Vertical Expansion: A Solution for Future Container Terminals

Container terminals play a major role in the growth of international trade. They need to accommodate the increasing number of containers although their space is limited, particularly close to major cities. One approach, often used in practice, is horizontal expansion through expensive land reclamation projects. In contrast, vertical expansion uses the available land more efficiently by storing containers in high-bay warehouses. In this paper, we study a next-generation container terminal consisting of container storage towers. A container tower is a cylindrical structure that consists of multiple levels of storage locations, lifts, and input/output (I/O) points (or depots). The lifts can rotate and can move containers horizontally and vertically to transport containers between the storage locations and the I/O points. We investigate several design questions: (1) What is the optimal configuration of a container tower? (2) How does a container tower compare with a traditional container block of the same storage capacity in terms of throughput capacity? (3) Is a container tower financially feasible compared with an existing container block of the same storage capacity? (4) What are the impacts of varying design parameters on the container tower performance and its financial feasibility? Question 1 is answered by obtaining closed-form expressions for the tower travel time, formulating the problem as a nonlinear optimization model, and deriving closed-form expressions for the tower optimal configuration. Questions 2 and 3 are answered by using closed-form expressions to compare the performance of two systems. Question 4 is answered by a sensitivity analysis for the design parameters of the container tower. The results show that, compared with a traditional container block, the container tower can increase the annual throughput while saving on the required footprint at competitive investment costs. In particular, the container tower can increase the annual throughput up to 120% compared with a container block of the same storage capacity.