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Super Best Case

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Get The NPV Upper Bound

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. See a detailed comparison of these two approaches below.

Gap problem and Production Control:
In modern 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.
Predefined cut-offs and cut-off 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.
Single Sequence and Multiple Scenarios
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.
Bench by Bench and Math Optimization
In the modern technology the mining sequence is done following an order of benches inside the pre-defined pits' order. In MiningMath that is not necessary. The mathematical optimization is done in a single step through the use of surfaces, not being bound to fixed benches.
Partial Benches and Entire Benches
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.
Slope Approximations and Precise Slopes:
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.

This setup serves as a reference to challenge the Best Case obtained by other means, including more recent academic/commercial DBS technologies available. The block periods and destinations optimized by MiningMath could be imported back into your preferred mining package, for comparison, pushback design or scheduling purposes. This is all available for free!


  • Processing capacity: 10 Mt per year.

  • Stockpiling parameters on.

  • Timeframe: Years (1).

Figure 3: Production constraints

Advanced experience and refinements

It is important to mention that if you have multiple destinations, extra processing, or dump routes, it could be added for proper cutoff optimization. Besides that, the surfaces obtained here could be used in further steps or imported back into any mining package for pushback design and scheduling.

A refinement of the 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 Validation step could be used as restrict mining for the runs here.

These scenarios might take longer and the main recommendation is to use powerful machine to run it, in parallel, while other optimizations are performed.

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