This paper considers a real operational problem of routing and scheduling a fleet of fuel supply vessels used to service customer ships anchored outside a major port. The problem can be formulated as a rich multi-trip vehicle routing problem, including constraints related to stowage and time-dependent sailing times. An arc-flow and a path-flow model are developed and compared. A computational study shows that the path-flow model is superior and can be used in real planning situations. We also discuss how the model can be used in a real-time setting when new orders arrive and deviations from the plan occur.