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Math Optimization models that integrate multiple business’ areas

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Updated on March 18, 2024

7. NPV upper bound

Estimated reading: 3 minutes 160 views

Before adding more complex constraints to your project, it is important to have some general idea of how high the NPV of your project can be. The NPV upper bound is an unrealistic limit, but it can help as a reference point as you progress through the project and add all its constraints at different steps.

At this stage, you can add some surface representing any restricted area in the project. Learn more about force or restrict mining areas. For the Marvin example there is no such restriction. However, if you are using your own data set, make sure that your surface files are well formatted as detailed here. You can use any previously generated surface, such as the topography, as an initial example to help you in this process.

You can run a scenario similar to the validation one including any force or restricted mining areas. The figure below shows an illustrative setup.

Super Best Case

The Super Best Case is the recommended approach to define the NPV upper bound. It aims to maximize the discounted cash flow of a project by exploring the entire solution space, with the only constraint being processing capacity. It is a global, multi-period optimization that seeks to uncover the full upside potential for the project’s net present value.

MiningMath allows you to control the entire production
without oscillations due to our global optimization.
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.
The mathematical optimization is done in a single
step through the use of surfaces, not being bound to fixed benches.
MiningMath navigates through the solution space by using surfaces
that will never result in split benches, leading to a more precise optimization.
MiningMath 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 MiningMath's algorithm to control the overall slope angle precisely,
with no errors that could have a strong impact on transition zones.

Set up

For the Marvin dataset, you can setup the Super Best Case similarly to the validation stage, but including the limit for processing capacity, which in this case is 30Mt per year.

Results

After running the Super Best Case scenario evaluate the results. You can check if restrictions are respected and if results in the report are reasonable.

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Tip: It is important to mention that if you have multiple destinations, extra processing, or dump routes, it could be added for proper destination optimization (note that MiningMath does not apply the concept of cut-off grades). Besides that, the surfaces obtained here could be used in further steps or imported back into any mining package for pushback design and scheduling

Getting Started - Previous 6. Validation stage Next - Getting Started 8. Refining the NPV upper bound
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