Incorporating Fixed Costs

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⚠️ Caution

This methodology is an experimental approach, and MiningMath was not specifically designed for this use case. Unexpected results may occur. If you encounter any issues or inconsistencies, we recommend reaching out to our support team for further assistance.

Fixed costs are expenses that do not vary with production or mining volume, such as equipment maintenance, infrastructure, and fixed labor costs. They are fundamental to the economic viability of the operation, ensuring the financial sustainability of the mine regardless of production variations. In MiningMath, these fixed costs can be directly incorporated into the mining model, ensuring they are considered in decision-making processes.

In MiningMath, it is possible to perform pit optimization, aiming at maximizing undiscounted cash flow while considering fixed costs and all desired constraints. This allows for an economic feasibility assessment of certain regions throughout the project’s lifespan. To achieve this, it is necessary to use binary decision variables, which require additional configurations in the block model and the pit optimization scenario.

Block Model Configuration Steps

1. Add a Special Block Just Above the Topography

Create a block just above the defined topography, avoiding the model's edges. Alternatively, select an existing block at the topography level; in this case, its related variables values must be considered in the analysis of the results.
To prevent interference with scenario constraints, this block should have:
- Very low density;
- A slope of 89.9999;
- Null values for any additional constraints imposed in the scenario.
The block should contain the fixed cost value for all economic value variables.

2. Add a Binary Decision Variable for the Region

Create a new variable in the block model for binary decision-making.
This variable should:
- Have a negative value equal to the number of blocks in the region or an even smaller value for the special block.
- Have a value of 1 for all blocks in the region with fixed operational costs.
- Have a value of 0 for all other blocks that do not belong to the region.

3. Import the Block Model

Perform the standard block model import.
During variable type definition, set the created decision variable as SUM.

4. Validate the Imported Variable

After importation, visualize the block model using the software viewer.
Check that the values assigned to the binary decision variable are correct and properly distributed as expected.

Scenario Configuration Steps

1. Create a Pit Optimization Scenario

Create a pit optimization scenario where the pit's lifespan is limited to a defined period.
Include all project constraints for the mine’s lifespan.
It is recommended to avoid geometric constraints to reduce optimization complexity.

2. Create the Binary Restriction

In the sums tab, set the maximum value to 0 for the special variable created.

3. Execute the Scenario

Run the scenario and validate the obtained results.

Final Considerations

Implementing this approach enables a more effective and realistic modeling of fixed costs within mining planning. Additionally, MiningMath’s flexibility allows users to evolve their modeling over time, expanding to more sophisticated scenarios and ensuring better operational results.

This methodology can also serve as a first step toward a more complete transition to a fully optimized environment, reducing dependence on manual solutions and increasing the reliability of internal reports.

Furthermore, in the long term, MiningMath can be integrated into short- and medium-term planning, providing a continuous optimization process that may eventually replace the use of other tools.

With this configuration, whenever any block in the region is mined, the special block containing the fixed cost must also be mined. This ensures compliance with the restriction and guarantees that the fixed cost is properly included in the mining scenario.

This process should be repeated for each different fixed cost and region that needs to be included in the model to ensure proper cost allocation across the entire mining plan.

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