Hierarchical Control of Equipment in Automated Container Terminals

The performance of container terminals needs to be improved to adapt the growth of handled containers and maintain port sustainability. This paper provides a methodology to improve the throughput of the container terminal in an energy-efficient way. The behaviors of equipment are considered as consisting of a higher level and a lower level representing discrete-event dynamics and continuous-time dynamics, respectively. These dynamics need to be controlled. For controlling the higher level dynamics, a minimal makespan problem is solved. For this, the minimal time required for carrying out a task at the lower level is needed. The minimal time for carrying out a task at the lower level is obtained by Pontryagin's Minimum Principle. The actual operation time, allowed by the higher level for completing a task by one piece of equipment at the lower level, is determined by the scheduling algorithm at the higher level. The lower level dynamics are controlled using optimal control to achieve the minimal energy consumption when the operation time allowed is given. A simulation illustrates how energy-efficient management of equipment for the minimal makespan could be obtained by the proposed methodology.