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Discounted vs. Undiscounted Cash Flow

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MiningMath’s objective function maximizes the discounted flow for the entire life of the mine, all in a single math optimization step, considering all needed constraints simultaneously. On the other hand, other packages that use the LG/Pseudoflow methods to perform pit optimization aim to maximize the undiscounted cash flow for each revenue factor provided. Hence, the MiningMath solution is not easily comparable to undiscounted flow approaches that only consider slope angles.

Figures 1 and 2 provide a visual comparison between undiscounted and discounted cash flows. This comparison indicates that MiningMath’s decision not to mine certain regions is likely due to the higher cost of waste removal outweighing the potential profit from extracting hidden ore. Despite discounting, the revenue from the hidden ore is insufficient to cover the extraction costs in these areas.

Example of discounted and undiscounted cashflow
Figure 1: Undiscounted versus discounted cash flow optimization.
Figure 2: Undiscounted versus discounted cash flow optimization regarding a minimum mining width.

Comparing the different methodologies​

A proper comparison between both methodologies could be done if you import the final pit surface obtained from the other mining package into MiningMath, and use it as Force/Restrict mining. By utilizing this surface as a guide, MiningMath can precisely optimize scheduling within the specific boundaries delineated by the imported surface. This integration simplifies the comparison of NPV between MiningMath and various other mining packages, giving a more comprehensive evaluation of the methodologies employed by each one.

If you want to emphasize the cash flow in the early mining periods, simply create a decision tree varying the discount rate. The higher the rate value, the more weight will be given to the early periods, leading the undiscounted cash flow to have higher values at the beginning, while later periods will be heavily penalized by the discount rate.

If you wish to mimic the same greedy behavior as in the context of nested pits in MiningMath, you should drop all constraints and set a 1-1 (only) interval with the desired ore productions, asking MiningMath to focus solely on maximizing the cash flow of this single pit, regardless of the long-term consequences, as in the picture below and similar to this process.

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