We solve a central problem in the liner shipping industry called the Liner Shipping Fleet Repositioning Problem (LSFRP). The LSFRP poses a large financial burden on liner shipping firms. During repositioning, vessels are moved between routes in a liner shipping network. Liner carriers wish to reposition vessels as cheaply as possible without disrupting the cargo flows of the network. The LSFRP is characterized by chains of interacting activities with a multi-commodity flow over paths defined by

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... the activities chosen. Despite its industrial importance, the LSFRP has received little attention in the literature. We introduce a novel mathematical model and a simulated annealing algorithm for the LSFRP with cargo flows that makes use of a carefully constructed graph and evaluate these approaches on real world data from our industrial collaborator. Additionally, we compare the performance of our approach against an actual repositioning scenario, one of many undertaken by our industrial collaborator in 2011. Our simulated annealing algorithm is able to increase the profit earned on our industrial collaborator's scenario from $18.1 million to $31.8 million dollars using only a few minutes of CPU time, showing that our algorithm could be used in a decision support system to solve the LSFRP.