Positioning empty containers is one of the most effective ways to solve the container imbalance problem and is affected by the capacity of depots. A shipping company will be more competitive if the depot capacity is large. This study provides a decision tool for planning the expansion of depot capacity. Mathematical models are utilized to minimize the total relevant costs that include the capacity expansion cost, storage space leasing cost, inventory holding cost, container leasing cost, and positioning cost. The problem is formulated as a mixed integer program. Then, we develop a heuristic algorithm that is based on Lagrangian relaxation. Computational experiments are conducted to evaluate the performance of the proposed algorithm.
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