A mathematical model and an optimal solution for offsetting greenhouse gases using native species from the Brazilian Cerrado vegetation

The intensification of global warming, driven by anthropogenic greenhouse gas (GHG) emissions, necessitates the implementation of efficient carbon offsetting strategies. While reforestation is a primary mechanism for carbon sequestration, organizations often struggle to balance environmental compliance with cost-effectiveness. This research addresses this challenge by developing a mathematical optimization model and a desktop software tool designed to minimize the total cost of carbon neutralization using native species from the Brazilian Cerrado, specifically in the Tocantins region. The study utilizes the GHG Protocol to quantify emissions and translates complex environmental regulations, such as Resolution SMA 58, into rigorous mathematical constraints. The methodology employs Integer Linear Programming solved via the Branch-and-Bound (B&B) technique using the GNU Linear Programming Kit (GLPK). These constraints account for essential ecological parameters, including mandatory percentages of zoochorous, threatened, pioneer, and non-pioneer species. Computational results, based on a practical scenario of neutralizing 200 tCO2e over a ten-year horizon, demonstrate that the model successfully identifies an optimal planting configuration of 2,800 trees at a minimum cost of R$15,715.00. Unlike simplified calculation methods that ignore species-specific variables, this model ensures full adherence to legal requirements while providing a realistic financial outlook. The study concludes that the developed tool offers a transparent, agile, and scientifically robust solution for companies aiming for carbon neutrality, facilitating the recovery of degraded areas within the Cerrado biome through optimized resource allocation and intelligent system management.