An optimization model for locating fuel treatments across a landscape to reduce expected fire losses

Locating fuel treatments with scarce resources is an important consideration in landscape-level fuel management. This paper developed a mixed integer programming (MIP) model for allocating fuel treatments across a landscape based on spatial information for fire ignition risk, conditional probabilities of fire spread between raster cells, fire intensity levels, and values at risk. The fire ignition risk in each raster cell is defined as the probability of fire burning a cell because of the ignition within that cell. The conditional probability that fire would spread between adjacent cells A and B is defined as the probability of a fire spreading into cell B after burning in cell A. This model locates fuel treatments by using a fire risk distribution map calculated through fire simulation models. Fire risk is assumed to accumulate across a landscape following major wind directions and the MIP model locates fuel treatments to efficiently break this pattern of fire risk accumulation. Fuel treatment resources are scarce and such scarcity is introduced through a budget constraint. A test case is designed based on a portion of the landscape (15 552 ha) within the Southern Sierra fire planning unit to demonstrate the data requirements, solution process, and model results. Fuel treatment schedules, based upon single and dual wind directions, are compared.