Berth Allocation Problem with Quay Crane Assignment for Container Terminals Based on Rolling-Horizon Strategy

In order to solve the large-scale integral dynamic scheduling of continuous berths and quay cranes problem, a method based on rolling-horizon strategy is proposed. A multiobjective optimization model that is established minimizes the total penalty costs considering vessels’ deviations to their preferred berthing positions, delayed times for berthing comparing to their estimated arrival times, and delayed times for departure comparing to their estimated departure times. Then, the scheduling process was divided into a set of continual scheduling interval according to the dynamic arrival sequences. Meanwhile, rolling-horizon strategies for setting rolling and frozen windows and the parameter updating strategy are designed. The input parameters of the model in the next rolling window are updated according to the optimal results of each time window which have been obtained. The model is solved by choosing appropriate rolling and freezing window lengths that represents the numbers of adjacent vessels in the sequence of calling vessels. The holistic optimal solution is obtained by gradually rolling and combining the results of each window. Finally, a case study indicated that the rolling schedule can solve large-scale scheduling problems, and the efficiency of the proposed approach relates to the size of rolling window, freeze ship quantity, and rolling frequency.