A dispatching problem for fire and rescue services is considered, where firefighters have to be allocated to vehicles, and vehicles dispatched to an emergency. A mathematical model for the problem is formulated, capable of managing multiple alarm plans for each emergency considered. The model is solved both exactly and heuristically, using input data from a fire and rescue service area in Skane, Sweden. The results show that the exact solution method might be too time consuming in some cases, but that the heuristic in most cases finds the optimal solution.