treemun-sim 1.1.4

Growth, yield, and management simulator for Chilean plantation forests

Treemun: a growth and yield simulator for chilean plantation forest

A Python package that implements a discrete-time simulation framework for evaluating management policies in Pinus radiata and Eucalyptus globulus forest stands, with integrated optimization capabilities for forest management planning.

Key Features:

• Forest growth simulation for Pinus and Eucalyptus species
• Multiple configurable management policies
• Total aereal biomass calculation using allometric equations
• Random forest landscape generation (instance building)
• Includes a forest management optimization model example
• Support for multiple optimization solvers
• Data preparation for optimization algorithms
• Guaranteed reproducibility through seeds

Mathematical Model

The optimization module implements a Mixed-Integer Linear Programming (MILP) model for strategic forest management planning, extending Johnson and Scheurman's (1977) Model I formulation to address multi-species plantation management.

Problem Formulation

The model addresses the landscape-level forest management problem where a heterogeneous forest landscape is partitioned into a set I of management units (stands) that can be managed using different policies j ∈ J over a planning horizon T. The objective is to determine the optimal policy assignment for each stand to maximize the Net Present Value (NPV) of biomass collection while ensuring sustainability and even-flow constraints.

Decision Variables and Parameters

Decision Variables:

• x_ij: Binary variable indicating whether policy j is assigned to stand i (x_ij = 1 if assigned, 0 otherwise)
• v_t: Auxiliary continuous variable tracking total biomass collected in period t

Parameters:

• a_ijt: Biomass collected from stand i under policy j in period t (m³)
• a_ij^T: Standing biomass in stand i under policy j at the end of planning horizon (m³)
• r^t: Biomass revenue in period t ($/m³)
• τ: Annual discount rate
• B: Minimum required standing biomass at planning horizon end (m³)

Model Formulation

0. Objective Function (NPV Maximization): $$\text{maximize } \sum_{i \in I} \sum_{j \in J} \sum_{t \in T} \frac{r^t \cdot a_{ijt} \cdot x_{ij}}{(1+\tau)^t}$$

Subject to:

1. Single Policy Assignment Constraint: $$\sum_{j \in J} x_{ij} = 1 \quad \forall i \in I$$

2. Biomass Collection Tracking: $$\sum_{i \in I} \sum_{j \in J} a_{ijt} \cdot x_{ij} = v_t \quad \forall t \in T$$

3. Even-Flow Constraint (Non-decreasing harvest): $$v_{t+1} \geq v_t \quad \forall t \in T \setminus {|T|}$$

4. Sustainability Constraint: $$\sum_{i \in I} \sum_{j \in J} a_{ij}^T \cdot x_{ij} \geq B$$

5. Variable Domains: $$x_{ij} \in {0,1} \quad \forall i \in I, j \in J$$ $$v_t \geq 0 \quad \forall t \in T$$

This formulation seek to identify landscape’s policy plan that maximizes the NPV across the planning horizon (Eq. 0) considering that: (i) at most one policy j is selected for each stand i (Eq. 1), (ii) the biomass collected is non-decreasing over time, therefore the biomass collected in period t + 1 must be at least as much as in period t (Eqs. 2 & 3), and (iii) at the end of the planning horizon, a minimum total amount of standing biomass (defined as B) is guaranteed (Eq. 4). The last restriction (equation 5) refers to the nature of the variables.

Installation

Basic Installation

pip install treemun-sim

Installation with Optimization Solvers

# With free CBC solver (recommended)
pip install treemun-sim[solvers]

# With commercial solvers (requires licenses)
pip install treemun-sim[solvers-extended]

# Complete installation with development tools
pip install treemun-sim[complete]

Solver Requirements

• CBC: ✅ Included with [solvers] installation
• CPLEX: Requires IBM ILOG CPLEX license

Basic Usage

Forest Simulation

import treemun_sim as tm

# Simulation with default parameters
forest, summary, final_biomass, collected_biomass = tm.simular_bosque()

print(f"Generated {len(forest)} stand-policy combinations")
print(f"Total optimization data points: {len(collected_biomass)}")

