Incorporating Fixed Costs

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.

How MiningMath handles fixed costs

In MiningMath, fixed costs can be directly incorporated into the mining model, ensuring they are considered in decision-making processes.

MiningMath also allows for pit optimization, aiming to maximize undiscounted cash flow while considering fixed costs and all desired constraints. This enables an economic feasibility assessment of specific regions throughout the project’s lifespan. To do this, binary decision field must be used, which require additional configurations in the block model and the pit optimization scenario.

Experimental approach!

This methodology is an experimental approach, and MiningMath wasn’t specifically built for this use case. Unforeseen results might arise. If you experience any issues or inconsistencies, we suggest contacting our support team for help.

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 field 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 also contain the fixed cost value for all economic value fields.

Example of creating a block with coordinates above the topography.

Example of block above the topography with very low density, slope equal 89.999 and null proc hours (same as 0).

Example of block above the topography with very low density, slope equal 89.999 and null proc hours equal (same as 0). Fixed cost values are also added to the economic fields.

2. Add a binary decision field for the region

Create a new field in the block model for binary decision-making. This field 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.

Example of new field named Reg1 in the block model for binary decision-making

Example of values for new field Reg1. Blocks included in the region have value 1. The special block has a very negative value.

3. Import the block model

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

4. Validate the imported field

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

Single block above the topography with very negative value for Reg1.

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. Additionally, include all project constraints for the mine’s entire lifespan. To streamline the optimization process, it is recommended to avoid geometric constraints, as this will help reduce complexity.

2. Create the binary restriction

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

3. Execute the scenario

Run the scenario and validate the obtained results.

Final considerations

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.

Realistic cost modeling for better planning

This approach enables a more effective and realistic modeling of fixed costs within mining planning. 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.

MiningMath

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