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A stochastic mixed integer program for modeling wildfire behavior and optimizing fire suppression operations




Belval, Erin Jean McCowen, author
Wei, Yu, advisor
Bevers, Michael, committee member
Reich, Robin, committee member
Labadie, John, committee member

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Wildfire suppression decisions combine multiple objectives and risk management to form a complex background against which decision makers attempt to determine efficient management actions in a short period of time. Their decisions are necessarily dynamic in nature as a sequence of random events unfolds at each fire. This dissertation presents a stochastic mixed integer program with full recourse to simulate spatially explicit fire behavior for a single fire representing a distribution of probable changes in behavior in response to weather changes. Suppression decisions and fire behavior respond dynamically to these weather events and to each other. Initially, a deterministic mixed integer program is developed to explore how to integrate spatial fire behavior with suppression actions into a mathematical programming framework. The model uses a raster landscape. Fire behavior includes fire arrival time and fireline intensity at each cell and the minimum travel time path by which fire reached the cell. Spatially explicit fireline intensities and arrival times are dependent upon the fire spread paths, therefore fire suppression actions that change the minimum travel time path also change the fireline intensity and arrival time. Weather is modeled as constant. Test cases for the deterministic model provide examples of spatially explicit fire behavior and corresponding optimal suppression strategies for a variety of suppression levels. Next, a stochastic mixed integer program is developed that expands upon the capabilities of the deterministic model. The stochastic model allows uncertain fire behavior to be simulated by referring to probabilistic weather decision trees. The fire behavior in the stochastic model interacts dynamically with both weather changes and suppression decisions. Constraints are included to characterize fire as ecologically beneficial or harmful based upon the fireline intensity, which allows the model to examine multiple policy objectives. A selection of alternative policy objectives is modeled in test cases, including minimizing the total expected area burned, minimizing the expected area burned at an ecologically harmful fireline intensity, maximizing the expected area burned at an ecologically beneficial fireline intensity, and minimizing expected fireline production. Explicit nonanticipativity constraints ensure that the model produces suppression decisions that account for uncertainty in weather forecasts. In the final model formulation, detailed fire control constraints are incorporated into the stochastic mixed integer fire growth and behavior program to model more realistic suppression decisions. These constraints account for spatial restrictions for fire crew travel and operations; for example, a crew's travel path must be continuous. Crew safety is also addressed; crews must keep a safety buffer zone between themselves and the fire. Fireline quality issues are accounted for by comparing control line capacity with fireline intensity to determine when a fireline will hold. The model lets crews work at varying production rates throughout their shifts, giving the model the flexibility to fit work assignments with the predicted fire behavior.


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wildfire behavior
stochastic optimization
wildfire management
fire suppression
integer programming


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