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We study the problem of locating fire suppression resources in a burning landscape in order to minimise the total area burned. The landscape is modelled as a directed graph, with nodes representing regions of the landscape, and arcs representing adjacency relationships. The fire spread is modelled using the minimum travel time principle. We propose a non-linear integer programming formulation and an exact solution approach utilising logic-based Benders decomposition. We benchmark the approach against a mixed integer program and an iterated local search metaheuristic from the literature. We are able to solve challenging instances to proven optimality in a reasonable amount of time.