The berth and quay cranes integrated scheduling based on redundancy policy

The arrival time of each container vessel berthing at a container terminal and the numbers of the containers loaded on and off the vessel are disturbed stochastically since their being affected by many random factors. In order to make the plans of berth allocation and quay cranes scheduling implemented successfully, this paper proposes a mathematical model of the robustly planning for berth allocation and quay cranes integrated scheduling. Based on the trade-off between service level and robustness of the plans, the mathematical model optimizes the weighted sum of the service level and the robustness indicator by making decision on berthing position on the terminal, berthing time and the buffer time for each vessel. Through analyzing the properties of the model it is found that there must be a “lower-left tight” plan which is optimal. Then an improved genetic algorithm is designed to solve the problem according to the properties. The simulation tests show that the optimal solution or the approximately optimal solution of the model can absorb the perturbation, avoid the interim adjustment plan and reduce the delay time of each vessel. Especially, it remarkably reduces the number of the vessels with more containers loaded on and off them and enhances the robustness of the terminal operations plan.