Logistics service providers (LSPs) offering container transport to the hinterland of the Netherlands face the challenge of efficiently using the capacity of the barge in order to minimize cost, while part of the relevant information is still lacking at the moment decisions have to be made. The existing infrastructure and the transportation activities are studied and modeled as an online optimization problem with simultaneously vehicle routing and container-to-mode assignment. A characteristic of great importance in the problem is the uncertainty element that reflects in the requested appointment times that have to be confirmed by another agent in the network. An online optimization approach is proposed, where the input data come in sequentially and decisions have to be made in between, because new information becomes available only after the decision has been made. At each decision moment, the uncertainty element is converted to an offline optimization problem by disregarding the uncertainty or by simulating various potential future scenarios. Subsequently, the problem is modeled as a multi-commodity network design problem on a time-space graph. Four different solution methods are developed in order to solve the online optimization problem. Three confirmation based methods concern a model in which the uncertainty element is partially disregarded, by assuming that each requested appointment time will be scheduled at a specific time relative to the requested one. Alternatively, a much more complex method is developed in which various future scenarios are simulated for the requested appointment times given their probability vector. The simulation based model seeks robust solutions that are resistant to change, i.e., feasible and (sub)optimal for every potential future scenario that has been simulated. Using randomly generated (but realistic) instances, the computational results show that the proposed simulation model surpasses the simpler models both in terms of outcomes, robustness and reliability. However, the practical relevance is somewhat restricted in the sense that the model is built on several assumptions.