A Lagrangian relaxation approach for the integrated quay crane and internal truck assignment in container terminals

The planning decisions related to the assignment of quay cranes and internal trucks to the berthed vessels in container terminals are typically made independently. However, a more reliable estimation for the vessels' handling times as well as the truck requirements can be achieved when such planning decisions are made simultaneously. This paper presents a mathematical model that can be used to solve the quay crane assignment problem, the specific quay crane assignment problem and the assignment of internal trucks to each quay crane simultaneously. The proposed model considers important practical aspects such as the limited availability and operation cost of the internal trucks. A Lagrangian relaxation, and subgradient optimisation procedure-based heuristic is proposed for the model. The performance of the proposed heuristic algorithm is investigated using actual container terminal data.