The Vehicle Routing Problem with Time Windows (VRPTW) is an important logistics problem which in the real-world appears to be multi-objective. Most research in this area has been carried out using classic datasets designed for the single-objective case, like the well-known Solomon's problem instances. Some unrealistic assumptions are usually made when using these datasets in the multi-objective case (e.g. assuming that one unit of travel time corresponds to one unit of travel distance). Additionally, there is no common VRPTW multi-objective oriented framework to compare the performance of algorithms because different implementations in the literature tackle different sets of objectives. In this work, we investigate the conflicting (or not) nature of various objectives in the VRPTW and show that some of the classic test instances are not suitable for conducting a proper multi-objective study. The insights of this study have led us to generate some problem instances using data from a real-world distribution company. Experiments in these new dataset using a standard evolutionary algorithm (NSGA-II) show stronger evidence of multi-objective features. Our contribution focuses on achieving a better understanding about the multi-objective nature of the VRPTW, in particular the conflicting relationships between 5 objectives: number of vehicles, total travel distance, makespan, total waiting time, and total delay time.