Abstract In distribution problems, a fleet of vehicles serves the demand of a set of customers. Each customer is typically served by a single vehicle. However, more cost effective distribution plans may exist if some customers are served by more than one vehicle, i.e., if some deliveries are split. We characterize distribution environments in which allowing split deliveries is likely to be beneficial. We show, through an empirical study, that the largest benefits are obtained when mean customer demand is a little over half the vehicle capacity and customer demand variance is relatively small.