Forest Management Optimization

import treemun_sim as tm

# Generate forest data

horizon = 15
num_stands = 100

forest, summary, final_biomass, collected_biomass = tm.simular_bosque(
    horizonte=horizon,
    num_rodales=num_stands
)

# Create optimization model
model = tm.forest_management_optimization_model(
    bosque=forest,
    a_i_j_T=final_biomass,
    a_i_j_t=collected_biomass,
    horizon=horizon,
    pine_revenue=12,           # $/m³
    eucalyptus_revenue=10,     # $/m³
    min_ending_biomass=25000,  # m³
    discount_rate=0.08         # 8% annual
)

# Solve model
results = tm.solve_model(model, solver_name='cbc', gap=0.01)

# Extract solution
solution = tm.extract_results(model, results)

if solution:
    print(f"Optimal NPV: ${solution['objective_value']:,.2f}")
    print(f"Pine stands managed: {solution['total_pinus_stand_treated']}")
    print(f"Pine stands planning: {solution['pinus_stand_plan']}")
    print(f"Eucalyptus stands managed: {solution['total_eucalyptus_stand_treated']}")
    print(f"Eucalyptus stands planning: {solution['eucalyptus_stand_plan']}")
    print("Total biomass collected per period:", solution['total_harvest_per_period'])

Visual Examples

The following figures illustrate how different management policies affect biomass dynamics over time (30 years horizon) for representative stands:

Pinus radiata Stand Simulation

The figure shows three management policies applied to a single Pinus radiata stand:

• Policy 1: Thinning at 12 years, harvest at 24 years (longer rotation)
• Policy 2: Thinning at 9 years, harvest at 18 years (intensive management)
• Policy 3: Thinning at 11 years, harvest at 20 years (intermediate strategy)

Each policy produces different biomass trajectories, affecting both total yield and temporal distribution of harvests.

Eucalyptus globulus Stand Simulation

The figure demonstrates three harvest-only policies for an Eucalyptus globulus stand:

• Policy 1: 10-year rotations (frequent short rotations)
• Policy 2: 11-year rotations (moderate cycle)
• Policy 3: 12-year rotations (longer maturation period)

The visualization shows how rotation length affects cumulative biomass production and harvest timing across the planning horizon.

These examples demonstrate the package's capability to simulate complex stand dynamics under different management regimes, providing the foundation data for optimization models.

Advanced Usage

Custom Simulation Parameters

import treemun_sim as tm

# Custom simulation
forest, summary, final_biomass, collected_biomass = tm.simular_bosque(
    policies_pino=[(9, 18), (10, 20), (11, 22)],  # (thinning, harvest)
    policies_eucalyptus=[(9,), (10,), (11,)],     # (harvest,)
    horizonte=15,
    num_rodales=100,
    semilla=1234
)

# Results analysis
for i, df in enumerate(forest[:3]):  # First 3 stands
    print(f"Stand {i+1}:")
    print(f"  - Species: {df['Especie'].iloc[0]}")
    print(f"  - Policy: {df['politica'].iloc[0]}")
    print(f"  - Final biomass: {df['biomasa'].iloc[-1]:.2f} tons")

Variable Revenue in Optimization

# Variable revenue over time
pine_revenues = [10, 11, 12, 13, 14]  # Increasing revenues for 5-year horizon
eucalyptus_revenues = [8, 9, 10, 11, 12]

model = tm.forest_management_optimization_model(
    bosque=forest,
    a_i_j_T=final_biomass,
    a_i_j_t=collected_biomass,
    horizon=15,
    pine_revenue=pine_revenues,        # Variable revenue
    eucalyptus_revenue=eucalyptus_revenues,
    min_ending_biomass=25000,
    discount_rate=0.08
)

API Reference

Simulation Function

simular_bosque()

