With the rapid development of UAV technology, the increasing application of UAV swarms in fields such as disaster relief has effectively ensured the safety of people’s lives and property. However, as the scope of disaster relief task allocation continues to expand, the scale and complexity of these problems are also increasing, posing new challenges for UAV swarm task allocation technology. This paper focuses on the application of scheduling UAV swarms in forest firefighting. It constructs a mathematical optimization model that considers an array of limitations, such as UAV range and firefighting capacity, to efficiently schedule a limited number of UAVs to complete as many firefighting tasks as possible. The constructed mathematical problem is NP-hard, and this paper proposes a warm-up heuristic to facilitate the solving procedure. Experimental results show that the proposed scheme can effectively increase the number of completed tasks, and the solution time of the proposed algorithm is significantly lower than that of commercial solvers, such as CPELX.