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.

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Hazard fuel reduction and wildland fire preparedness programs are two important budgeting components in the US National Park Service strategic wildland fire planning. During the planning process, each national park independently conducts analysis to understand the benefits from investing in each program to mitigate fire risks and improve ecosystem benefits. The national program analysis imports the cost-effective frontiers of investment in both programs from each national park. The national program then allocates cost-effective funding to the parks and implements required national policies while minimizing disruption to current programs of work. In this study, we test and compare two alternative modeling methods for budget allocation between the fuel treatment and preparedness programs responding to changes in funding levels nationally. One approach uses a nonlinear programming model (NLP) to maximize the benefits of investments in both programs with a set of feasibility constraints. The other approach uses a simulation-based gradient method to manage program budget changes. Both approaches are designed to focus on national level program efficiency while mitigating potential program disruptions; however, different approaches suggest different budgeting allocation strategies. This study compares the trade-offs between efficiency and the level of disruption of different budget allocation methods. Discoveries could help managers to select and implement an efficient and viable analytical system to study the value of funding increases, the cost of budget reductions, and guide landscape allocations. It will also identify national impacts by accumulating allocations to individual units across the national parks in the United States.

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