Optimizing forest planning: Balancing timber production and carbon sequestration through a multi-objective disjunctive formulation

This work introduces a multi-objective model for the Forest Planning Problem (FPP), designed to optimize forest management by determining the best combination of silvicultural treatments, land harvesting proportions, net carbon sequestration, and timber flow. Using Generalized Disjunctive Programming (GDP), the model addresses two conflicting objectives: maximizing net present value and maximizing $C{O}_2$ sequestration, while accounting for carbon sequestration losses from third parties. The model is reformulated as a mixed-integer linear programming (MILP) problem using both Hull reformulation and Big-M reformulation and validated with data from a forest company in Misiones, Argentina. Results show that increasing forest area reduces reliance on external timber, and that stand characteristics and diverse prescriptions are more effective for improving $C{O}_2$ sequestration than simply expanding forest area. Additionally, the Hull reformulation proves more robust for complex problems, while Big-M is advantageous for simpler cases.