Scheduling activities with time-dependent durations and resource consumptions

In this paper we study the problem of scheduling a given sequence of activities where each activity consumes a resource with limited availability. Activity durations as well as resource consumptions are assumed to be time-dependent. Because of the interaction of time-dependent activity durations and resource consumptions, scheduling policies based on starting each activity in the sequence as early as possible may fail due to unnecessarily high resource consumptions exceeding the limited availability of the resource. We propose a dynamic discretization discovery algorithm that generates a partially time-expanded network during the search. We propose an acceleration technique allowing to significantly reduce the computational effort if the approach is embedded in an iterative solution procedure that frequently evaluates activity sequences which start with the same activities. Furthermore, we extend our approach to the case where resources can be replenished between subsequent activities. We evaluate our approach as a route evaluation method for the case of routing a fleet of electric vehicles in which travel durations and the energy consumed when travelling from one location to another depend on the time of the day.