# Treemun: a growth and yield simulator for chilean plantation forest

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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.

**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

### 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 $j \in J$ 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)
- $\tau$: Annual discount rate
- $B$: Minimum required standing biomass at planning horizon end (m³)

### Model Formulation

**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 enables strategic forest management decisions that balance economic objectives with ecological sustainability requirements, ensuring continuous timber supply while maintaining forest ecosystem services.

## Installation

### Basic Installation
```bash
pip install treemun-sim
```

### Installation with Optimization Solvers
```bash
# 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
```python
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
```python
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 for representative stands:

### Pinus radiata Stand Simulation
![Pinus radiata policies](docs/images/grafico_final_policies_pino.svg)

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
![Eucalyptus globulus policies](docs/images/grafico_final_policies_eucalipto.svg)

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

`final_biomass` structure:
```python
{
    (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
```bash
# CBC (recommended - included with treemun-sim[solvers])
pip install pulp

```

### Commercial Solvers
```bash
# 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](LICENSE) file for details.

## Author

**Felipe Ulloa-Fierro**
- Email: felipe.ulloa@utalca.cl
- 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 1.1.1. https://pypi.org/project/treemun-sim/
```