A mixed integer program to model spatial wildfire behavior and suppression placement decisions

Wildfire suppression combines multiple objectives and dynamic fire behavior to form a complex problem for decision makers. This paper presents a mixed integer program designed to explore integrating spatial fire behavior and suppression placement decisions into a mathematical programming framework. Fire behavior and suppression placement decisions are modeled using nodes associated with cell centers from raster landscapes. The nodes at which suppression is located are determined by control variables. Response variables include fire spread paths, arrival times, and fireline intensities for each node. Both fire arrival times and fireline intensities are necessary to address ecological objectives and fire control. Test cases for this model provide examples of fire behavior interacting with suppression placement to achieve multiple objectives.