Quay crane allocation problem with the internal truck capacity constraint in container terminals

In container terminals, discharging and loading of vessels are critical planning decisions which highly depend on the interaction between the quay cranes and internal trucks, they also have a significant impact on the terminal performance and revenue. Decisions on the assignments of quay cranes and internal trucks to the berthed vessels are typically made sequentially. However, the applicability of the handling plan can be improved when these two decisions are made simultaneously. This paper introduces an approach for assigning quay cranes and internal trucks to the berthed vessels simultaneously with consideration of the internal truck limited availability. A two phase solution methodology is proposed. In the first phase, a mixed integer programming model is formulated which provides the number of quay cranes assigned to each vessel, as well as the number of internal trucks assigned to each quay crane at each time period. In the second phase, a heuristic is used to solve the specific quay crane assignment problem. Using a numerical example, the benefits of the proposed approach are demonstrated.