In the context of smart cities, unmanned aerial vehicles (UAVs) offer an alternative way of gathering data and delivering products. On the one hand, in congested urban areas UAVs might represent a faster way of performing some operations than employing road vehicles. On the other hand, they are constrained by driving-range limitations. This paper copes with a version of the well-known Team Orienteering Problem in which a fleet of UAVs has to visit a series of customers. We assume that the rewarding quantity that each UAV receives by visiting a customer is a random variable, and that the service time at each customer depends on the collected reward. The goal is to find the optimal set of customers that must be visited by each UAV without violating the driving-range constraint. A simheuristic algorithm is proposed as a solving approach, which is then validated via a series of computational experiments.