Data collection is an important mechanism for wireless sensor networks to be viable. This paper addresses the Aerial Data Collection Problem (ADCP) from a set of mobile wireless sensors located on the ground, using a fleet of flying devices. The objective is i) to deploy a set of Unmanned Aerial Vehicles (UAVs) in a 3D space to cover and collect data from all the mobile wireless sensors at each time step through a ground-to-air communication, ii) to send these data to a central base station using multi-hop wireless air-to-air communications through the network of UAVs, iii) while minimizing the total deployment cost (communication and deployment) over time. The Aerial Data Collection Problem (ADCP) is a complex time and space coverage, and connectivity problem. We first present a mixed-integer linear program solving ADCP optimally for small instances. Then, we develop a second model solved by column generation for larger instances, with optimal or heuristic pricing programs. Results show that our approach provides very accurate solutions minimizing the data collection cost. Moreover, only a very small number of columns are generated throughout the resolution process, showing the efficiency of our approach.