A stochastic mixed integer program to model spatial wildfire behavior and suppression placement decisions with uncertain weather

Abstract

Wildfire behavior is a complex and stochastic phenomenon that can present unique tactical management challenges. This paper investigates a multistage stochastic mixed integer program with full recourse to model spatially explicit fire behavior and to select suppression locations for a wildland fire. Simplified suppression decisions take the form of “suppression nodes”, which are placed on a raster landscape for multiple decision stages. Weather scenarios are used to represent a distribution of probable changes in fire behavior in response to random weather changes, modeled using probabilistic weather trees. Multistage suppression decisions and fire behavior respond to these weather events and to each other. Nonanticipativity constraints ensure that suppression decisions account for uncertainty in weather forecasts. Test cases for this model provide examples of fire behavior interacting with suppression to achieve a minimum expected area impacted by fire and suppression.

Designing Operationally Relevant Daily Large Fire Containment Strategies Using Risk Assessment Results

“…Building and solving a large SP model with many stochastic scenarios would be computationally challenging but could provide one robust containment option suitable for all considered scenarios. Fire suppression SP models [10,16,[47][48][49][50][51] have been built to solve small-to moderate-sized problems; they often rely on heuristics to control model size and find "good" instead of optimal solutions. A potential future research direction could be building SP models to capture fire uncertainties and implement efficient solution algorithms to solve those models.…”

“…Delaying fire spread and reinforcing containment lines with aerial resources are also common tasks that help minimize losses. Published OR modeling research is reflective of these realities, focusing on construction of containment lines to manage the extent and location of burned areas [14][15][16], and the allocation of resources to point protect structures such as homes [17][18][19].…”

A review of challenges to determining and demonstrating efficiency of large fire management

“…Petrovic and Carlson 2012;Belval et al 2015Belval et al , 2016, the reality is that prospective determination of plausibly efficient strategies remains elusive. That is, although the approach of Rodríguez y Silva and González-Cabán (2016) can determine the efficiency of past actions, it does not evaluate a range of other suppression strategies and tactics in terms of how they might be more or less efficient.…”

Modeling Ground Firefighting Resource Activities to Manage Risk Given Uncertain Weather

“…A stochastic mixed integer programming (SMIP) model [23] to optimize suppression decisions that dynamically interact with uncertain fire behavior on a single fire was developed by Belval et al [24]. That model provided a framework for selecting suppression activities that alter resultant fire behavior; first stage decisions were the initial suppression actions and second stage decisions were follow up suppression actions.…”

“…In addition, that model incorporated flexible decision points, which allowed a variety of management styles to be represented. The model presented in Belval et al [24] integrates suppression decisions using "suppression node placements" which model the timing and placement of suppression actions on the landscape. However, two of the main assumptions underlying the suppression node placement model of suppression are simplistic.…”