MiningMath

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Get the NPV upper bound better than the Best Case scenario!

Super Best Case

Estimated reading: 7 minutes 1743 views

In the search for the upside potential for the NPV of a given project, this setup explores the whole solution space without any other constraints but processing capacities, in a global multi-period optimization fully focused on maximizing the project’s discounted cashflow.

As MiningMath optimizes all periods simultaneously, without the need for revenue factors, it has the potential to find higher NPVs than traditional procedures based on LG/Pseudoflow nested pits, which do not account for processing capacities (gap problems), cutoff policy optimization and discount rate. Traditionally, these, and many other, real-life aspects are only accounted for later, through a stepwise process, limiting the potentials of the project.

MiningMath’s Super Best Case serves as a reference to challenge the best case obtained by other means, including more recent academic/commercial DBS technologies available. See a detailed comparison of these two approaches below.

In modern/traditional technology, large size differences between consecutive periods may render them impractical, leading to the “gap” problem. Such a gap is caused by a scaling revenue factor that might limit a large area of being mined until some threshold value is tested. MiningMath allows you to control the entire production without oscillations due to our global optimization.

In the modern/traditional methodology the decisions on block destinations can be taken following some techniques such as: fixed predefined values based on grades/lithologies post-processing cutoff optimization based on economics post-processing based on math programming or even multiple rounds combining these techniques. With MiningMath the destination optimization happens within a global optimization in a single step, maximizing NPV and accounting simultaneously for capacities, sinking rates, widths, discounting, blending, and many other required constraints.

Modern technology is restricted to pre-defined, less diverse sequences because it is based on step-wise process built upon revenue factor variation, nested pits, and pushbacks. These steps limit the solution space for the whole process. MiningMath performs a global optimization, without previous steps limiting the solution space at each change. Hence, a completely different scenario can appear, increasing the variety of solutions.

Due to tonnage restrictions, modern technology might need to mine partial benches in certain periods. With MiningMath’s technology, there isn’t such a division. MiningMath navigates through the solution space by using surfaces that will never result in split benches, leading to a more precise optimization.

Due to tonnage restrictions, modern technology might need to mine partial benches in certain periods. With MiningMath’s technology, there isn’t such a division. MiningMath navigates through the solution space by using surfaces that will never result in split benches, leading to a more precise optimization.

Modern approaches present a difference between the optimization input parameters for OSA (Overall Slope Angle) and what is measured from output pit shells, due to the use of the “block precedence” methodology. MiningMath works with “surface-constrained production scheduling” instead. It defines surfaces that describe the group of blocks that should be mined, or not, considering productions required, and points that could be placed anywhere along the Z-axis. This flexibility allows the elevation to be above, below, or matching a block’s centroid, which ensures that MiningMath’s algorithm can control the OSA precisely, with no errors that could have a strong impact on transition zones.

Example

Setting up the Super Best Case is simple. There are only two necessary restrictions:

  1. Processing capacity: 10 Mt per year.

  2. Timeframe: Years (1).

Depending on your block model, additional parameters may need to be specified. For example, if you have multiple destinations these could be added for proper destination optimization. The figure below provides a comprehensive overview, highlighting the essential parameters required for running the Super Best Case scenario using the pre-installed Marvin dataset.

Results

Results can be analysed in the Viewer tab and the exported report file. For the pre-installed Marvin dataset, note how the sequencing has no gap problems, and the production is kept close to the limit without without violating any restrictions.

Super Best Case Sequencing
Sequencing Slice
Super Best Case production tonnages

Export files

The block periods and destinations optimized by MiningMath’s Super Best Case (or any other scenario) can be exported in a CSV format. You could use these result to import back into your preferred mining package, for comparison, pushback design or scheduling purposes. Export options are depicted below.

Adding constraints

A refinement of the super best case could be done by adding more constraints, preferably one at the time to evaluate each impact in “reserves”, potential conflicts between them, and so on. You can try to follow the suggestions below for this improvement:

  • All blending constraints

  • All restrict mining aspects due to forbidden areas

  • Extra processing or dump routes for proper cutoff optimization

  • Sum variables (with caution), just in case some aspect must be controlled for the whole LOM at once.

  • In case more efficiency is needed, the resulting surface obtained in the Constraints Validationstep could be used as restrict mining for the runs here.

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