The Liner Shipping Fleet Repositioning Problem (LSFRP) poses a large financial burden on liner shipping firms. During repositioning, vessels are moved between services in a liner shipping network. The LSFRP is characterized by chains of interacting activities, many of which have costs that are a function of their duration; for example, sailing slowly between two ports is cheaper than sailing quickly. Despite its great industrial importance, the LSFRP has received little attention in the literature. We show how the LSFRP can be solved sub-optimally using the planner POPF and optimally with a mixed-integer program (MIP) and a novel method called Temporal Optimization Planning (TOP). We evaluate the performance of each of these techniques on a dataset of real-world instances from our industrial collaborator, and show that automated planning scales to the size of problems faced by industry.