This paper extends the existing vehicle routing models by incorporating unanticipated delays at the customers' docking stations in time-dependent environments, i.e., where speeds are not constant throughout the planning horizon. A model is presented that is capable of optimizing the relevant costs taking into account these unplanned delays. The theoretical implications on the composition of the routing schedules are examined in detail. Experiments using a Tabu Search heuristic on a large number of datasets are provided. Based on these experiments, the generated routing schedules are analyzed and the cost-benefit trade-off between routing schedules that are protected against delays and routing schedules that are not protected against these delays are examined. Structural properties of the different solutions that have higher endurance capabilities with regards to the disruptions are highlighted.