Urban areas have been facing the challenge of increased demand for urban transportation due to the expansion of opportunities for activities and the growth of e-commerce. These areas constantly face congestion, leading to more emissions and noise/air pollution. These circumstances have led to a strong interest in sustainability in mobility and logistics in urban areas. In particular, integrating mobility and logistics in a multimodal transport network instead of conventional transportation in which mobility and logistics are handled separately has caught interest. It is expected that the utilisation of water transit as a major means of urban transportation is important for the realisation of a sustainable multimodal urban transport network where abundant waterways are available, and combining mobility and logistics in the urban ferry system has the potential to provide more efficient urban transportation. To investigate the potential of such a system, a dynamic centralised fleet management model that optimises the operation of waterborne vessels is developed in this thesis, considering an electric waterborne vessel system for heterogeneous on-demand service that serves stochastic passenger travel and parcel delivery requests. The model dynamically optimises the operation of vessels by applying a rolling horizon and updates the operation plan every time a new request is inserted. Two solving algorithms, the exact method and the insertion heuristic, are proposed. The computational experiments are conducted by taking the city of Fredrikstad in Norway as the case location to evaluate the solving capability of the proposed solving algorithms and to assess the efficiency and service level of the transport system by comparing the performance with the conventional fixed purpose vessels under different demand scenarios. The demand scenarios are generated using a stochastic approach, which applies a non-homogeneous Poisson process for passenger requests and a probabilistic approach for parcel requests. The results suggest that the proposed insertion heuristic is capable of being applied to this model by providing good solutions in a significantly shorter computational time. Also, combining mobility and logistics results in higher efficiency and service levels for all demand scenarios than those of the fixed purpose vessels. To conclude, a model that determines the operation of electric waterborne vessels for on-demand heterogeneous services considering the stochasticity of the demand is developed in this thesis. The results show the capability of the proposed model to dynamically optimise the operation and the benefits of combining mobility and logistics in vessels for heterogeneous on-demand service.