Recent events have shown the destructive consequences that wildfires can have on the environment, people's lives, and the economy. Elevated fuel loads (i.e., the amount of flammable material in an area) increase the likeliness as well as the severity of accidental and human-caused fires. Fuel management operations help to reduce the impact of fires by applying treatments on the landscape that decrease fuel load. However, their planning poses a complicated decision problem, which includes multiple sources of uncertainty. In this paper, a problem for fuel treatment planning is presented, formulated, and solved. The optimisation model identifies the best subset of units in the landscape to be treated to minimise the impact of the worst-case wildfire. The model, bilevel in nature, is reformulated as a single-level integer program. Due to its size, which would make it intractable for realistic instances, a solution algorithm applying bound-based filters that reduce the size of the optimisation model while preserving optimality has been devised. Extensive computational testing on randomly generated instances illustrates that the proposed approach is very successful at solving the problem and that the filters indeed reduce the total solution time. Finally, the algorithm is applied to a case study on a landscape in Andalusia, Spain, which shows the capabilities of the proposed approach in addressing a real-world problem.