Resource allocation for wildland fire suppression planning using a stochastic program

Abstract

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.