Mathematically calculating the transit time of cargo through a liner shipping network with various trans-shipment policies

This paper derives the mathematical expressions for the transit time of cargo through a liner shipping network. Main efforts are devoted to deriving the calculation expressions of the connection time of cargo during trans-shipment. For the forward and many-to-one trans-shipment policies, we conduct a minor correction towards the expressions in existing studies to improve the completeness. Meanwhile, we propose an alternative but more straightforward calculation method for connection time which bypasses the complicated inductive argument in existing studies. Then we introduce two new trans-shipment policies: backward trans-shipment and one-to-many trans-shipment, and mathematically calculate the corresponding connection times. Numerical experiments also deliver some managerial insights into the effectiveness of backward trans-shipment in transit time control.