions of linear programming problems contaminated with uncertain data. Mathematical Programming, 88, 414–424.
Bertsimas, D., & Sim, M. (2003). Robust discrete optimization. Mathematical Programming, 98, 49–71.
Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations Research, 52, 35–53.
Bierwirth, C., & Meisel, F. (2010). A survey of berth allocation and quay crane scheduling problems in container terminals. European Journal of Operational Research, 202(3), 615–627.
Birge, J. R. Louveaux, F. (1997). Introduction to Stochastic Programming, Springer.
Buhrkal, K., Zuglian, S., Ropke, S., Larsen, J., & Lusby, R. (2011). Models for the discrete berth allocation problem: A computational comparison. Transportation Research Part E, 47(4), 461–473.
Cordeau, J. F., Laporte, G., Legato, P., & Moccia, L. (2005). Models and tabu search heuristics for the berth-allocation problem. Transportation Science, 39(4), 526–538.
Du, Y., Xu, Y. Chen, P. (2010). A feedback procedure for robust berth allocation with stochastic vessel delays, Proceedings of the 8th World Congress on Intelligent Control and Automation, Jinan, China.
Han, X.-L., Lu, Z.-Q., & Xi, L.-F. (2010). A proactive approach for simultaneous berth and quay crane scheduling problem with stochastic arrival and handling time. European Journal of Operational Research, 207(3), 1327–1340.
Hendriks, M., Laumanns, M., Lefeber, E., & Udding, J. (2010). Robust cyclic berth planning of container vessels. OR Spectrum, 32, 501–517.
Imai, A., Nagaiwa, K., & Chan, W. T. (1997). Efficient planning of berth allocation for container terminals in Asia. Journal of Advanced Transportation, 31(1), 75–94.
Imai, A., Nishimura, E., & Papadimitriou, S. (2001). The dynamic berth allocation problem for a container port. Transportation Research Part B, 35(4), 401–417.
Imai, A., Nishimura, E., & Papadimitriou, S. (2003). Berth allocation with service priority. Transportation Research Part B, 37(5), 437–457.
Imai, A., Sun, X., Nishimura, E., & Papadimitriou, S. (2005). Berth allocation in a container port: using a continuous location space approach. Transportation Research Part B, 39(3), 199–221.
Kall, P., & Mayer, J. (Eds.). (2005). Stochastic Linear Programming. Models, Theory and Computation, Springer
Kim, K. H., & Moon, K. C. (2003). Berth scheduling by simulated annealing. Transportation Research Part B, 37(6), 541–560.
Moorthy, R., & Teo, C. P. (2006). Berth management in container terminal: the template design problem. OR Spectrum, 28(4), 495–518.
Soyster, A. (1973). Convex programming with set-inclusive constraints and application to inexact linear programming. Operations Research, 21(5), 1154–1157.
Stahlbock, R., & Voss, S. (2008). Operations research at container terminals: a literature update. OR Spectrum, 30(1), 1–52.
Steenken, D., Voss, S., & Stahlbock, R. (2004). Container terminal operation and operations research - a classification and literature review. OR Spectrum, 26(1), 3–49.
Umang, N., Bierlaire, M., & Vacca, I. (2013). Exact and heuristic methods to solve the berth allocation problem in bulk ports. Transportation Research Part E, 54, 14–31.
Wallace, S., & Ziemba, W. (1997). Applications of stochastic programming, (Mps-Siam Series on Optimization). Philadelphia, PA, USA: Society for Industrial and Applied Mathematics.
Xu, Y., Chen, Q., & Quan, X. (2012). Robust berth scheduling with uncertain vessel delay and handling time. Annals of Operations Research, 192, 123–140.
Zeng, Q., Yang, Z., & Hu, X. (2012). Disruption recovery model for berth and quay crane scheduling in container terminals. Engineering Optimization, 43, 967–983.
Zhen, L., & Chang, D. F. (2012). A bi-objective model for robust berth allocation scheduling. Computers and Industrial Engineering, 63, 262–273.
Zhen, L., Lee, L. H., & Chew, E. P. (2011). A decision model for berth allocation under uncertainty. European Journal of Operational Research, 212, 54–68.
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Umang, N., Bierlaire, M. & Erera, A.L. Real-time management of berth allocation with stochastic arrival and handling times. J Sched 20, 67–83 (2017). https://doi.org/10.1007/s10951-016-0480-2
- Berth scheduling
- Real-time reoptimization
- Port logistics
- Mixed integer programming
- Set partitioning