In this paper we study time-dependent scheduling problems where activities consume a resource with limited availability. Activity durations as well as resource consumptions are assumed to be time-dependent and the resource can be replenished between activities. Because of the interaction of time-dependent activity durations and resource consumptions, scheduling policies based on starting all activities as early as possible may fail due to unnecessarily high resource consumptions. We propose a dynamic discretization discovery algorithm that generates a partially time-expanded network during the search. We propose preloading techniques allowing to significantly reduce the computational effort if the approach is embedded in an iterative solution procedure that frequently evaluates activity sequences that start with the same activities. We evaluate our approaches on a case of routing a fleet of electric vehicles in which vehicles can recharge batteries during the route.