A novel methodology for integrating scheduling and routing of moveable vessels for the optimal operation of pipeless plants is presented in this work. Herring-bone layout is assumed for processing stations. The proposed mathematical model is based on state-task-network process representation and unit-specific event based continuous-time formulation. Vessels are treated as states, the feasible routes for vessel transfer between different stations are considered as units and the movement of vessels on a route is considered as a routing task. The computational performance of the proposed formulation is illustrated through an example drawn from literature.