An Econometric Model of Wildfire Suppression Productivity

We estimate a model of suppression productivity for individual fires, where suppression productivity is measured in terms of the reduction in the estimated market value of wildfire losses. Estimation results show that at the margin, every dollar increase in suppression costs reduces resource damage by 12 cents, while each dollar invested in pre-suppression reduces suppression expenditures by 3.76 dollars. These results suggest that there is an over-allocation of fire management funds to suppression activities relative to prevention measures in terms of cost-effectiveness. This paper provides an empirical basis for a widely used economic model of wildfire management that seeks to minimize the sum of suppression costs and economic losses from wildfires, the cost plus net value change model of fire suppression (C+NVC).wildfire suppression, productivity

The Non-Uniform k-Center Problem

In this paper, we introduce and study the Non-Uniform k-Center problem (NUkC). Given a finite metric space $(X,d)$ and a collection of balls of radii $\{r_1\geq \cdots \ge r_k\}$, the NUkC problem is to find a placement of their centers on the metric space and find the minimum dilation $\alpha$, such that the union of balls of radius $\alpha\cdot r_i$ around the $i$th center covers all the points in $X$. This problem naturally arises as a min-max vehicle routing problem with fleets of different speeds. The NUkC problem generalizes the classic $k$-center problem when all the $k$ radii are the same (which can be assumed to be $1$ after scaling). It also generalizes the $k$-center with outliers (kCwO) problem when there are $k$ balls of radius $1$ and $\ell$ balls of radius $0$. There are $2$-approximation and $3$-approximation algorithms known for these problems respectively; the former is best possible unless P=NP and the latter remains unimproved for 15 years. We first observe that no $O(1)$-approximation is to the optimal dilation is possible unless P=NP, implying that the NUkC problem is more non-trivial than the above two problems. Our main algorithmic result is an $(O(1),O(1))$-bi-criteria approximation result: we give an $O(1)$-approximation to the optimal dilation, however, we may open $\Theta(1)$ centers of each radii. Our techniques also allow us to prove a simple (uni-criteria), optimal $2$-approximation to the kCwO problem improving upon the long-standing $3$-factor. Our main technical contribution is a connection between the NUkC problem and the so-called firefighter problems on trees which have been studied recently in the TCS community.Comment: Adjusted the figur

Resource allocation for wildland fire suppression planning using a stochastic program

2011 Fall.Includes bibliographical references.Resource allocation for wildland fire suppression problems, referred to here as Fire-S problems, have been studied for over a century. Not only have the many variants of the base Fire-S problem made it such a durable one to study, but advances in suppression technology and our ever-expanding knowledge of and experience with wildland fire behavior have required almost constant reformulations that introduce new techniques. Lately, there has been a strong push towards randomized or stochastic treatments because of their appeal to fire managers as planning tools. A multistage stochastic program with variable recourse is proposed and explored in this paper as an answer to a single-fire planning version of the Fire-S problem. The Fire-S stochastic program is discretized for implementation according to scenario trees, which this paper supports as a highly useful tool in the stochastic context. Our Fire-S model has a high level of complexity and is parameterized with a complicated hierarchical cluster analysis of historical weather data. The cluster analysis has some incredibly interesting features and stands alone as an interesting technique apart from its application as a parameterization tool in this paper. We critique the planning model in terms of its complexity and options for an operational version are discussed. Although we assume no interaction between fire spread and suppression resources, the possibility of incorporating such an interaction to move towards an operational, stochastic model is outlined. A suppression budget analysis is performed and the familiar "production function" fire suppression curve is created, which strongly indicates the Fire-S model performs in accordance with fire economic theory as well as its deterministic counterparts. Overall, this exploratory study demonstrates a promising future for the existence of tractable stochastic solutions to all variants of Fire-S problems

A review of operations research methods applicable to wildfire management

Across the globe, wildfire-related destruction appears to be worsening despite increased fire suppression expenditure. At the same time, wildfire management is becoming increasingly complicated owing to factors such as an expanding wildland-urban interface, interagency resource sharing and the recognition of the beneficial effects of fire on ecosystems. Operations research is the use of analytical techniques such as mathematical modelling to analyse interactions between people, resources and the environment to aid decision-making in complex systems. Fire managers operate in a highly challenging decision environment characterised by complexity, multiple conflicting objectives and uncertainty. We assert that some of these difficulties can be resolved with the use of operations research methods. We present a range of operations research methods and discuss their applicability to wildfire management with illustrative examples drawn from the wildfire and disaster operations research literature

Review of California Wildfire Evacuations from 2017 to 2019

Between 2017 and 2019, California experienced a series of devastating wildfires that together led over one million people to be ordered to evacuate. Due to the speed of many of these wildfires, residents across California found themselves in challenging evacuation situations, often at night and with little time to escape. These evacuations placed considerable stress on public resources and infrastructure for both transportation and sheltering. In the face of these clear challenges, transportation and emergency management agencies across California have widely varying levels of preparedness for major disasters, and nearly all agencies do not have the public resources to adequately and swiftly evacuate all populations in danger. To holistically address these challenges and bolster current disaster and evacuation planning, preparedness, and response in California, we summarize the evacuations of eleven major wildfires in California between 2017 and 2019 and offer a cross-comparison to highlight key similarities and differences. We present results of new empirical data we collected via an online survey of individuals impacted by: 1) the 2017 October Northern California Wildfires (n=79), 2) the 2017 December Southern California Wildfires (n=226), and 3) the 2018 Carr Wildfire (n=284). These data reveal the decision-making of individuals in these wildfires including choices related to evacuating or staying, departure timing, route, sheltering, destination, transportation mode, and reentry timing. We also present results related to communication and messaging, non-evacuee behavior, and opinion of government response. Using the summarized case studies and empirical evidence, we present a series of recommendations for agencies to prepare for, respond to, and recover from wildfires

A Spatial Optimization Model for Resource Allocation for Wildfire Suppression and Resident Evacuation

Wildland-urban interface wildfires have been a significant threat in many countries. This thesis presents an integer two-stage stochastic goal programming model for comprehensive, efficient response to wildfire including firefighting resource allocation and resident evacuation. In contrast to other natural disasters, the progression of wildfires depends on not only the probabilistic fire spread scenarios but also decisions made during firefighting. The proposed model optimizes the resource preparations before the fire starts and resource allocation decisions during the fire event. This model takes into account different wildfire spread scenarios and their impact on high-risk areas. The two objectives considered are minimizing the total cost of operations and property loss and minimizing the number of people at risk to be evacuated. A case study based on Santa Clara County in California, United States of America, is presented to demonstrate the model performance. Quantitative experiments show that this model can help to find efficient solutions by considering a trade-off between two objectives, and varying cell size based on scenarios reduces problem dimension and improves solution time

New Integrality Gap Results for the Firefighters Problem on Trees

The firefighter problem is NP-hard and admits a $(1-1/e)$ approximation based on rounding the canonical LP. In this paper, we first show a matching integrality gap of $(1-1/e+\epsilon)$ on the canonical LP. This result relies on a powerful combinatorial gadget that can be used to prove integrality gap results for many problem settings. We also consider the canonical LP augmented with simple additional constraints (as suggested by Hartke). We provide several evidences that these constraints improve the integrality gap of the canonical LP: (i) Extreme points of the new LP are integral for some known tractable instances and (ii) A natural family of instances that are bad for the canonical LP admits an improved approximation algorithm via the new LP. We conclude by presenting a $5/6$ integrality gap instance for the new LP.Comment: 22 page