Dynamic crane deployment in container storage yards

Storage yards at container terminals serve as temporary buffers for inbound and outbound containers. Rubber tyred gantry cranes (RTGCs) are the most frequently used equipment in yards for container handling. The efficiency of yard operations heavily depends on the productivity of these RTGCs. As the workload distribution in the yard changes over time, dynamic deployment of RTGCs among storage blocks (container stacking areas) is an important issue of terminal operations management. This paper addresses the crane deployment problem. Given the forecast workload of each block in each period of a day, the objective is to find the times and routes of crane movements among blocks so that the total delayed workload in the yard is minimized. The problem is formulated as a mixed integer programming (MIP) model and solved by Lagrangean relaxation. To improve the performance of this approach, we augment the Lagrangean relaxation model by adding additional constraints and modify the solution procedure accordingly. Computational experiments show that the modified Lagrangean relaxation method generates excellent solutions in short time.