Bilevel optimization approach for fuel treatment planning

Various fuel treatment practices involve removing all or some of the vegetation (fuel) from a landscape to reduce the potential for fires and their severity. Fuel treatments form the first line of defense against large-scale wildfires. In this study, we formulate and solve a bilevel integer programming model, where the fuel treatment planner (modeled as the leader) determines appropriate locations and types of treatments to minimize expected losses from wildfires. The follower (i.e., the lower-level decision-maker) corresponds to nature, which is adversarial to the leader and designs a wildfire attack (i.e., locations and time periods, where and when, respectively, wildfires occur) to disrupt the leader's objective function, e.g., the total expected area burnt. Both levels in the model involve integrality restrictions for decision variables; hence, we explore the model's difficulty from the computational complexity perspective. Then, we design specialized solution methods for general and some special cases. We perform experiments with semi-synthetic and real-life instances to illustrate the performance of our approaches. We also explore numerically the fundamental differences in the structural properties of solutions arising from bilevel model and its single-level counterpart. These disparities encompass factors like the types of treatments applied and the choice of treated areas. Additionally, we conduct various types of sensitivity analysis on the performance of the obtained policies and illustrate the value of the bilevel solutions.