A Simulation and Stochastic Integer Programming Approach to Wildfire Initial Attack Planning Lewis Ntaimo, Julian A. Gallego-Arrubla, Jianbang Gan, Curt Stripling, Joshua Young, and Thomas Spencer Abstract: Wildfires are a threat to public safety, property, and forests. Wildfire managers deploy fighting resources to fire bases before fires occur and dispatch them to fires during the initial attack to minimize the number of escaped fires that can cause unacceptable costs and losses. To address the deployment and dispatch problem, we combine fire behavior simulation and a two-stage stochastic integer programming model called the explicit fire growth response model (EFGRM) to make deployment decisions in the first stage before fires occur and make dispatch decisions regarding the optimal mix of resources to send to multiple fires in each fire day scenario in the second stage after fires occur. The objective is to minimize the number of escaped fires, cost of resource deployment, expected suppression cost, and net value change. We use our methodology to position dozers in Texas District 12 (TX12), a fire planning unit in East Texas managed by the Texas Forest Service (TFS). The results reveal that the initial distribution of dozers in TX12 at the time of this study was not consistent with the historical density of fires. The results of our methodology suggest a different distribution of dozers across TX12. FOR.SCI. 59(1):105–117. Keywords: wildfire management, fire suppression, fire simulation, optimization, stochastic programming W ILDFIRES ARE A CHALLENGING PROBLEM WORLDWIDE and pose a threat to public safety, property, and forests. A study conducted by the Texas Forest Service (TFS) in 2007 revealed deficiencies in their capacity response in terms of the availability of fire- fighting resources based on the conditions they had in 2000 (TFS 2007). This situation was due to a resource deficit caused by a significant decline in the number of operations dozers at the fire bases. It revealed the need for new models to assist in effectively using the available limited resources and in deciding where to place new ones for effective initial attack. In this work, we consider the problem of optimal resource planning for initial attack for a fire planning unit. The problem we address involves making strategic de- cisions regarding the optimal deployment (or redeployment) of multiple firefighting resources (e.g. different types of dozers) to bases at the beginning of the fire season before fires occur and operational decisions regarding which of the resources at the bases to dispatch to reported fires on a daily basis. We assume that deployment (or redeployment) plans are made at the beginning of the fire season before fires occur, whereas dispatch plans are made on a daily basis when fires occur. The aim is to contain the fires before they become too large to contain (escaped fires). Initial attack success is affected by several factors such as the number and types of available resources, budget constraints, and uncertainty about the daily number, location, and behavior of fires. Fire behavior includes the rate of spread and direction, fireline intensity, and flame length, all of which depend on dynamic weather conditions, fuels, and terrain. These factors together with the combinatorial nature of the deployment and dispatch decisions make this problem very challenging. We formulate a two-stage stochastic integer program- ming (Stewardship Incentive Program [SIP]) (e.g. Ruszc- zynski and Shapiro 2003) explicit fire growth response model (EFGRM) that allows for deployment decisions to be made in the first stage before fires occur and dispatch decisions to be made in the second stage for a given fire day scenario. A fire day scenario is a likely day with multiple fires whose likelihood of locations and behavior are known based on historical data and fire behavior simulation. The objective of EFGRM is to minimize the number of escaped fires and the cost of resource deployment and expected suppression and net value change. We propose a new methodology that combines simula- tion and two-stage SIP. To the best of our knowledge, this work considers the first stochastic initial attack model that integrates fire behavior simulation and SIP toward making effective strategic decisions regarding the deployment of firefighting resources to bases under future uncertainty in fire behavior and occurrence. In terms of application, we provide a practical demonstration of use of the new meth- odology to position 28 dozers in a fire district in East Texas. The computational results provided by the methodology include deployment plans (dozers to bases) and the associ- ated resource rental and relocations costs, scenario dispatch plans (dozers to fires), and the expected number of fires Manuscript received February 16, 2011; accepted January 17, 2012; published online March 1, 2012; http://dx.doi.org/10.5849/forsci.11-022. Lewis Ntaimo (ntaimo@tamu.edu), Texas A&M University, Department of Industrial and Systems Engineering, College Station, TX. Julian A. Gallego- Arrubla (kamizama77@tamu.edu), Texas A&M University. Jianbang Gan (j-gan@tamu.edu), Texas A&M University. Curt Stripling (cstripling@ tfs.tamu.edu), Texas Forest Service. Joshua Young (jyoung@tfs.tamu.edu), Texas Forest Service. Thomas Spencer (tspencer@tfs.tamu.edu), Texas Forest Service. Acknowledgments: All previously published work cited in the article has been fully acknowledged. Copyright © 2013 by the Society of American Foresters. Forest Science 59(1) 2013 105 Downloaded from https://academic.oup.com/forestscience/article-abstract/59/1/105/4583674 by guest on 05 May 2019