Parameter	Type	Default	Description
policies_pino	List[Tuple[int, int]]	16 policies	Pine policies: [(thinning_age, harvest_age), ...]
policies_eucalyptus	List[Tuple[int]]	4 policies	Eucalyptus policies: [(harvest_age,), ...]
horizonte	int	30	Time horizon in years
num_rodales	int	100	Number of stands to generate
semilla	int	5555	Seed for reproducibility

Optimization Functions

forest_management_optimization_model()

Parameter	Type	Description
bosque	List[pd.DataFrame]	Forest simulation data
a_i_j_T	Dict	Final standing biomass by stand-policy
a_i_j_t	Dict	Harvestable biomass by period
horizon	int	Planning horizon in years
pine_revenue	float or List[float]	Pine biomass revenue ($/m³)
eucalyptus_revenue	float or List[float]	Eucalyptus biomass revenue ($/m³)
min_ending_biomass	float	Minimum final period biomass guaranteed
discount_rate	float	Annual discount rate for NPV

solve_model()

Parameter	Type	Description
model	ConcreteModel	Pyomo optimization model
solver_name	str	Solver name ('cbc', 'cplex')
gap	float	Relative optimality gap (default: 0.01)
executable_path	str	Path to solver executable (optional)
tee	bool	Display solver output (default: True)

extract_results()

Returns a dictionary with:

• objective_value: Optimal NPV for the planning
• total_harvest_per_period: Schedule for collected biomass
• pinus_stand_plan: Policy assignments for pine stands
• eucalyptus_stand_plan: Policy assignments for eucalyptus stands
• total_pinus_stand_treated: Count of pine stands
• total_eucalyptus_stand_treated: Count of eucalyptus stands

Output Data Structure

Forest DataFrame

Each element in forest contains:

• periodo: Time period (1 to horizonte)
• edad_rodal: Stand age in each period
• biomasa: Total biomass in tons
• bioOPT: biomass collected in tons (considers only thinned and harvested biomass amounts)
• condición: Management status ("sin manejo" (no managed) / "con manejo" (managed)
• kitral_class: Classification according to Kitral's System (Chilean fuel model)
• politica: Applied policy identifier

Optimization Dictionaries

`collected_biomass structure:

{
    (period, species, policy, stand_id): biomass_value,
    ...
}

`final_biomass structure:

{
    (stand_id, policy): biomass_value,
    ...
}

Supported Species

Pinus

• Policies: Thinning + Harvest
• Constraint: Thinning age < harvest age
• Default policies: 16 combinations (thinning ages: 9-12 years; harvest ages: 18-24 years)

Eucalyptus

• Policies: Harvest only
• Harvest ages: Any year
• Default policies: 4 options (9-12 years)

Use Cases

• Forest research: Analysis of different management strategies
• Tactical and Strategic planning: Mid/Long-term forest management optimization
• Sustainability assessment: Balancing economic and ecological objectives
• Policy evaluation: Comparing management alternatives performances
• Education: Teaching forest management and optimization concepts

Solver Installation Guide

Free Solvers

# CBC (recommended - included with treemun-sim[solvers])
pip install pulp

Commercial Solvers

# CPLEX (requires IBM license)
pip install cplex

Contributing

Contributions are welcome. To contribute:

1. Fork the repository
2. Create a feature branch
3. Commit your changes
4. Push to the branch
5. Open a Pull Request

License

This project is licensed under the MIT License - see the LICENSE file for details.

Author

Felipe Ulloa-Fierro

• Email: [e-mail]
• Institution: Universidad de Talca

Reference

Johnson, K. N., & Scheurman, H. L. (1977). Techniques for prescribing optimal timber harvest and investment under different objectives—discussion and synthesis. Forest Science, 23(suppl_1), a0001–z0001. https://doi.org/10.1093/FORESTSCIENCE/23.S1.A0001

Citation

If you use Treemun in your research, you can cite it as:

Ulloa-Fierro, F. (2025). Treemun: A Growth and Yield Simulator for Chilean Plantation Forest. 
Python Package Version 1.1.4 https://pypi.org/project/treemun-sim/