A review of optimization and decision models of prescribed burning for wildfire management.

Prescribed burning is an essential forest management tool that requires strategic planning to effectively address its multidimensional impacts, particularly given the influence of global climate change on fire behavior. Despite the inherent complexity in planning prescribed burns, limited efforts have been made to comprehensively identify the critical elements necessary for formulating effective models. In this work, we present a systematic review of the literature on optimization and decision models for prescribed burning, analyzing 471 academic papers published in the last 25 years. Our study identifies four main types of models: spatial-allocation, spatial-extent, temporal-only, and spatial-temporal. We observe a growing number of studies on modeling prescribed burning, primarily due to the expansion in spatial-allocation and spatial-temporal models. There is also an increase in complexity as the models consider more elements affecting prescribed burning effectiveness. We identify the essential components for optimization models, including stakeholders, decision variables, objectives, and influential factors, to enhance model practicality. The review also examines solution techniques, such as integer programming in spatial allocation, stochastic dynamic programming in probabilistic models, and multiobjective programming in balancing trade-offs. These techniques' strengths and limitations are discussed to help researchers adapt methods to specific challenges in prescribed burning optimization. In addition, we investigate general assumptions in the models and challenges in relaxation to enhance practicality. Lastly, we propose future research to develop more comprehensive models incorporating dynamic fire behaviors, stakeholder preferences, and long-term impacts. Enhancing these models' accuracy and applicability will enable decision-makers to better manage wildfire treatment outcomes.