Generating minimum-time and secure software update schedules for controllable power loads in low-voltage distribution grids is a problem of increasing importance because of accelerating integration of renewable energy resources. In this paper, we call such a problem the software update rollout problem and present a mathematical framework for its modeling and solution. First, it is shown that this problem can be understood as a multi-resource bin packing problem. Then several approximate and exact solution schemes are discussed, the former using greedy approximate algorithms and the later using integer linear programming (ILP). These schemes are then evaluated on benchmark networks of realistic size (CIGRE-LV, TPC 83-bus distribution system). Experimental results show that both greedy and ILP approaches perform well for real-time purposes. In particular, the greedy approach can attain high-quality approximate solutions almost instantly while the ILP approach can not only provide solutions with certifiable optimality gaps but also include extra constraints (e.g., precedence) as needed.