Optimal container dispatching policy and its structure in a shuttle service with finite capacity and random demands

This paper considers the container-dispatching problem including laden container distributing and empty container repositioning in a two-terminal shuttle service with finite shipping capacity and random customer demands. Unmet demands within one period due to unavailable shipping capacity or insufficient empty containers will be lost based on the assumption that customers have limited patience and the fact that container shipping is a highly competitive sector. The objective is to seek effective container dispatching policies by minimising the total costs incurred by container inventory, container repositioning and lost sales. The optimal dispatching policy is derived by applying the Markov decision process theory. The structural characteristics of the optimal policy are investigated through numerical examples. Based on these structural properties, a four-parameter threshold police is constructed. A range of numerical examples demonstrates that the proposed threshold policy performs extremely close to or indeed the same as the optimal policy. More importantly, the proposed policy has an explicit form, which is easy-to-understand and easy-to-operate from the managerial and operational perspectives.