We investigate a specific truck scheduling problem at cross-docks in the postal service industry on an operational level aiming to maximise the number of duly parcels assuming fixed departure times of the outbound trucks. The inbound gates and the conveyors as means of transportation inside the hub constitute the bottleneck resources. As a novel extension, we propose flexible unloading speeds to efficiently utilise the scarce resources. We formalise the problem with a mixed integer program and explicitly incorporate controllable unloading speeds of the inbound trucks. We determine the computational complexity and develop a genetic algorithm to efficiently solve the problem. Our investigation focuses on both the performance of the genetic algorithm and the applicability of the results in a real-world environment by implementing scheduling policies in a simulation model that considers individual parcel interactions. Based on our experimental results, we can state that especially in problem settings with scarce conveyor capacities, our approach to incorporate controllable unloading speeds has the potential of significantly increasing the number of duly parcels.